how to solve percent problems in algebra

• + ACCUPLACER Mathematics
• + ACT Mathematics
• + AFOQT Mathematics
• + ALEKS Tests
• + ASVAB Mathematics
• + ATI TEAS Math Tests
• + Common Core Math
• + DAT Math Tests
• + FSA Tests
• + FTCE Math
• + GED Mathematics
• + Georgia Milestones Assessment
• + GRE Quantitative Reasoning
• + HiSET Math Exam
• + HSPT Math
• + ISEE Mathematics
• + PARCC Tests
• + Praxis Math
• + PSAT Math Tests
• + PSSA Tests
• + SAT Math Tests
• + SBAC Tests
• + SIFT Math
• + SSAT Math Tests
• + STAAR Tests
• + TABE Tests
• + TASC Math
• + TSI Mathematics
• + ACT Math Worksheets
• + Accuplacer Math Worksheets
• + AFOQT Math Worksheets
• + ALEKS Math Worksheets
• + ASVAB Math Worksheets
• + ATI TEAS 6 Math Worksheets
• + FTCE General Math Worksheets
• + GED Math Worksheets
• + 3rd Grade Mathematics Worksheets
• + 4th Grade Mathematics Worksheets
• + 5th Grade Mathematics Worksheets
• + 6th Grade Math Worksheets
• + 7th Grade Mathematics Worksheets
• + 8th Grade Mathematics Worksheets
• + 9th Grade Math Worksheets
• + HiSET Math Worksheets
• + HSPT Math Worksheets
• + ISEE Middle-Level Math Worksheets
• + PERT Math Worksheets
• + Praxis Math Worksheets
• + PSAT Math Worksheets
• + SAT Math Worksheets
• + SIFT Math Worksheets
• + SSAT Middle Level Math Worksheets
• + 7th Grade STAAR Math Worksheets
• + 8th Grade STAAR Math Worksheets
• + THEA Math Worksheets
• + TABE Math Worksheets
• + TASC Math Worksheets
• + TSI Math Worksheets
• + AFOQT Math Course
• + ALEKS Math Course
• + ASVAB Math Course
• + ATI TEAS 6 Math Course
• + CHSPE Math Course
• + FTCE General Knowledge Course
• + GED Math Course
• + HiSET Math Course
• + HSPT Math Course
• + ISEE Upper Level Math Course
• + SHSAT Math Course
• + SSAT Upper-Level Math Course
• + PERT Math Course
• + Praxis Core Math Course
• + SIFT Math Course
• + 8th Grade STAAR Math Course
• + TABE Math Course
• + TASC Math Course
• + TSI Math Course
• + Number Properties Puzzles
• + Algebra Puzzles
• + Geometry Puzzles
• + Intelligent Math Puzzles
• + Ratio, Proportion & Percentages Puzzles
• + Other Math Puzzles

How to Solve Percent Problems? (+FREE Worksheet!)

Learn how to calculate and solve percent problems using the percent formula.

Related Topics

• How to Find Percent of Increase and Decrease
• How to Find Discount, Tax, and Tip
• How to Do Percentage Calculations
• How to Solve Simple Interest Problems

Step by step guide to solve percent problems

• In each percent problem, we are looking for the base, or part or the percent.
• Use the following equations to find each missing section. Base \(= \color{black}{Part} \ ÷ \ \color{blue}{Percent}\) \(\color{ black }{Part} = \color{blue}{Percent} \ ×\) Base \(\color{blue}{Percent} = \color{ black }{Part} \ ÷\) Base

Percent Problems – Example 1:

\(2.5\) is what percent of \(20\)?

In this problem, we are looking for the percent. Use the following equation: \(\color{blue}{Percent} = \color{ black }{Part} \ ÷\) Base \(→\) Percent \(=2.5 \ ÷ \ 20=0.125=12.5\%\)

The Absolute Best Books to Ace Pre-Algebra to Algebra II

The Ultimate Algebra Bundle From Pre-Algebra to Algebra II

Percent problems – example 2:.

\(40\) is \(10\%\) of what number?

Use the following formula: Base \(= \color{ black }{Part} \ ÷ \ \color{blue}{Percent}\) \(→\) Base \(=40 \ ÷ \ 0.10=400\) \(40\) is \(10\%\) of \(400\).

Percent Problems – Example 3:

\(1.2\) is what percent of \(24\)?

In this problem, we are looking for the percent. Use the following equation: \(\color{blue}{Percent} = \color{ black }{Part} \ ÷\) Base \(→\) Percent \(=1.2÷24=0.05=5\%\)

The Best Book to Help You Ace Pre-Algebra

Pre-Algebra for Beginners The Ultimate Step by Step Guide to Preparing for the Pre-Algebra Test

Percent problems – example 4:.

\(20\) is \(5\%\) of what number?

Use the following formula: Base \(= \color{black}{Part} \ ÷ \ \color{blue}{Percent}\) \(→\) Base \(=20÷0.05=400\) \( 20\) is \(5\%\) of \(400\).

Exercises for Calculating Percent Problems

Solve each problem..

• \(51\) is \(340\%\) of what?
• \(93\%\) of what number is \(97\)?
• \(27\%\) of \(142\) is what number?
• What percent of \(125\) is \(29.3\)?
• \(60\) is what percent of \(126\)?
• \(67\) is \(67\%\) of what?

Download Percent Problems Worksheet

• \(\color{blue}{15}\)
• \(\color{blue}{104.3}\)
• \(\color{blue}{38.34}\)
• \(\color{blue}{23.44\%}\)
• \(\color{blue}{47.6\%}\)
• \(\color{blue}{100}\)

The Greatest Books for Students to Ace the Algebra

Pre-Algebra Exercise Book A Comprehensive Workbook + PreAlgebra Practice Tests

Pre-algebra in 10 days the most effective pre-algebra crash course, college algebra practice workbook the most comprehensive review of college algebra, high school algebra i a comprehensive review and step-by-step guide to mastering high school algebra 1, 10 full length clep college algebra practice tests the practice you need to ace the clep college algebra test.

by: Effortless Math Team about 4 years ago (category: Articles , Free Math Worksheets )

Effortless Math Team

Related to this article, more math articles.

• Top 5 ACT Math Study Guides
• Full-Length 7th Grade GMAS Math Practice Test
• SHSAT Math Worksheets: FREE & Printable
• Geometry Puzzle – Challenge 72
• How to Find Determinants of a Matrix?
• The Ultimate Praxis Core Math Formula Cheat Sheet
• Full-Length PSAT Math Practice Test
• 6th Grade PARCC Math Practice Test Questions
• How to Find Midpoint? (+FREE Worksheet!)
• How to Apply Integers Addition and Subtraction Rules?

What people say about "How to Solve Percent Problems? (+FREE Worksheet!) - Effortless Math: We Help Students Learn to LOVE Mathematics"?

No one replied yet.

Leave a Reply Cancel reply

You must be logged in to post a comment.

Pre-Algebra Practice Workbook The Most Comprehensive Review of Pre-Algebra

Algebra i practice workbook the most comprehensive review of algebra 1, algebra ii practice workbook the most comprehensive review of algebra 2, algebra i for beginners the ultimate step by step guide to acing algebra i, algebra ii for beginners the ultimate step by step guide to acing algebra ii, pre-algebra tutor everything you need to help achieve an excellent score.

• ATI TEAS 6 Math
• ISEE Upper Level Math
• SSAT Upper-Level Math
• Praxis Core Math
• 8th Grade STAAR Math

Limited time only!

Save Over 45 %

It was $89.99 now it is $49.99

Login and use all of our services.

Effortless Math services are waiting for you. login faster!

Register Fast!

Password will be generated automatically and sent to your email.

After registration you can change your password if you want.

• Math Worksheets
• Math Courses
• Math Topics
• Math Puzzles
• Math eBooks
• GED Math Books
• HiSET Math Books
• ACT Math Books
• ISEE Math Books
• ACCUPLACER Books
• Premium Membership
• Youtube Videos
• Google Play
• Apple Store

Effortless Math provides unofficial test prep products for a variety of tests and exams. All trademarks are property of their respective trademark owners.

• Bulk Orders
• Refund Policy

• school Campus Bookshelves
• menu_book Bookshelves
• perm_media Learning Objects
• login Login
• how_to_reg Request Instructor Account
• hub Instructor Commons
• Download Page (PDF)
• Download Full Book (PDF)
• Periodic Table
• Physics Constants
• Scientific Calculator
• Reference & Cite
• Tools expand_more
• Readability

selected template will load here

This action is not available.

4.2: Percents Problems and Applications of Percent

• Last updated
• Save as PDF
• Page ID 142718

• Morgan Chase
• Clackamas Community College via OpenOregon

You may use a calculator throughout this module.

Recall: The amount is the answer we get after finding the percent of the original number. The base is the original number, the number we find the percent of. We can call the percent the rate.

When we looked at percents in a previous module, we focused on finding the amount. In this module, we will learn how to find the percentage rate and the base.

\(\text{Amount}=\text{Rate}\cdot\text{Base}\)

\(A=R\cdot{B}\)

We can translate from words into algebra.

• “is” means equals
• “of” means multiply
• “what” means a variable

Solving Percent Problems: Finding the Rate

Suppose you earned \(56\) points on a \(60\)-point quiz. To figure out your grade as a percent, you need to answer the question “\(56\) is what percent of \(60\)?” We can translate this sentence into the equation \(56=R\cdot60\).

Exercises \(\PageIndex{1}\)

1. \(56\) is what percent of \(60\)?

2. What percent of \(120\) is \(45\)?

1. \(93\%\) or \(93.3\%\)

2. \(37.5\%\)

Be aware that this method gives us the answer in decimal form and we must move the decimal point to convert the answer to a percent.

Also, if the instructions don’t explicitly tell you how to round your answer, use your best judgment: to the nearest whole percent or nearest tenth of a percent, to two or three significant figures, etc.

Solving Percent Problems: Finding the Base

Suppose you earn \(2\%\) cash rewards for the amount you charge on your credit card. If you want to earn $ \(50\) in cash rewards, how much do you need to charge on your card? To figure this out, you need to answer the question “\(50\) is \(2\%\) of what number?” We can translate this into the equation \(50=0.02\cdot{B}\).

3. $ \(50\) is \(2\%\) of what number?

4. \(5\%\) of what number is \(36\)?

3. $ \(2,500\)

5. An \(18\%\) tip will be added to a dinner that cost $ \(107.50\). What is the amount of the tip?

6. The University of Oregon women’s basketball team made \(13\) of the \(29\) three-points shots they attempted during a game against UNC. What percent of their three-point shots did the team make?

7. \(45\%\) of the people surveyed answered “yes” to a poll question. If \(180\) people answered “yes”, how many people were surveyed altogether?

5. $ \(19.35\)

6. \(44.8\%\) or \(45\%\)

7. \(400\) people were surveyed

Solving Percent Problems: Percent Increase

When a quantity changes, it is often useful to know by what percent it changed. If the price of a candy bar is increased by \(50\) cents, you might be annoyed because it’s it’s a relatively large percentage of the original price. If the price of a car is increased by \(50\) cents, though, you wouldn’t care because it’s such a small percentage of the original price.

To find the percent of increase:

• Subtract the two numbers to find the amount of increase.
• Using this result as the amount and the original number as the base, find the unknown percent.

Notice that we always use the original number for the base, the number that occurred earlier in time. In the case of a percent increase, this is the smaller of the two numbers.

8. The price of a candy bar increased from $ \(0.89\) to $ \(1.39\). By what percent did the price increase?

9. The population of Portland in 2010 was \(583,793\). The estimated population in 2019 was \(654,741\). Find the percent of increase in the population. [1]

8. \(56.2\%\) increase

9. \(12.2\%\) increase

Solving Percent Problems: Percent Decrease

Finding the percent decrease in a number is very similar.

To find the percent of decrease:

• Subtract the two numbers to find the amount of decrease.

Again, we always use the original number for the base, the number that occurred earlier in time. For a percent decrease, this is the larger of the two numbers.

10. During a sale, the price of a candy bar was reduced from $ \(1.39\) to $ \(0.89\). By what percent did the price decrease?

11. The number of students enrolled at Clackamas Community College decreased from \(7,439\) in Summer 2019 to \(4,781\) in Summer 2020. Find the percent of decrease in enrollment.

10. \(36.0\%\) decrease

11. \(35.7\%\) decrease

Relative Error

In an earlier module, we said that a measurement will always include some error, no matter how carefully we measure. It can be helpful to consider the size of the error relative to the size of what is being measured. As we saw in the examples above, a difference of \(50\) cents is important when we’re pricing candy bars but insignificant when we’re pricing cars. In the same way, an error of an eighth of an inch could be a deal-breaker when you’re trying to fit a screen into a window frame, but an eighth of an inch is insignificant when you’re measuring the length of your garage.

The expected outcome is what the number would be in a perfect world. If a window screen is supposed to be exactly \(25\) inches wide, we call this the expected outcome, and we treat it as though it has infinitely many significant digits. In theory, the expected outcome is \(25.000000...\)

To find the absolute error , we subtract the measurement and the expected outcome. Because we always treat the expected outcome as though it has unlimited significant figures, the absolute error should have the same precision (place value) as the measurement , not the expected outcome .

To find the relative error , we divide the absolute error by the expected outcome. We usually express the relative error as a percent. In fact, the procedure for finding the relative error is identical to the procedures for finding a percent increase or percent decrease!

To find the relative error:

• Subtract the two numbers to find the absolute error.
• Using the absolute error as the amount and the expected outcome as the base, find the unknown percent.

Exercisew \(\PageIndex{1}\)

12. A window screen is measured to be \(25\dfrac{3}{16}\) inches wide instead of the advertised \(25\) inches. Determine the relative error, rounded to the nearest tenth of a percent.

13. The contents of a box of cereal are supposed to weigh \(10.8\) ounces, but they are measured at \(10.67\) ounces. Determine the relative error, rounded to the nearest tenth of a percent.

12. \(0.1875\div25\approx0.8\%\)

13. \(0.13\div10.8\approx1.2\%\)

The tolerance is the maximum amount that a measurement is allowed to differ from the expected outcome. For example, the U.S. Mint needs its coins to have a consistent size and weight so that they will work in vending machines. A dime (10 cents) weighs \(2.268\) grams, with a tolerance of \(\pm0.091\) grams. [2] This tells us that the minimum acceptable weight is \(2.268-0.091=2.177\) grams, and the maximum acceptable weight is \(2.268+0.091=2.359\) grams. A dime with a weight outside of the range \(2.177\leq\text{weight}\leq2.359\) would be unacceptable.

A U.S. nickel (5 cents) weighs \(5.000\) grams with a tolerance of \(\pm0.194\) grams.

14. Determine the lowest acceptable weight and highest acceptable weight of a nickel.

15. Determine the relative error of a nickel that weighs \(5.21\) grams.

A U.S. quarter (25 cents) weighs \(5.670\) grams with a tolerance of \(\pm0.227\) grams.

16. Determine the lowest acceptable weight and highest acceptable weight of a quarter.

17. Determine the relative error of a quarter that weighs \(5.43\) grams.

14. \(4.806\) g; \(5.194\) g

15. \(0.21\div5.000=4.2\%\)

16. \(5.443\) g; \(5.897\) g

17. \(0.24\div5.670\approx4.2\%\)

• www.census.gov/quickfacts/fact/table/portlandcityoregon,OR,US/PST045219 ↵
• https://www.usmint.gov/learn/coin-and-medal-programs/coin-specifications and https://www.thesprucecrafts.com/how-much-do-coins-weigh-4171330 ↵

Solving Percent Problems

Learning Objective(s)

·          Identify the amount, the base, and the percent in a percent problem.

·          Find the unknown in a percent problem.

Introduction

Percents are a ratio of a number and 100. So they are easier to compare than fractions, as they always have the same denominator, 100. A store may have a 10% off sale. The amount saved is always the same portion or fraction of the price, but a higher price means more money is taken off. Interest rates on a saving account work in the same way. The more money you put in your account, the more money you get in interest. It’s helpful to understand how these percents are calculated.

Parts of a Percent Problem

Jeff has a coupon at the Guitar Store for 15% off any purchase of $100 or more. He wants to buy a used guitar that has a price tag of $220 on it. Jeff wonders how much money the coupon will take off the original $220 price.

Problems involving percents have any three quantities to work with: the percent , the amount , and the base .

The percent has the percent symbol (%) or the word “percent.” In the problem above, 15% is the percent off the purchase price.

The base is the whole amount. In the problem above, the whole price of the guitar is $220, which is the base.

The amount is the number that relates to the percent. It is always part of the whole. In the problem above, the amount is unknown. Since the percent is the percent off , the amount will be the amount off of the price .

You will return to this problem a bit later. The following examples show how to identify the three parts, the percent, the base, and the amount.

The previous problem states that 30 is a portion of another number. That means 30 is the amount. Note that this problem could be rewritten: 20% of what number is 30?

Solving with Equations

Percent problems can be solved by writing equations. An equation uses an equal sign (= ) to show that two mathematical expressions have the same value.

Percents are fractions, and just like fractions, when finding a percent (or fraction, or portion) of another amount, you multiply.

The percent of the base is the amount.

Percent of the Base is the Amount.

Percent · Base = Amount

Once you have an equation, you can solve it and find the unknown value. To do this, think about the relationship between multiplication and division. Look at the pairs of multiplication and division facts below, and look for a pattern in each row.

Multiplication and division are inverse operations. What one does to a number, the other “undoes.”

When you have an equation such as 20% · n = 30, you can divide 30 by 20% to find the unknown: n =  30 ÷ 20%.

You can solve this by writing the percent as a decimal or fraction and then dividing.

n = 30 ÷ 20% =  30 ÷ 0.20 = 150

You can estimate to see if the answer is reasonable. Use 10% and 20%, numbers close to 12.5%, to see if they get you close to the answer.

10% of 72 = 0.1 · 72 = 7.2

20% of 72 = 0.2 · 72 = 14.4

Notice that 9 is between 7.2 and 14.4, so 12.5% is reasonable since it is between 10% and 20%.

This problem is a little easier to estimate. 100% of 24 is 24. And 110% is a little bit more than 24. So, 26.4 is a reasonable answer.

Using Proportions to Solve Percent Problems

Let’s go back to the problem that was posed at the beginning. You can now solve this problem as shown in the following example.

You can estimate to see if the answer is reasonable. Since 15% is half way between 10% and 20%, find these numbers.

10% of 220 = 0.1 · 220 = 22

20% of 220 = 0.2 · 220 = 44

The answer, 33, is between 22 and 44. So $33 seems reasonable.

There are many other situations that involve percents. Below are just a few.

Virtual Help

• Chat with library staff now
• Contact your library
• Math: Basic Tutorials
• Portal Home

Solving Percent Application Problems

Math: basic tutorials : solving percent application problems.

• Introduction to Fractions
• Equivalent Fractions
• Simplifying Fractions
• Mixed Numbers & Improper Fractions
• Multiplying Fractions
• Dividing Fractions
• Adding Fractions
• Subtracting Fractions
• Decimals and Rounding
• Introduction to Percentage
• Simple Operations with Percent
• Solving Percent Change Problems
• Equation Basics
• One-Step Linear Equations
• Multiple-Step Linear Equations
• Rearranging Formulas
• Solving Systems of Linear Equations
• Addition and Subtraction of Polynomials
• Multiplying Polynomials
• Introduction to Factoring Polynomials
• Division of Algebraic Expressions
• Order of Operations
• Exponent Rules
• Scientific Notation
• Angle and Triangle Basics
• Pythagorean Theorem
• Primary Trigonometric Ratios
• Rates and Ratios
• Proportions
• Back to Math Hub

Once you know the basics of how to solve operations with percent, you can use those methods to solve application problems. This section explains how to find the base, part, and percent in a word problem, and use them to solve the problem.

Example and Activity

What is the sale price of a coat that is normally 95 dollars and is discounted by 20 percent.

Line 1: What are you being asked to find. We are being asked to find the sale price.

Line 2: Choose a variable to represent it. Let s be the sale price.

Line 3: Write a sentence that gives the information to write an equation to find s. If the discount is 20 percent, this means the sale price is 80 percent of the original price.

Line 4: Translate the words into algebra, so the equation is s equals 0 decimal 8 0 times 95.

Line 5: Multiply to solve for s, so s equals 76.

Line 6: Write a statement that answers the question. The sale price of the coat is 76 dollars.

A cupcake contains 480 calories, and 240 of those calories are from fat. What percent of the total calories come from fat?

Line 1: What are you being asked to find? We are being asked to find the percent of the calories that from fat.

Line 2: Choose a variable to represent it. Let p be the percent from fat.

Line 3: Write a sentence that gives the information to find p. What percent of 480 is 240?

Line 4: Translate the words into algebra, so the equation is p time 480 equals 240.

Line 5: Divide both sides of the equation by 480 to solve for p, so the equation is 480p divided by 480 equals 240 divided by 480.

Line 6: Simplify to get p equals 0 decimal 5.

Line 5: Convert the decimal to a percent by multiplying by 100 percent so p = 50 percent.

Line 7: Write a statement that answers the question. Therefore, 50 percent of the calories in the cupcake are from fat.

Source: " Prealgebra - opens in a new window " by Lynn Marecek & Mary Anne Anthony-Smith is licensed under CC BY 4.0 - opens in a new window / A derivative from the original work - opens in a new window

Try this activity to test your skills. If you have trouble, check out the information in the module for help.

Summary and Worksheet

• Summary: Solving Percent Application Problems - PDF - Opens in a new window This document contains a short (1 – 2 page) summary of this topic as well as detailed examples to illustrate key concepts. Use this summary to review this topic.
• Worksheet: Solving Percent Application Problems - PDF - Opens in a new window This document contains practice questions on this topic. Use the worksheet to test your knowledge and practice the skills learned in this module. The answers to the practice questions are provided at the end.
• << Previous: Simple Operations with Percent
• Next: Solving Percent Change Problems >>

Note: This material is meant as a general guide, if your professor's instructions differ from the information we've provided, always follow your professor's instructions. Also note, icons on this site are used through a Noun Project Pro license. Please be sure to provide proper attribution if you reuse them.

• Last Updated: Aug 22, 2023 3:28 PM
• URL: https://tlp-lpa.ca/math-tutorials

Calcworkshop

How to Solve Percent Problems? 13 Amazing Examples!

// Last Updated: January 20, 2020 - Watch Video //

Ratios and proportions help us in solving problems with percents .

Jenn, Founder Calcworkshop ® , 15+ Years Experience (Licensed & Certified Teacher)

Because a percent is the ratio (fraction) of one number to another.

In other words, its a number divided by 100.

What is most important to note is that our overall goal is to translate each problem into an algebraic expression by looking for keywords such as “of” and “is,” and then solve for the unknown variable.

First, we will look at how a percent is created by understanding it is simply a proportion:

Percents as a Proportion

And we will quickly see that most problems will follow a very simple Percents Formula, as Khan Academy so accurately states.

Together will look at how to change percents to fractions, percents to decimals, and decimals to percents for various problems.

Additionally, we will look at real-world examples, such as finding the percent of commission, the price of an item with a percent discount, change in population, as well as mixture problems.

Solving Percents (How-To) – Video

Get access to all the courses and over 450 HD videos with your subscription

Monthly and Yearly Plans Available

Get My Subscription Now

Still wondering if CalcWorkshop is right for you? Take a Tour and find out how a membership can take the struggle out of learning math.

• Math Test Prep & More

Solving Percentage Problems

There are two easy ways of solving Percentage problems. We will look at translating the word problem into algebraic expressions in this video. This method requires you to just write the word problem mathematically and solve the resulting equation

We will learn how to find the percent of a number. We will also learn what percentage a number is of another number, and finally we will use percentage to find a number

Let’s look at these individually and we will use the idea of proportion to make these even easier.

Finding the percentage of a number

Find 60% of 200.

Here we know 60% is 60/100 .

“of” in mathematics means multiplication

So writing this algebraically we will have

  60/100  x 200

From here we just simplify to get 120

so 60% of 200 is 120. Watch video for details

Find 50% of 24.

This will be 50/100 times 24.

Again we know that "of" in mathematics means multiplication

We can solve this to get 12

Therefore 50% of 24 is 12. Watch video for details

What percentage of a number is another number?

Let's look at this question. What percent of 10 is 2?

The statement “What percent” is what we are looking for, so let’s represent it by P%.

We know that P% is P/100.

Also we know “of” means multiplication.

“Is” is the same as “is equal to”.

So we have equal to 2.

We will have P/100 x 10 = 2

From here we can just solve for P.

So our answer is 20%. Watch video for details

Please do not get confused when things are twisted. It is the same procedure.

8 is what percentage of 24?

So we know we can write it as

8 = P% x 24.

Again we change the P% to P/100.

"of" means multiplication

"is" means "equal to"

So now we solve for P.

After solving we will have 33.33%

Use percent to find a number

5% of what number is 20.

Here again we can just follow the mathematical meaning.

First we know 5% means 5/100.

“of” means multiplication.

“What number” is what we are looking for, so we will represent it by N.

We know “is” means equal to.

Then we have our 20.

So we have 5/100 x N = 20

We can now simply solve for N.

 N = 400. Watch video for details

This brings us to the end of this Lesson. Have a Great Day

Want More? Get Our Premium Course

Solving Percent Problems

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.

• Solve equations and inequalities
• Simplify expressions
• Factor polynomials
• Graph equations and inequalities
• Advanced solvers
• All solvers
• Arithmetics
• Determinant
• Percentages
• Scientific Notation
• Inequalities

Enter the value(s) for the required question and click the adjacent Go button.

PERCENTAGES

This section will explain how to apply algebra to percentage problems.

In algebra problems, percentages are usually written as decimals.

Example 1. Ethan got 80% of the questions correct on a test, and there were 55 questions. How many did he get right?

The number of questions correct is indicated by:

Ethan got 44 questions correct.

Explanation: % means "per one hundred". So 80% means 80/100 = 0.80.

Example 2. A math teacher, Dr. Pi, computes a student’s grade for the course as follows:

a. Compute Darrel's grade for the course if he has a 91 on the homework, 84 for his test average, and a 98 on the final exam.

Darrel’s grade for the course is an 89.6, or a B+.

b. Suppose Selena has an 89 homework average and a 97 test average. What does Selena have to get on the final exam to get a 90 for the course?

The difference between Part a and Part b is that in Part b we don’t know Selena’s grade on the final exam.

So instead of multiplying 30% times a number, multiply 30% times E. E is the variable that represents what Selena has to get on the final exam to get a 90 for the course.

Because Selena studied all semester, she only has to get a 79 on the final to get a 90 for the course.

Example 3. Sink Hardware store is having a 15% off sale. The sale price of a toilet is $97; find the retail price of the toilet.

a. Complete the table to find an equation relating the sale price to the retail price (the price before the sale).

Vocabulary: Retail price is the original price to the consumer or the price before the sale. Discount is how much the consumer saves, usually a percentage of the retail price. Sale Price is the retail price minus the discount.

b. Simplify the equation.

Explanation: The coefficient of R is one, so the arithmetic for combining like terms is 1 - 0.15 = .85. In other words, the sale price is 85% of the retail price.

c. Solve the equation when the sale price is $97.

The retail price for the toilet was $114.12. (Note: the answer was rounded to the nearest cent.)

The following diagram is meant as a visualization of problem 3.

The large rectangle represents the retail price. The retail price has two components, the sale price and the discount. So Retail Price = Sale Price + Discount If Discount is subtracted from both sides of the equation, a formula for Sale Price is found. Sale Price = Retail Price - Discount

Percentages play an integral role in our everyday lives, including computing discounts, calculating mortgages, savings, investments, and estimating final grades. When working with percentages, remember to write them as decimals, to create tables to derive equations, and to follow the proper procedures to solve equations.

Study Tip: Remember to use descriptive letters to describe the variables.

CHAPTER 1 REVIEW

This unit introduces algebra by examining similar models. You should be able to read a problem and create a table to find an equation that relates two variables. If you are given information about one of the variables, you should be able to use algebra to find the other variable.

Signed Numbers:

Informal Rules:

Adding or subtracting like signs: Add the two numbers and use the common sign.

Adding or subtracting unlike signs: Subtract the two numbers and use the sign of the larger, (more precisely, the sign of the number whose absolute value is largest.)

Multiplying or dividing like signs: The product or quotient of two numbers with like signs is always positive.

Multiplying or dividing unlike signs: The product or quotient of two numbers with unlike signs is always negative.

Order of operations: P lease E xcuse M y D ear A unt S ally 1. Inside P arentheses, (). 2. E xponents. 3. M ultiplication and D ivision (left to right) 4. A ddition and S ubtraction (left to right)

Study Tip: All of these informal rules should be written on note cards.

Introduction to Variables:

Generate a table to find an equation that relates two variables.

Example 6. A car company charges $14.95 plus 35 cents per mile.

Simplifying Algebraic Equations:

Combine like terms:

Solving Equations:

1. Simplify both sides of the equation. 2. Write the equation as a variable term equal to a constant. 3. Divide both sides by the coefficient or multiply by the reciprocal. 4. Three possible outcomes to solving an equation. a. One solution ( a conditional equation ) b. No solution ( a contradiction ) c. Every number is a solution (an identity )

Applications of Linear Equations:

This section summarizes the major skills taught in this chapter.

Example 9. A cell phone company charges $12.50 plus 15 cents per minute after the first six minutes.

a. Create a table to find the equation that relates cost and minutes.

c. If the call costs $23.50, how long were you on the phone?

If the call costs $23.50, then you were on the phone for approximately 79 minutes.

Literal Equations:

A literal equation involves solving an equation for one of two variables.

Percentages:

Write percentages as decimals.

Example 11. An English teacher computes his grades as follows:

Sue has an 87 on the short essays and a 72 on the research paper. If she wants an 80 for the course, what grade does Sue have to get on the final?

Sue has to get a 78.36 in the final exam to get an 80 for the course.

Study Tips:

1. Make sure you have done all of the homework exercises. 2. Practice the review test on the following pages by placing yourself under realistic exam conditions. 3. Find a quiet place and use a timer to simulate the test period. 4. Write your answers in your homework notebook. Make copies of the exam so you may then re-take it for extra practice. 5. Check your answers. 6. There is an additional exam available on the Beginning Algebra web page. 7. DO NOT wait until the night before the exam to study.

Math Topics

More solvers.

• Add Fractions
• Simplify Fractions

Percent Maths Problems

A free service from Mattecentrum

Calculating with percentages

• Calculating with percentage I
• Calculating with percentage II
• Calculating with percentage III

As we discussed in pre-algebra, percent is a ratio that compares a number to 100. Percent means per hundred. Percent is usually expressed with the percent symbol %.

Percent problems are usually solved by using proportions.

In a classroom 14 of the 21 students are female. How many percent does that correspond to?

We know that the ratio of girls to all students is

$$\frac{14}{21}$$

And we know that this ratio is a proportion to a ratio with the denominator 100.

$$\frac{14}{21}=\frac{x}{100}$$

As we saw in the last section from here we can calculate x

$$x=100\cdot \frac{14}{21}$$

$$x=\frac{1400}{21}$$

$$x\approx 67$$

i.e. 67% of the students in the class are female.

One of the ratios in these proportions is always a comparison of two numbers (above 14/21). This numbers are called the percentage (14) and the base (21). The other ratio is called the rate and always has the denominator 100.

$$\frac{percentage}{base}=rate$$

Another way of saying this is that

$$percent=\frac{part}{whole}$$

Percent of change, or p%, indicates how much a quantity has increased or decreased in comparison with the original amount. It's calculated as:

$$percent\: of\: change=\frac{amount\: of\: increase\: or\: decrease}{old\: amount}$$

Johnny is at the store where there is a big sign telling him that there is a $4.99 discount on a shirt that originally costs $39.99. But how big is the discount in percent?

$$\frac{\$ 4.99}{\$ 39.99}\approx 0.12$$

$$0.12=12\%$$

The price of the shirt has decreased by 12%.

Video lesson

A price increases from $500 to $585. How big is the increase in percent?

• The coordinate plane
• Linear equations in the coordinate plane
• The slope of a linear function
• The slope-intercept form of a linear equation
• Writing linear equations using the slope-intercept form
• Writing linear equations using the point-slope form and the standard form
• Parallel and perpendicular lines
• Scatter plots and linear models
• Solving linear inequalities
• Solving compound inequalities
• Solving absolute value equations and inequalities
• Linear inequalities in two variables
• Graphing linear systems
• The substitution method for solving linear systems
• The elimination method for solving linear systems
• Systems of linear inequalities
• Properties of exponents
• Scientific notation
• Exponential growth functions
• Monomials and polynomials
• Special products of polynomials
• Polynomial equations in factored form
• Use graphing to solve quadratic equations
• Completing the square
• The quadratic formula
• The graph of a radical function
• Simplify radical expressions
• Radical equations
• The Pythagorean Theorem
• The distance and midpoint formulas
• Simplify rational expression
• Multiply rational expressions
• Division of polynomials
• Add and subtract rational expressions
• Solving rational equations
• Algebra 2 Overview
• Geometry Overview
• SAT Overview
• ACT Overview

How can Australia solve the math teacher shortage? It can start by training more existing teachers to teach math

I magine if you enrolled your child in swimming lessons but instead of a qualified swimming instructor, they were taught freestyle technique by a soccer coach.

Something similar is happening in classrooms around Australia every day. As part of the ongoing teacher shortage, there are significant numbers of teachers teaching " out-of-field ." This means they are teaching subjects they are not qualified to teach.

One of the subjects where out-of-field teaching is particularly common is math.

A 2021 report on Australia's teaching workforce found that 40% of those teaching high school mathematics are out-of-field (English and science were 28% and 29%, respectively).

Another 2021 study of students in Year 8 found they were more likely to be taught by teachers who had specialist training in both math and math education if they went to a school in an affluent area rather than a disadvantaged one (54% compared with 31%).

Our new report looks at how we can fix this situation by training more existing teachers in math education.

Why is this a problem?

Mathematics is one of the key parts of school education. But we are seeing worrying signs students are not receiving the math education they need.

The 2021 study of Year 8 students showed those taught by teachers with a university degree majoring in math had markedly higher results, compared with those taught by out-of-field teachers.

We also know math skills are desperately needed in the broader workforce. The burgeoning worlds of big data and artificial intelligence rely on mathematical and statistical thinking, formulae and algorithms. Math has also been identified as a national skill shortages priority area .

What do we do about this?

There have been repeated efforts to address teacher shortages, including trying to retain existing mathematics teachers, having specialist teachers teaching across multiple schools and higher salaries . There is also a push to train more teachers from scratch, which of course will take many years to implement.

There is one strategy, however, that has not yet been given much attention by policy makers: upgrading current teachers' math and statistics knowledge and their skills in how to teach these subjects.

They already have training and expertise in how to teach and a commitment to the profession. Specific training in math will mean they can move from being out-of-field to "in-field".

How to give teachers this training

A new report commissioned by mathematics and statistics organizations in Australia (including the Australian Mathematical Sciences Institute) looks at what is currently available in Australia to train teachers in math.

It identified 12 different courses to give existing teachers math teaching skills. They varied in terms of location, duration (from six months to 18 months full-time) and aims.

For example, some were only targeted at teachers who want to teach math in the junior and middle years of high school. Some taught university-level math and others taught school-level math. Some had government funding support; others could cost students more than A$37,000.

Overall, we found the current system is confusing for teachers to navigate. There are complex differences between states about what qualifies a teacher to be "in-field" for a subject area.

In the current incentive environment, we found these courses cater to a very small number of teachers. For example, in 2024 in New South Wales this year there are only about 50 government-sponsored places available.

This is not adequate. Pre-COVID, it was estimated we were losing more than 1,000 equivalent full-time math teachers per year to attrition and retirement and new graduates were at best in the low hundreds.

But we don't know exactly how many extra teachers need to be trained in math. One of the key recommendations of the report is for accurate national data of every teacher's content specializations.

We need a national approach

The report also recommends a national strategy to train more existing teachers to be math teachers. This would replace the current piecemeal approach.

It would involve a standard training regime across Australia with government and school-system incentives for people to take up extra training in math.

There is international evidence to show a major upskilling program like this could work.

In Ireland, where the same problem was identified, the government funds a scheme run by a group of universities. Since 2012, teachers have been able to get a formal qualification (a professional diploma). Between 2009 and 2018 the percentage of out-of-field math teaching in Ireland dropped from 48% to 25%.

To develop a similar scheme here in Australia, we would need coordination between federal and state governments and universities. Based on the Irish experience, it would also require several million dollars in funding.

But with students receiving crucial math lessons every day by teachers who are not trained to teach math, the need is urgent.

The report mentioned in this article was commissioned by the Australian Mathematical Sciences Institute, the Australian Mathematical Society, the Statistical Society of Australia, the Mathematics Education Research Group of Australasia and the Actuaries Institute.

This article is republished from The Conversation under a Creative Commons license. Read the original article .

Provided by The Conversation

25,000+ students realised their study abroad dream with us. Take the first step today

Meet top uk universities from the comfort of your home, here’s your new year gift, one app for all your, study abroad needs, start your journey, track your progress, grow with the community and so much more.

Verification Code

An OTP has been sent to your registered mobile no. Please verify

Thanks for your comment !

Our team will review it before it's shown to our readers.

• School Education /

AIMath Review: Advanced AI Math Solver to Revolutionize Math Problem Solving 

• Updated on  
• Apr 2, 2024

AIMath Review: Are you a student looking for an efficient and reliable solution to tackle your math assignments? With technology advancing at an unprecedented pace, it’s no surprise that traditional math problem-solving methods can feel time-consuming and challenging.

But fear not! AI math solvers like AIMath can revolutionize the way you approach math homework. It’s designed to help you solve math problems with ease and precision.

In this review, we will take a closer look at its features, accuracy, and benefits. Now let’s dive right in!

This Blog Includes:

Overview of ai math, unparalleled accuracy and reliability, detailed step-by-step instructions, round-the-clock availability, extensive coverage of math topics, simple & intuitive interface, valuable supplementary resource for math education, exam preparation and grade boosting, flexible learning at your own pace, step 1: input your questions, step 2: retrieve accurate answers, step 3: learn and improve.

AIMath is an innovative and advanced math AI solver designed specifically to assist students in solving a wide range of mathematical problems. With AIMath, students can input their math problems and receive step-by-step solutions accompanied by clear explanations.

AIMath acts as a reliable companion for students seeking efficient and reliable solutions to tackle their math assignments, whether they’re grappling with basic arithmetic or tackling complex calculus problems.

Also Read: Multiplication and Division Word Problems

Comprehensive Features of AIMath

Here are some key benefits of using this math AI solver.

AIMath prides itself on its exceptional accuracy and reliability. With advanced algorithms and machine learning techniques , AIMath delivers precise solutions for even the most complex math problems. Say goodbye to errors and gain the utmost confidence in your work with AIMath by your side.

AIMath provides comprehensive and detailed step-by-step instructions to guide you through the problem-solving process. Each solution is accompanied by clear explanations, helping you understand the underlying concepts and techniques required to solve math problems. With AIMath, you can build a solid foundation of understanding and master various mathematical concepts.

AIMath is available round the clock, ready to assist you whenever you need help with your math assignments. Whether it’s late at night or early morning, AIMath offers on-demand assistance, ensuring uninterrupted support whenever you require it. Say goodbye to waiting and complete your math tasks efficiently with AIMath’s 24/7 availability.

Imagine effortlessly handling even the most challenging math assignments in record time. AIMath’s powerful algorithms allow you to quickly solve a wide range of math problems, from basic arithmetic to advanced calculus and beyond. Whether you’re struggling with algebraic equations or geometric theorems, AIMath is here to make your academic life easier.

AIMath features a simple and intuitive interface, designed to enhance your math-solving experience. With easy navigation and user-friendly controls, AIMath ensures a hassle-free experience. Focus on solving math problems efficiently and effectively with AIMath’s streamlined interface, making your math journey smoother and more enjoyable.

Must Read: 20 Most Famous Indian Mathematicians

Why Should You Use AIMath?

AIMath serves as a valuable supplement to your math education. It offers additional guidance, explanations, and practice to reinforce your understanding of mathematical concepts. AIMath helps you excel in math by providing a reliable resource to complement your learning, ensuring a comprehensive and enriching educational experience.

AIMath is an excellent tool for exam preparation. It offers practice problems, step-by-step solutions, and in-depth explanations that can help you review and reinforce key concepts. By using AIMath, you can sharpen your skills, identify areas for improvement, and ultimately boost your grades in math exams and assignments.

AIMath understands that everyone learns at their own pace. With AIMath, you can learn math at a speed that suits you. Whether you prefer a rapid pace or a more leisurely approach, AIMath adapts to your learning style, providing solutions and guidance tailored to your individual speed and comprehension.

How to Use AIMath?

Using this math AI tool is simple and straightforward. Here’s how.

Begin by inputting your math questions or problems into the system. Whether it’s a basic arithmetic problem or a complex calculus equation, AIMath is equipped to handle a wide range of math topics.

Once you’ve entered your questions, AIMath will process the information and provide you with accurate answers. The powerful algorithms and machine learning techniques behind AIMath ensure that the solutions generated are reliable and precise. AIMath goes beyond just delivering the final answer, providing detailed step-by-step instructions and clear explanations for each solution.

By reviewing these solutions, you can deepen your understanding of the underlying concepts and improve your problem-solving skills. AIMath helps you learn, grow, and become more proficient in math, empowering you to tackle future problems with confidence.

AIMath is a game-changing AI math solver that revolutionizes the way we approach math problem-solving. With its advanced AI technology, AIMath offers unparalleled accuracy, detailed step-by-step instructions, and extensive coverage of math topics. 

This valuable resource acts as a reliable companion, providing support and guidance to students facing daunting math problems. By utilizing this math AI solver as a supplementary resource for math education, students can enhance their understanding, improve problem-solving skills, and boost their grades.

Team Leverage Edu

Leave a Reply Cancel reply

Save my name, email, and website in this browser for the next time I comment.

Contact no. *

Connect With Us

25,000+ students realised their study abroad dream with us. Take the first step today.

Resend OTP in

Need help with?

Study abroad.

UK, Canada, US & More

IELTS, GRE, GMAT & More

Scholarship, Loans & Forex

Country Preference

New Zealand

Which English test are you planning to take?

Which academic test are you planning to take.

Not Sure yet

When are you planning to take the exam?

Already booked my exam slot

Within 2 Months

Want to learn about the test

Which Degree do you wish to pursue?

When do you want to start studying abroad.

January 2024

September 2024

What is your budget to study abroad?

How would you describe this article ?

Please rate this article

We would like to hear more.

Have something on your mind?

Make your study abroad dream a reality in January 2022 with

India's Biggest Virtual University Fair

Essex Direct Admission Day

Why attend .

Don't Miss Out

Help | Advanced Search

Computer Science > Computation and Language

Title: large language models are unconscious of unreasonability in math problems.

Abstract: Large language models (LLMs) demonstrate substantial capabilities in solving math problems. However, they tend to produce hallucinations when given questions containing unreasonable errors. In this paper, we study the behavior of LLMs when faced with unreasonable math problems and further explore their potential to address these problems. First, we construct the Unreasonable Math Problem (UMP) benchmark to examine the error detection ability of LLMs. Experiments show that LLMs are able to detect unreasonable errors, but still fail in generating non-hallucinatory content. In order to improve their ability of error detection and correction, we further design a strategic prompt template called Critical Calculation and Conclusion(CCC). With CCC, LLMs can better self-evaluate and detect unreasonable errors in math questions, making them more reliable and safe in practical application scenarios.

Submission history

Access paper:.

• HTML (experimental)
• Other Formats

References & Citations

• Google Scholar
• Semantic Scholar

BibTeX formatted citation

Bibliographic and Citation Tools

Code, data and media associated with this article, recommenders and search tools.

• Institution

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs .

• Share full article

For more audio journalism and storytelling, download New York Times Audio , a new iOS app available for news subscribers.

Ronna McDaniel, TV News and the Trump Problem

The former republican national committee chairwoman was hired by nbc and then let go after an outcry..

This transcript was created using speech recognition software. While it has been reviewed by human transcribers, it may contain errors. Please review the episode audio before quoting from this transcript and email [email protected] with any questions.

From “The New York Times,” I’m Michael Barbaro. This is “The Daily.”

[MUSIC PLAYING]

Today, the saga of Ronna McDaniel and NBC and what it reveals about the state of television news headed into the 2024 presidential race. Jim Rutenberg, a “Times” writer at large, is our guest.

It’s Monday, April 1.

Jim, NBC News just went through a very public, a very searing drama over the past week, that we wanted you to make sense of in your unique capacity as a longtime media and political reporter at “The Times.” This is your sweet spot. You were, I believe, born to dissect this story for us.

Oh, brother.

Well, on the one hand, this is a very small moment for a major network like NBC. They hire, as a contributor, not an anchor, not a correspondent, as a contributor, Ronna McDaniel, the former RNC chairwoman. It blows up in a mini scandal at the network.

But to me, it represents a much larger issue that’s been there since that moment Donald J. Trump took his shiny gold escalator down to announce his presidential run in 2015. This struggle by the news media to figure out, especially on television, how do we capture him, cover him for all of his lies, all the challenges he poses to Democratic norms, yet not alienate some 74, 75 million American voters who still follow him, still believe in him, and still want to hear his reality reflected in the news that they’re listening to?

Right. Which is about as gnarly a conundrum as anyone has ever dealt with in the news media.

Well, it’s proven so far unsolvable.

Well, let’s use the story of what actually happened with Ronna McDaniel and NBC to illustrate your point. And I think that means describing precisely what happened in this situation.

The story starts out so simply. It’s such a basic thing that television networks do. As elections get underway, they want people who will reflect the two parties.

They want talking heads. They want insiders. They want them on their payroll so they can rely on them whenever they need them. And they want them to be high level so they can speak with great knowledge about the two major candidates.

Right. And rather than needing to beg these people to come on their show at 6 o’clock, when they might be busy and it’s not their full-time job, they go off and they basically put them on retainer for a bunch of money.

Yeah. And in this case, here’s this perfect scenario because quite recently, Ronna McDaniel, the chairwoman of the Republican National Committee through the Trump era, most of it, is now out on the market. She’s actually recently been forced out of the party. And all the networks are interested because here’s the consummate insider from Trump world ready to get snatched up under contract for the next election and can really represent this movement that they’ve been trying to capture.

So NBC’S key news executives move pretty aggressively, pretty swiftly, and they sign her up for a $300,000 a year contributor’s contract.

Nice money if you can get it.

Not at millions of dollars that they pay their anchors, but a very nice contract. I’ll take it. You’ll take it. In the eyes of NBC execs she was perfect because she can be on “Meet the Press” as a panelist. She can help as they figure out some of their coverage. They have 24 hours a day to fill and here’s an official from the RNC. You can almost imagine the question that would be asked to her. It’s 10:00 PM on election night. Ronna, what are the Trump people thinking right now? They’re looking at the same numbers you are.

That was good, but that’s exactly it. And we all know it, right? This is television in our current era.

So last Friday, NBC makes what should be a routine announcement, but one they’re very proud of, that they’ve hired Ronna McDaniel. And in a statement, they say it couldn’t be a more important moment to have a voice like Ronna’s on the team. So all’s good, right? Except for there’s a fly in the ointment.

Because it turns out that Ronna McDaniel has been slated to appear on “Meet the Press,” not as a paid NBC contributor, but as a former recently ousted RNC chair with the “Meet The Press” host, Kristen Welker, who’s preparing to have a real tough interview with Ronna McDaniel. Because of course, Ronna McDaniel was chair of the party and at Trump’s side as he tried to refuse his election loss. So this was supposed to be a showdown interview.

From NBC News in Washington, the longest-running show in television history. This is “Meet The Press” with Kristen Welker.

And here, all of a sudden, Kristin Welker is thrown for a loop.

In full disclosure to our viewers, this interview was scheduled weeks before it was announced that McDaniel would become a paid NBC News contributor.

Because now, she’s actually interviewing a member of the family who’s on the same payroll.

Right. Suddenly, she’s interviewing a colleague.

This will be a news interview, and I was not involved in her hiring.

So what happens during the interview?

So Welker is prepared for a tough interview, and that’s exactly what she does.

Can you say, as you sit here today, did Joe Biden win the election fair and square?

He won. He’s the legitimate president.

Did he win fair and square?

Fair and square, he won. It’s certified. It’s done.

She presses her on the key question that a lot of Republicans get asked these days — do you accept Joe Biden was the winner of the election?

But, I do think, Kristen —

Ronna, why has it taken you until now to say that? Why has it taken you until now to be able to say that?

I’m going to push back a little.

McDaniel gets defensive at times.

Because I do think it’s fair to say there were problems in 2020. And to say that does not mean he’s not the legitimate president.

But, Ronna, when you say that, it suggests that there was something wrong with the election. And you know that the election was the most heavily scrutinized. Chris Krebs —

It’s a really combative interview.

I want to turn now to your actions in the aftermath of the 2020 election.

And Welker actually really does go deeply into McDaniel’s record in those weeks before January 6.

On November 17, you and Donald Trump were recorded pushing two Republican Michigan election officials not to certify the results of the election. And on the call —

For instance, she presses McDaniel on McDaniel’s role in an attempt to convince a couple county commissioner level canvassers in Michigan to not certify Biden’s victory.

Our call that night was to say, are you OK? Vote your conscience. Not pushing them to do anything.

McDaniel says, look, I was just telling them to vote their conscience. They should do whatever they think is right.

But you said, do not sign it. If you can go home tonight, do not sign it. How can people read that as anything other than a pressure campaign?

And Welker’s not going to just let her off the hook. Welker presses her on Trump’s own comments about January 6 and Trump’s efforts recently to gloss over some of the violence, and to say that those who have been arrested, he’ll free them.

Do you support that?

I want to be very clear. The violence that happened on January 6 is unacceptable.

And this is a frankly fascinating moment because you can hear McDaniel starting to, if not quite reverse some of her positions, though in some cases she does that, at least really soften her language. It’s almost as if she’s switching uniforms from the RNC one to an NBC one or almost like breaking from a role she was playing.

Ronna, why not speak out earlier? Why just speak out about that now?

When you’re the RNC chair, you kind of take one for the whole team, right? Now, I get to be a little bit more myself.

She says, hey, you know what? Sometimes as RNC chair, you just have to take it for the team sometimes.

Right. What she’s really saying is I did things as chairwoman of the Republican National committee that now that I no longer have that job, I can candidly say, I wished I hadn’t done, which is very honest. But it’s also another way of saying I’m two faced, or I was playing a part.

Ronna McDaniel, thank you very much for being here this morning.

Then something extraordinary happens. And I have to say, I’ve never seen a moment like this in decades of watching television news and covering television news.

Welcome back. The panel is here. Chuck Todd, NBC News chief political analyst.

Welker brings her regular panel on, including Chuck Todd, now the senior NBC political analyst.

Chuck, let’s dive right in. What were your takeaways?

And he launches right into what he calls —

Look, let me deal with the elephant in the room.

The elephant being this hiring of McDaniel.

I think our bosses owe you an apology for putting you in this situation.

And he proceeds, on NBC’S air, to lace into management for, as he describes it, putting Welker in this crazy awkward position.

Because I don’t know what to believe. She is now a paid contributor by NBC News. I have no idea whether any answer she gave to you was because she didn’t want to mess up her contract.

And Todd is very hung up on this idea that when she was speaking for the party, she would say one thing. And now that she’s on the payroll at NBC, she’s saying another thing.

She has credibility issues that she still has to deal with. Is she speaking for herself, or is she speaking on behalf of who’s paying her?

Todd is basically saying, how are we supposed to know which one to believe.

What can we believe?

It is important for this network and for always to have a wide aperture. Having ideological diversity on this panel is something I prided myself on.

And what he’s effectively saying is that his bosses should have never hired her in this capacity.

I understand the motivation, but this execution, I think, was poor.

Someone said to me last night we live in complicated times. Thank you guys for being here. I really appreciate it.

Now, let’s just note here, this isn’t just any player at NBC. Chuck Todd is obviously a major news name at the network. And him doing this appears to just open the floodgates across the entire NBC News brand, especially on its sister cable network, MSNBC.

And where I said I’d never seen anything like what I saw on “Meet the Press” that morning, I’d never seen anything like this either. Because now, the entire MSNBC lineup is in open rebellion. I mean, from the minute that the sun comes up. There is Joe Scarborough and Mika Brzezinski.

We weren’t asked our opinion of the hiring. But if we were, we would have strongly objected to it.

They’re on fire over this.

believe NBC News should seek out conservative Republican voices, but it should be conservative Republicans, not a person who used her position of power to be an anti-democracy election denier.

But it rolls out across the entire schedule.

Because Ronna McDaniel has been a major peddler of the big lie.

The fact that Ms. McDaniel is on the payroll at NBC News, to me that is inexplicable. I mean, you wouldn’t hire a mobster to work at a DA’s office.

Rachel Maddow devotes an entire half hour.

It’s not about just being associated with Donald Trump and his time in the Republican Party. It’s not even about lying or not lying. It’s about our system of government.

Thumbing their noses at our bosses and basically accusing them of abetting a traitorous figure in American history. I mean, just extraordinary stuff. It’s television history.

And let’s face it, we journalists, our bosses, we can be seen as crybabies, and we’re paid complaining. Yeah, that’s what we’re paid to do. But in this case, the NBC executives cannot ignore this, because in the outcry, there’s a very clear point that they’re all making. Ronna McDaniel is not just a voice from the other side. She was a fundamental part of Trump’s efforts to deny his election loss.

This is not inviting the other side. This is someone who’s on the wrong side —

Of history.

Of history, of these moments that we’ve covered and are still covering.

And I think it’s fair to say that at this point, everyone understands that Ronna McDaniel’s time at NBC News is going to be very short lived. Yeah, basically, after all this, the executives at NBC have to face facts it’s over. And on Tuesday night, they release a statement to the staff saying as much.

They don’t cite the questions about red lines or what Ronna McDaniel represented or didn’t represent. They just say we need to have a unified newsroom. We want cohesion. This isn’t working.

I think in the end, she was a paid contributor for four days.

Yeah, one of the shortest tenures in television news history. And look, in one respect, by their standards, this is kind of a pretty small contract, a few hundred thousand dollars they may have to pay out. But it was way more costly because they hired her. They brought her on board because they wanted to appeal to these tens of millions of Americans who still love Donald J. Trump.

And what happens now is that this entire thing is blown up in their face, and those very same people now see a network that, in their view, in the view of Republicans across the country, this network will not accept any Republicans. So it becomes more about that. And Fox News, NBC’S longtime rival, goes wall to wall with this.

Now, NBC News just caved to the breathless demands from their far left, frankly, emotionally unhinged host.

I mean, I had it on my desk all day. And every minute I looked at that screen, it was pounding on these liberals at NBC News driving this Republican out.

It’s the shortest tenure in TV history, I think. But why? Well, because she supports Donald Trump, period.

So in a way, this leaves NBC worse off with that Trump Republican audience they had wanted to court than maybe even they were before. It’s like a boomerang with a grenade on it.

Yeah, it completely explodes in their face. And that’s why to me, the whole episode is so representative of this eight-year conundrum for the news media, especially on television. They still haven’t been able to crack the code for how to handle the Trump movement, the Trump candidacy, and what it has wrought on the American political system and American journalism.

We’ll be right back.

Jim, put into context this painful episode of NBC into that larger conundrum you just diagnosed that the media has faced when it comes to Trump.

Well, Michael, it’s been there from the very beginning, from the very beginning of his political rise. The media was on this kind of seesaw. They go back and forth over how to cover him. Sometimes they want to cover him quite aggressively because he’s such a challenging candidate. He was bursting so many norms.

But at other times, there was this instinct to understand his appeal, for the same reason. He’s such an unusual candidate. So there was a great desire to really understand his voters. And frankly, to speak to his voters, because they’re part of the audience. And we all lived it, right?

But just let me take you back anyway because everything’s fresh again with perspective. And so if you go back, let’s look at when he first ran. The networks, if you recall, saw him as almost like a novelty candidate.

He was going to spice up what was expected to be a boring campaign between the usual suspects. And he was a ratings magnet. And the networks, they just couldn’t get enough of it. And they allowed him, at times, to really shatter their own norms.

Welcome back to “Meet the Press,” sir.

Good morning, Chuck.

Good morning. Let me start —

He was able to just call into the studio and riff with the likes of George Stephanopoulos and Chuck Todd.

What does it have to do with Hillary?

She can’t talk about me because nobody respects women more than Donald Trump.

And CNN gave him a lot of unmitigated airtime, if you recall during the campaign. They would run the press conferences.

It’s the largest winery on the East Coast. I own it 100 percent.

And let him promote his Trump steaks and his Trump wine.

Trump steaks. Where are the steaks? Do we have steaks?

I mean, it got that crazy. But again, the ratings were huge. And then he wins. And because they had previously given him all that airtime, they’ve, in retrospect, sort of given him a political gift, and more than that now have a journalistic imperative to really address him in a different way, to cover him as they would have covered any other candidate, which, let’s face it, they weren’t doing initially. So there’s this extra motivation to make up for lost ground and maybe for some journalistic omissions.

Right. Kind of correct for the lack of a rigorous journalistic filter in the campaign.

Exactly. And the big thing that this will be remembered for is we’re going to call a lie a lie.

I don’t want to sugarcoat this because facts matter, and the fact is President Trump lies.

Trump lies. We’re going to say it’s a lie.

And I think we can’t just mince around it because they are lies. And so we need to call them what they are.

We’re no longer going to use euphemisms or looser language we’re. Going to call it for what it is.

Trump lies in tweets. He spreads false information at rallies. He lies when he doesn’t need to. He lies when the truth is more than enough for him.

CNN was running chyrons. They would fact check Trump and call lies lies on the screen while Trump is talking. They were challenging Trump to his face —

One of the statements that you made in the tail end of the campaign in the midterms that —

Here we go.

That — well, if you don’t mind, Mr. President, that this caravan was an invasion.

— in these crazy press conferences —

They’re are hundreds of miles away, though. They’re hundreds and hundreds of miles away. That’s not an invasion.

Honestly, I think you should let me run the country. You run CNN. And if you did it well, your ratings —

Well, let me ask — if I may ask one other question. Mr. President, if I may ask another question. Are you worried —

That’s enough. That’s enough.

And Trump is giving it right back.

I tell you what, CNN should be ashamed of itself having you working for them. You are a rude, terrible person. You shouldn’t be working for CNN.

Very combative.

So this was this incredibly fraught moment for the American press. You’ve got tens of millions of Trump supporters seeing what’s really basic fact checking. These look like attacks to Trump supporters. Trump, in turn, is calling the press, the reporters are enemies of the people. So it’s a terrible dynamic.

And when January 6 happens, it’s so obviously out of control. And what the traditional press that follows, traditional journalistic rules has to do is make it clear that the claims that Trump is making about a stolen election are just so abjectly false that they don’t warrant a single minute of real consideration once the reporting has been done to show how false they are. And I think that American journalism really emerged from that feeling strongly about its own values and its own place in society.

But then there’s still tens of millions of Trump voters, and they don’t feel so good about the coverage. And they don’t agree that January 6 was an insurrection. And so we enter yet another period, where the press is going to have to now maybe rethink some things.

In what way?

Well, there’s a kind of quiet period after January 6. Trump is off of social media. The smoke is literally dissipating from the air in Washington. And news executives are kind of standing there on the proverbial battlefield, taking a new look at their situation.

And they’re seeing that in this clearer light, they’ve got some new problems, perhaps none more important for their entire business models than that their ratings are quickly crashing. And part of that diminishment is that a huge part of the country, that Trump-loving part of the audience, is really now severed from him from their coverage.

They see the press as actually, in some cases, being complicit in stealing an election. And so these news executives, again, especially on television, which is so ratings dependent, they’ve got a problem. So after presumably learning all these lessons about journalism and how to confront power, there’s a first subtle and then much less subtle rethinking.

Maybe we need to pull back from that approach. And maybe we need to take some new lessons and switch it up a little bit and reverse some of what we did. And one of the best examples of this is none other than CNN.

It had come under new management, was being led by a guy named Chris Licht, a veteran of cable news, but also Stephen Colbert’s late night show in his last job. And his new job under this new management is we’re going to recalibrate a little bit. So Chris Licht proceeds to try to bring the network back to the center.

And how does he do that?

Well, we see some key personalities who represented the Trump combat era start losing air time and some of them lose their jobs. There’s talk of, we want more Republicans on the air. There was a famous magazine article about Chris Licht’s balancing act here.

And Chris Licht says to a reporter, Tim Alberta of the “Atlantic” magazine, look, a lot in the media, including at his own network, quote unquote, “put on a jersey, took a side.” They took a side. And he says, I think we understand that jersey cannot go back on him. Because he says in the end of the day, by the way, it didn’t even work. We didn’t change anyone’s mind.

He’s saying that confrontational approach that defined the four years Trump was in office, that was a reaction to the feeling that TV news had failed to properly treat Trump with sufficient skepticism, that that actually was a failure both of journalism and of the TV news business. Is that what he’s saying?

Yeah. On the business side, it’s easier call, right? You want a bigger audience, and you’re not getting the bigger audience. But he’s making a journalistic argument as well that if the job is to convey the truth and take it to the people, and they take that into account as they make their own voting decisions and formulate their own opinions about American politics, if tens of millions of people who do believe that election was stolen are completely tuning you out because now they see you as a political combatant, you’re not achieving your ultimate goal as a journalist.

And what does Licht’s “don’t put a jersey back on” approach look like on CNN for its viewers?

Well, It didn’t look good. People might remember this, but the most glaring example —

Please welcome, the front runner for the Republican nomination for president, Donald Trump.

— was when he held a town hall meeting featuring Donald J. Trump, now candidate Trump, before an audience packed with Trump’s fans.

You look at what happened during that election. Unless you’re a very stupid person, you see what happens. A lot of the people —

Trump let loose a string of falsehoods.

Most people understand what happened. It was a rigged election.

The audience is pro-Trump audience, was cheering him on.

Are you ready? Are you ready? Can I talk?

Yeah, what’s your answer?

Can I? Do you mind?

I would like for you to answer the question.

OK. It’s very simple to answer.

That’s why I asked it.

It’s very simple. You’re a nasty person, I’ll tell you that.

And during, the CNN anchor hosting this, Kaitlan Collins, on CNN’s own air, it was a disaster.

It felt like a callback to the unlearned lessons of 2016.

Yeah. And in this case, CNN’s staff was up in arms.

Big shakeup in the cable news industry as CNN makes another change at the top.

Chris Licht is officially out at CNN after a chaotic run as chairman and CEO.

And Chris Licht didn’t survive it.

The chief executive’s departure comes as he faced criticism in recent weeks after the network hosted a town hall with Donald Trump and the network’s ratings started to drop.

But I want to say that the CNN leadership still, even after that, as they brought new leadership in, said, this is still the path we’re going to go on. Maybe that didn’t work out, but we’re still here. This is still what we have to do.

Right. And this idea is very much in the water of TV news, that this is the right overall direction.

Yeah. This is, by no means, isolated to CNN. This is throughout the traditional news business. These conversations are happening everywhere. But CNN was living it at that point.

And this, of course, is how we get to NBC deciding to hire Ronna McDaniel.

Right. Because they’re picking up — right where that conversation leaves off, they’re having the same conversation. But for NBC, you could argue this tension between journalistic values and audience. It’s even more pressing. Because even though MSNBC is a niche cable network, NBC News is part of an old-fashioned broadcast network. It’s on television stations throughout the country.

And in fact, those networks, they still have 6:30 newscasts. And believe it or not, millions of people still watch those every night. Maybe not as many as they used to, but there’s still some six or seven million people tuning in to nightly news. That’s important.

Right. We should say that kind of number is sometimes double or triple that of the cable news prime time shows that get all the attention.

On their best nights. So this is big business still. And that business is based on broad — it’s called broadcast for a reason. That’s based on broad audiences. So NBC had a business imperative, and they argue they had a journalistic imperative.

So given all of that, Jim, I think the big messy question here is, when it comes to NBC, did they make a tactical error around hiring the wrong Republican which blew up? Or did they make an even larger error in thinking that the way you handle Trump and his supporters is to work this hard to reach them, when they might not even be reachable?

The best way to answer that question is to tell you what they’re saying right now, NBC management. What the management saying is, yes, this was a tactical error. This was clearly the wrong Republican. We get it.

But they’re saying, we are going to — and they said this in their statement, announcing that they were severing ties with McDaniel. They said, we’re going to redouble our efforts to represent a broad spectrum of the American votership. And that’s what they meant was that we’re going to still try to reach these Trump voters with people who can relate to them and they can relate to.

But the question is, how do you even do that when so many of his supporters believe a lie? How is NBC, how is CNN, how are any of these TV networks, if they have decided that this is their mission, how are they supposed to speak to people who believe something fundamentally untrue as a core part of their political identity?

That’s the catch-22. How do you get that Trump movement person who’s also an insider, when the litmus test to be an insider in the Trump movement is to believe in the denialism or at least say you do? So that’s a real journalistic problem. And the thing that we haven’t really touched here is, what are these networks doing day in and day out?

They’re not producing reported pieces, which I think it’s a little easier. You just report the news. You go out into the world. You talk to people, and then you present it to the world as a nuanced portrait of the country. This thing is true. This thing is false. Again, in many cases, pretty straightforward. But their bread and butter is talking heads. It’s live. It’s not edited. It’s not that much reported.

So their whole business model especially, again, on cable, which has 24 hours to fill, is talking heads. And if you want the perspective from the Trump movement, journalistically, especially when it comes to denialism, but when it comes to some other major subjects in American life, you’re walking into a place where they’re going to say things that aren’t true, that don’t pass your journalistic standards, the most basic standards of journalism.

Right. So you’re saying if TV sticks with this model, the kind of low cost, lots of talk approach to news, then they are going to have to solve the riddle of who to bring on, who represents Trump’s America if they want that audience. And now they’ve got this red line that they’ve established, that that person can’t be someone who denies the 2020 election reality. But like you just said, that’s the litmus test for being in Trump’s orbit.

So this doesn’t really look like a conundrum. This looks like a bit of a crisis for TV news because it may end up meaning that they can’t hire that person that they need for this model, which means that perhaps a network like NBC does need to wave goodbye to a big segment of these viewers and these eyeballs who support Trump.

I mean, on the one hand, they are not ready to do that, and they would never concede that that’s something they’re ready to do. The problem is barring some kind of change in their news model, there’s no solution to this.

But why bar changes to their news model, I guess, is the question. Because over the years, it’s gotten more and more expensive to produce news, the news that I’m talking about, like recorded packages and what we refer to as reporting. Just go out and report the news.

Don’t gab about it. Just what’s going on, what’s true, what’s false. That’s actually very expensive in television. And they don’t have the kind of money they used to have. So the talking heads is their way to do programming at a level where they can afford it.

They do some packages. “60 Minutes” still does incredible work. NBC does packages, but the lion’s share of what they do is what we’re talking about. And that’s not going to change because the economics aren’t there.

So then a final option, of course, to borrow something Chris Licht said, is that a network like NBC perhaps doesn’t put a jersey on, but accepts the reality that a lot of the world sees them wearing a jersey.

Yeah. I mean, nobody wants to be seen as wearing a jersey in our business. No one wants to be wearing a jersey on our business. But maybe what they really have to accept is that we’re just sticking to the true facts, and that may look like we’re wearing a jersey, but we’re not. And that may, at times, look like it’s lining up more with the Democrats, but we’re not.

If Trump is lying about a stolen election, that’s not siding against him. That’s siding for the truth, and that’s what we’re doing. Easier said than done. And I don’t think any of these concepts are new.

I think there have been attempts to do that, but it’s the world they’re in. And it’s the only option they really have. We’re going to tell you the truth, even if it means that we’re going to lose a big part of the country.

Well, Jim, thank you very much.

Thank you, Michael.

Here’s what else you need to know today.

[PROTESTERS CHANTING]

Over the weekend, thousands of protesters took to the streets of Tel Aviv and Jerusalem in some of the largest domestic demonstrations against the government of Prime Minister Benjamin Netanyahu since Israel invaded Gaza in the fall.

[NON-ENGLISH SPEECH]

Some of the protesters called on Netanyahu to reach a cease fire deal that would free the hostages taken by Hamas on October 7. Others called for early elections that would remove Netanyahu from office.

During a news conference on Sunday, Netanyahu rejected calls for early elections, saying they would paralyze his government at a crucial moment in the war.

Today’s episode was produced by Rob Szypko, Rikki Novetsky, and Alex Stern, with help from Stella Tan.

It was edited by Brendan Klinkenberg with help from Rachel Quester and Paige Cowett. Contains original music by Marion Lozano, Dan Powell, and Rowan Niemisto and was engineered by Chris Wood. Our theme music is by Jim Brunberg and Ben Landsverk of Wonderly.

That’s it for “The Daily.” I’m Michael Barbaro. See you tomorrow.

• April 2, 2024   •   29:32 Kids Are Missing School at an Alarming Rate
• April 1, 2024   •   36:14 Ronna McDaniel, TV News and the Trump Problem
• March 29, 2024   •   48:42 Hamas Took Her, and Still Has Her Husband
• March 28, 2024   •   33:40 The Newest Tech Start-Up Billionaire? Donald Trump.
• March 27, 2024   •   28:06 Democrats’ Plan to Save the Republican House Speaker
• March 26, 2024   •   29:13 The United States vs. the iPhone
• March 25, 2024   •   25:59 A Terrorist Attack in Russia
• March 24, 2024   •   21:39 The Sunday Read: ‘My Goldendoodle Spent a Week at Some Luxury Dog ‘Hotels.’ I Tagged Along.’
• March 22, 2024   •   35:30 Chuck Schumer on His Campaign to Oust Israel’s Leader
• March 21, 2024   •   27:18 The Caitlin Clark Phenomenon
• March 20, 2024   •   25:58 The Bombshell Case That Will Transform the Housing Market
• March 19, 2024   •   27:29 Trump’s Plan to Take Away Biden’s Biggest Advantage

Hosted by Michael Barbaro

Featuring Jim Rutenberg

Produced by Rob Szypko ,  Rikki Novetsky and Alex Stern

With Stella Tan

Edited by Brendan Klinkenberg ,  Rachel Quester and Paige Cowett

Original music by Marion Lozano ,  Dan Powell and Rowan Niemisto

Engineered by Chris Wood

Listen and follow The Daily Apple Podcasts | Spotify | Amazon Music

Ronna McDaniel’s time at NBC was short. The former Republican National Committee chairwoman was hired as an on-air political commentator but released just days later after an on-air revolt by the network’s leading stars.

Jim Rutenberg, a writer at large for The Times, discusses the saga and what it might reveal about the state of television news heading into the 2024 presidential race.

On today’s episode

Jim Rutenberg , a writer at large for The New York Times.

Background reading

Ms. McDaniel’s appointment had been immediately criticized by reporters at the network and by viewers on social media.

The former Republican Party leader tried to downplay her role in efforts to overturn the 2020 election. A review of the record shows she was involved in some key episodes .

There are a lot of ways to listen to The Daily. Here’s how.

We aim to make transcripts available the next workday after an episode’s publication. You can find them at the top of the page.

The Daily is made by Rachel Quester, Lynsea Garrison, Clare Toeniskoetter, Paige Cowett, Michael Simon Johnson, Brad Fisher, Chris Wood, Jessica Cheung, Stella Tan, Alexandra Leigh Young, Lisa Chow, Eric Krupke, Marc Georges, Luke Vander Ploeg, M.J. Davis Lin, Dan Powell, Sydney Harper, Mike Benoist, Liz O. Baylen, Asthaa Chaturvedi, Rachelle Bonja, Diana Nguyen, Marion Lozano, Corey Schreppel, Rob Szypko, Elisheba Ittoop, Mooj Zadie, Patricia Willens, Rowan Niemisto, Jody Becker, Rikki Novetsky, John Ketchum, Nina Feldman, Will Reid, Carlos Prieto, Ben Calhoun, Susan Lee, Lexie Diao, Mary Wilson, Alex Stern, Dan Farrell, Sophia Lanman, Shannon Lin, Diane Wong, Devon Taylor, Alyssa Moxley, Summer Thomad, Olivia Natt, Daniel Ramirez and Brendan Klinkenberg.

Our theme music is by Jim Brunberg and Ben Landsverk of Wonderly. Special thanks to Sam Dolnick, Paula Szuchman, Lisa Tobin, Larissa Anderson, Julia Simon, Sofia Milan, Mahima Chablani, Elizabeth Davis-Moorer, Jeffrey Miranda, Renan Borelli, Maddy Masiello, Isabella Anderson and Nina Lassam.

Jim Rutenberg is a writer at large for The Times and The New York Times Magazine and writes most often about media and politics. More about Jim Rutenberg

Advertisement

Netflix's hit sci-fi series '3 Body Problem' is based on a real math problem that is so complex it's impossible to solve

• The three-body problem is a centuries-old physics question that puzzled Isaac Newton .
• It describes the orbits of three bodies, like planets or stars, trapped in each other's gravity.
• The problem is unsolvable and led to the development of chaos theory.

While Netflix's "3 Body Problem" is a science-fiction show, its name comes from a real math problem that's puzzled scientists since the late 1600s.

In physics, the three-body problem refers to the motion of three bodies trapped in each other's gravitational grip — like a three-star system.

It might sound simple enough, but once you dig into the mathematics, the orbital paths of each object get complicated very quickly.

Two-body vs. three- and multi-body systems

A simpler version is a two-body system like binary stars. Two-body systems have periodic orbits, meaning they are mathematically predictable because they follow the same trajectory over and over. So, if you have the stars' initial positions and velocities, you can calculate where they've been or will be in space far into the past and future.

However, "throwing in a third body that's close enough to interact leads to chaos," Shane Ross, an aerospace and ocean engineering professor at Virginia Tech, told Business Insider. In fact, it's nearly impossible to precisely predict the orbital paths of any system with three bodies or more.

While two orbiting planets might look like a ven diagram with ovular paths overlapping, the paths of three bodies interacting often resemble tangled spaghetti. Their trajectories usually aren't as stable as systems with only two bodies.

All that uncertainty makes what's known as the three-body problem largely unsolvable, Ross said. But there are certain exceptions.

The three-body problem is over 300 years old

The three-body problem dates back to Isaac Newton , who published his "Principia" in 1687.

In the book, the mathematician noted that the planets move in elliptical orbits around the sun. Yet the gravitational pull from Jupiter seemed to affect Saturn's orbital path.

Related stories

The three-body problem didn't just affect distant planets. Trying to understand the variations in the moon's movements caused Newton literal headaches, he complained.

But Newton never fully figured out the three-body problem. And it remained a mathematical mystery for nearly 200 years.

In 1889, a Swedish journal awarded mathematician Henri Poincaré a gold medal and 2,500 Swedish crowns, roughly half a year's salary for a professor at the time, for his essay about the three-body problem that outlined the basis for an entirely new mathematical theory called chaos theory .

According to chaos theory, when there is uncertainty about a system's initial conditions, like an object's mass or velocity, that uncertainty ripples out, making the future more and more unpredictable.

Think of it like taking a wrong turn on a trip. If you make a left instead of a right at the end of your journey, you're probably closer to your destination than if you made the mistake at the very beginning.

Can you solve the three-body problem?

Cracking the three-body problem would help scientists chart the movements of meteors and planets, including Earth, into the extremely far future. Even comparatively small movements of our planet could have large impacts on our climate, Ross said.

Though the three-body problem is considered mathematically unsolvable, there are solutions to specific scenarios. In fact, there are a few that mathematicians have found.

For example, three bodies could stably orbit in a figure eight or equally spaced around a ring. Both are possible depending on the initial positions and velocities of the bodies.

One way researchers look for solutions is with " restricted " three-body problems, where two main bodies (like the sun and Earth) interact and a third object with much smaller mass (like the moon) offers less gravitational interference. In this case, the three-body problem looks a lot like a two-body problem since the sun and Earth comprise the majority of mass in the system.

However, if you're looking at a three-star system, like the one in Netflix's show "3 Body Problem," that's a lot more complicated.

Computers can also run simulations far more efficiently than humans, though due to the inherent uncertainties, the results are typically approximate orbits instead of exact.

Finding solutions to three-body problems is also essential to space travel, Ross said. For his work, he inputs data about the Earth, moon, and spacecraft into a computer. "We can build up a whole library of possible trajectories," he said, "and that gives us an idea of the types of motion that are possible."

• Main content