Proportions Word Problems Worksheet: Answers and Explanations
- Worksheets By Grade
- Math Tutorials
- Pre Algebra & Algebra
- Exponential Decay
- B.B.A., Finance and Economics, University of Oklahoma
A proportion is a set of 2 fractions that equal each other. This article focuses on how to use proportions to solve real life problems.
Real World Uses of Proportions
- Modifying a budget for a restaurant chain that is expanding from 3 locations to 20 locations
- Creating a skyscraper from blueprints
- Calculating tips, commissions, and sales tax
Modifying a Recipe
On Monday, you are cooking enough white rice to serve exactly 3 people. The recipe calls for 2 cups of water and 1 cup of dry rice. On Sunday, you are going to serve rice to 12 people. How would the recipe change? If you’ve ever made rice, you know that this ratio—1 part dry rice and 2 parts water—is important. Mess it up, and you’ll be scooping a gummy mess on top of your guests' crawfish étouffée.
Because you are quadrupling your guest list (3 people * 4 = 12 people), you must quadruple your recipe. Cook 8 cups of water and 4 cups of dry rice. These shifts in a recipe demonstrate the heart of proportions: using a ratio to accommodate life's greater and smaller changes.
Algebra and Proportions 1
Sure, with the right numbers, you can forgo setting up an algebraic equation to determine the amounts of dry rice and water. What happens when the numbers are not so friendly, however? On Thanksgiving, you'll be serving rice to 25 people. How much water do you need?
Because the ratio of 2 parts water and 1 part dry rice applies to cooking 25 servings of rice, use a proportion to determine the quantity of ingredients.
Note : Translating a word problem into an equation is super important. Yes, you can solve an incorrectly set up equation and find an answer. You can also mix rice and water together to create "food" to serve at Thanksgiving. Whether the answer or food is palatable depends on the equation.
Think about what you know:
- 3 servings of cooked rice = 2 cups of water; 1 cup of dry rice 25 servings of cooked rice = ? cups of water; ? cup of dry rice
- 3 servings of cooked rice/25 servings of cooked rice = 2 cups of water/ x cups of water
- 3/25 = 2/ x
Cross multiply. Hint : Write these fractions vertically to get the full understanding of cross multiplying. To cross multiply, take the first fraction's numerator and multiply it by the second fraction's denominator. Then take the second fraction's numerator and multiply it by the first fraction's denominator.
3 * x = 2 * 25 3 x = 50 Divide both sides of the equation by 3 to solve for x . 3 x /3 = 50/3 x = 16.6667 cups of water Freeze- verify that the answer is correct. Is 3/25 = 2/16.6667? 3/25 = .12 2/16.6667= .12 Whoo hoo! The answer 16.6667 cups of water is correct.
Ratio and Proportions Word Problem 1: The Brownie Recipe
Damian is making brownies to serve at the family picnic. If the recipe calls for 2 ½ cups of cocoa to serve 4 people, how many cups will he need if there will be 60 people at the picnic? 37.5 cups
What do you know? 2 ½ cups = 4 people ? cups = 60 people 2 ½ cups/ x cups = 4 people/60 people 2 ½/ x = 4/60 Cross Multiply. 2 ½ * 60 = 4 * x 150 = 4 x Divide both sides by 4 to solve for x . 150/4 = 4 x /4 37.5 = x 37.5 cups
Use common sense to verify that the answer is correct. The initial recipe serves 4 people and is modified to serve 60 people. Of course, the new recipe has to serve 15 times more people. Therefore, the amount of cocoa has to be multiplied by 15. Is 2 ½ * 15 = 37.5? Yes.
Ratio and Proportions Word Problem 2: Growing Little Piglets
A piglet can gain 3 pounds in 36 hours. If this rate continues, the pig will reach 18 pounds in 216 hours.
What do you know? 3 pounds = 36 hours 18 pounds = ? hours 3 pounds/18 pounds = 36 hours/ ? hours 3/18 = 36/ x
Cross Multiply. 3 * x = 36 * 18 3 x = 648
Divide both sides by 3 to solve for x . 3 x /3 = 648/3 x = 216 216 hours
Use common sense to verify that the answer is correct. A piglet can gain 3 pounds in 36 hours, which is a rate of 1 pound for every 12 hours. That means that for every pound a piglet gains, 12 hours will pass. Therefore 18 *12, or 216 pounds, is the correct answer.
Ratio and Proportions Word Problem 3: The Hungry Rabbit
Denise’s rabbit can eat 70 pounds of food in 80 days. How long will it take the rabbit to eat 87.5 pounds? 100 days
What do you know? 70 pounds = 80 days 87.5 pounds = ? days 70 pounds/87.5 pounds = 80 days/ x days 70/87.5 = 80/ x
Cross Multiply. 70 * x = 80 * 87.5 70 x = 7000
Divide both sides by 70 to solve for x . 70 x /70 = 7000/70 x = 100
Use Algebra to verify the answer. Is 70/87.5 = 80/100? 70/87.5 = .8 80/100 = .8
Ratio and Proportions Word Problem 4: The Long Road Trip
Jessica drives 130 miles every two hours. If this rate continues, how long will it take her to drive 1,000 miles? 15.38 hours
What do you know? 130 miles = 2 hours 1,000 miles = ? hours 130 miles/1,000 miles = 2 hours/? hours 130/1000 = 2/ x
Cross Multiply. 130 * x = 2 * 1000 130 x = 2000
Divide both sides of the equation by 130 to solve for x . 130 x /130 = 2000/130 x = 15.38 hours
Use Algebra to verify the answer. Does 130/1000 = 2/15.38? 130/1000 = .13 2/15.38 is approximately .13
- Proportions Word Problems Worksheet 1
- How to Solve Proportions to Adjust a Recipe
- How to Solve Algebra Problems Step-By-Step
- How to Calculate Commissions Using Percents
- Algebra Age-Related Word Problem Worksheets
- Free Math Word Problem Worksheets for Fifth-Graders
- Quiz 8th-Graders With These Math Word Problems
- Mole Relations in Balanced Equations
- How to Solve a System of Linear Equations
- Worksheet for Chebyshev's Inequality
- What Is the Distributive Property Law in Mathematics?
- Math Glossary: Mathematics Terms and Definitions
- How to Do Algebra Word Problems
- 4th-Grade Math Word Problems
- Realistic Math Problems Help 6th-graders Solve Real-Life Questions
- Mole Ratio: Definition and Examples
- Number Charts
- Multiplication
- Long division
- Basic operations
- Telling time
- Place value
- Roman numerals
- Fractions & related
- Add, subtract, multiply, and divide fractions
- Mixed numbers vs. fractions
- Equivalent fractions
- Prime factorization & factors
- Fraction Calculator
- Decimals & Percent
- Add, subtract, multiply, and divide decimals
- Fractions to decimals
- Percents to decimals
- Percentage of a number
- Percent word problems
- Classify triangles
- Classify quadrilaterals
- Circle worksheets
- Area & perimeter of rectangles
- Area of triangles & polygons
- Coordinate grid, including moves & reflections
- Volume & surface area
- Pre-algebra
- Square Roots
- Order of operations
- Scientific notation
- Proportions
- Ratio word problems
- Write expressions
- Evaluate expressions
- Simplify expressions
- Linear equations
- Linear inequalities
- Graphing & slope
- Equation calculator
- Equation editor
- Elementary Math Games
- Addition and subtraction
- Math facts practice
- The four operations
- Factoring and number theory
- Geometry topics
- Middle/High School
- Statistics & Graphs
- Probability
- Trigonometry
- Logic and proof
- For all levels
- Favorite math puzzles
- Favorite challenging puzzles
- Math in real world
- Problem solving & projects
- For gifted children
- Math history
- Math games and fun websites
- Interactive math tutorials
- Math help & online tutoring
- Assessment, review & test prep
- Online math curricula
Real World Algebra by Edward Zaccaro
Algebra is often taught abstractly with little or no emphasis on what algebra is or how it can be used to solve real problems. Just as English can be translated into other languages, word problems can be "translated" into the math language of algebra and easily solved. Real World Algebra explains this process in an easy to understand format using cartoons and drawings. This makes self-learning easy for both the student and any teacher who never did quite understand algebra. Includes chapters on algebra and money, algebra and geometry, algebra and physics, algebra and levers and many more. Designed for children in grades 4-9 with higher math ability and interest but could be used by older students and adults as well. Contains 22 chapters with instruction and problems at three levels of difficulty.
- Pre-algebra lessons
- Pre-algebra word problems
- Algebra lessons
- Algebra word problems
- Algebra proofs
- Advanced algebra
- Geometry lessons
- Geometry word problems
- Geometry proofs
- Trigonometry lessons
- Consumer math
- Baseball math
- Math for nurses
- Statistics made easy
- High school physics
- Basic mathematics store
- SAT Math Prep
- Math skills by grade level
- Ask an expert
- Other websites
- K-12 worksheets
- Worksheets generator
- Algebra worksheets
- Geometry worksheets
- Free math problem solver
- Pre-algebra calculators
- Algebra Calculators
- Geometry Calculators
- Math puzzles
- Math tricks
- Member login
Proportion word problems
It is very important to notice that if the ratio on the left is a ratio of number of liters of water to number of lemons, you have to do the same ratio on the right before you set them equal.
More interesting proportion word problems
Check this site if you want to solve more proportion word problems.
Ratio word problems
Recent Articles
How to divide any number by 5 in 2 seconds.
Feb 28, 24 11:07 AM
Math Trick to Square Numbers from 50 to 59
Feb 23, 24 04:46 AM
Sum of Consecutive Odd Numbers
Feb 22, 24 10:07 AM
100 Tough Algebra Word Problems. If you can solve these problems with no help, you must be a genius!
Recommended
About me :: Privacy policy :: Disclaimer :: Donate Careers in mathematics
Copyright © 2008-2021. Basic-mathematics.com. All right reserved
If you're seeing this message, it means we're having trouble loading external resources on our website.
If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.
To log in and use all the features of Khan Academy, please enable JavaScript in your browser.
Course: 7th grade > Unit 1
- Worked example: Solving proportions
- Solving proportions
- Writing proportions example
- Writing proportions
- Proportion word problem: cookies
- Proportion word problem: hot dogs
Proportion word problems
- Your answer should be
- an integer, like 6
- a simplified proper fraction, like 3 / 5
- a simplified improper fraction, like 7 / 4
- a mixed number, like 1 3 / 4
- an exact decimal, like 0.75
- a multiple of pi, like 12 pi or 2 / 3 pi
Reading & Math for K-5
- Kindergarten
- Learning numbers
- Comparing numbers
- Place Value
- Roman numerals
- Subtraction
- Multiplication
- Order of operations
- Drills & practice
- Measurement
- Factoring & prime factors
Proportions
- Shape & geometry
- Data & graphing
- Word problems
- Children's stories
- Leveled Stories
- Context clues
- Cause & effect
- Compare & contrast
- Fact vs. fiction
- Fact vs. opinion
- Main idea & details
- Story elements
- Conclusions & inferences
- Sounds & phonics
- Words & vocabulary
- Reading comprehension
- Early writing
- Numbers & counting
- Simple math
- Social skills
- Other activities
- Dolch sight words
- Fry sight words
- Multiple meaning words
- Prefixes & suffixes
- Vocabulary cards
- Other parts of speech
- Punctuation
- Capitalization
- Narrative writing
- Opinion writing
- Informative writing
- Cursive alphabet
- Cursive letters
- Cursive letter joins
- Cursive words
- Cursive sentences
- Cursive passages
- Grammar & Writing
Breadcrumbs
Proportions Word Problems with Answers
In grade 6 students learn about ratios and proportions. We’ve created a series of proportions word problems worksheets and ratio word problems worksheets for students to practice.
Let’s take a more detailed look at how to solve proportions word problems.
First, what are proportions? Proportion means that two ratios (or fractions) are equal.
For example:
1 out of 3 is equal to 2 out of 6. The ratios are the same, so they are in proportion.
In a real-world example, you could apply it this way.
A ball of yarn’s length and weight are in proportion.100 meter of yarn weighs 3 ounces.200 meter of yarn weighs 6 ounces.
Proportions word problem
We’re making lemonade. If you mix 3 liters of water with 4 lemons to make lemonade, how many liters of water do you need for 8 lemons?
Let’s set up the ratios. We know they involve lemons and liters of water, like this:
We know the following from word problem. We’ll use an x for the unknown number:
Now we can place the numbers we know in the correct places in the equation.
We multiply across the known corners:
As this is a proportion, the sum of 4 x X also has to be 24.
Now, you can either divide 24 by 4, or you can write out the equation:
4 x X = 24. From learning our math facts, we know that 4 x 6 = 24.
Therefore, we need 6 liters of water for making lemonade with 8 lemons .
We’ve created two sets of free worksheets to practice proportions word problems:
Proportions word problems
Proportions word problems – using decimals
This content is available to members only.
Join K5 to save time, skip ads and access more content. Learn More
- Forgot Password?
IMAGES
VIDEO
COMMENTS
Think about what you know: 3 servings of cooked rice = 2 cups of water; 1 cup of dry rice. 25 servings of cooked rice = ? cups of water; ? cup of dry rice. 3 servings of cooked rice/25 servings of cooked rice = 2 cups of water/ x cups of water. 3/25 = 2/ x. Proportions Word Problems Worksheet 1.
Answer each question. Round your answer to the nearest tenth. Round dollar amounts to the nearest cent. 15) Asanji took a trip to Mexico. Upon leaving he decided to convert all of his Pesos back into dollars. How many dollars did he receive if he exchanged 42.7 Pesos at a rate of $5.30 = 11.1 Pesos? 16) The currency in Argentina is the Peso. The
Proportion Worksheets. Create proportion worksheets to solve proportions or word problems (e.g. speed/distance or cost/amount problems) — available both as PDF and html files. These are most useful when students are first learning proportions in 6th, 7th, and 8th grade. Options include using whole numbers only, numbers with a certain range ...
Cross product is usually used to solve proportion word problems. If you do a cross product, you will get: 4 × x = 3 × 8 4 × x = 24. Since 4 × 6 = 24, x = 6 6 liters should be mixed with 8 lemons. More interesting proportion word problems Problem # 2 A boy who is 3 feet tall can cast a shadow on the ground that is 7 feet long.
Proportion word problems. Google Classroom. Sam used 6 loaves of elf bread on an 8 day hiking trip. He wants to know how many loaves of elf bread ( b) he should pack for a 12 day hiking trip if he eats the same amount of bread each day.
use models to solve word problems. Repeat the types of word problems above, but ask about numbers of cats and dots in a pet shop instead. Model the problem by drawing circles for cats and squares for dogs. use proportions to solve word problems. Write the word problem from the box at the top of Workbook p. 193 on the board. Solve the problem as
Writing a proportion is helpful in solving many word problems. To write the proportion, carefully observe the word order in the problem. You will usually find two relationships in the problem. The first relationship should be between two known numbers, and the second relationship should have one . unknown. in it: the answer you are seeking. Write
A proportion, which is an equation with a ratio on each side, states that two ratios are equal. In these worksheets, your students will solve word problems that involve finding ratios and proportions. Students will find values when given a ratio. They will compare two ratios to determine which is bigger. They will fill in the blank to complete ...
Proportion means that two ratios (or fractions) are equal. For example: 1 out of 3 is equal to 2 out of 6. The ratios are the same, so they are in proportion. In a real-world example, you could apply it this way. A ball of yarn’s length and weight are in proportion.100 meter of yarn weighs 3 ounces.200 meter of yarn weighs 6 ounces.
College. Students learn to solve word problems involving proportions. For example: A math teacher must grade 36 final exams. She can grade 10 exams in 30 minutes. At this rate, how many minutes will it take her to grade all 36 exams? We help you determine the exact lessons you need. We provide you thorough instruction of every step.