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Ratio Problem Solving

Here we will learn about ratio problem solving, including how to set up and solve problems. We will also look at real life ratio problems.

There are also ratio problem solving worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

What is ratio problem solving?

Ratio problem solving is a collection of word problems that link together aspects of ratio and proportion into more real life questions. This requires you to be able to take key information from a question and use your knowledge of ratios (and other areas of the curriculum) to solve the problem.

A ratio is a relationship between two or more quantities . They are usually written in the form a:b where a and b are two quantities. When problem solving with a ratio, the key facts that you need to know are,

  • What is the ratio involved?
  • What order are the quantities in the ratio?
  • What is the total amount / what is the part of the total amount known?
  • What are you trying to calculate ?

As with all problem solving, there is not one unique method to solve a problem. However, this does not mean that there aren’t similarities between different problems that we can use to help us find an answer. 

The key to any problem solving is being able to draw from prior knowledge and use the correct piece of information to allow you to get to the next step and then the solution.

Let’s look at a couple of methods we can use when given certain pieces of information.

What is ratio problem solving?

When solving ratio problems it is very important that you are able to use ratios. This includes being able to use ratio notation. 

For example, Charlie and David share some sweets in the ratio of 3:5. This means that for every 3 sweets Charlie gets, David receives 5 sweets.

Charlie and David share 40 sweets, how many sweets do they each get?

We use the ratio to divide 40 sweets into 8 equal parts. 

Then we multiply each part of the ratio by 5.

3 x 5:5 x 5 = 15:25

This means that Charlie will get 15 sweets and David will get 25 sweets.

  • Dividing ratios

Step-by-step guide: Dividing ratios (coming soon)

Ratios and fractions (proportion problems)

We also need to consider problems involving fractions. These are usually proportion questions where we are stating the proportion of the total amount as a fraction.

Simplifying and equivalent ratios

  • Simplifying ratios

Equivalent ratios

Units and conversions ratio questions

Units and conversions are usually equivalent ratio problems (see above).

  • If £1:\$1.37 and we wanted to convert £10 into dollars, we would multiply both sides of the ratio by 10 to get £10 is equivalent to \$13.70.
  • The scale on a map is 1:25,000. I measure 12cm on the map. How far is this in real life, in kilometres? After multiplying both parts of the ratio by 12 you must then convert 12 \times 25000=300000 \ cm to km by dividing the solution by 100 \ 000 to get 3km.

Notice that for all three of these examples, the units are important. For example if we write the mapping example as the ratio 4cm:1km, this means that 4cm on the map is 1km in real life.

Top tip: if you are converting units, always write the units in your ratio.

Usually with ratio problem solving questions, the problems are quite wordy . They can involve missing values , calculating ratios , graphs , equivalent fractions , negative numbers , decimals and percentages .

Highlight the important pieces of information from the question, know what you are trying to find or calculate , and use the steps above to help you start practising how to solve problems involving ratios.

How to do ratio problem solving

In order to solve problems including ratios:

Identify key information within the question.

Know what you are trying to calculate.

Use prior knowledge to structure a solution.

Explain how to do ratio problem solving

Explain how to do ratio problem solving

Ratio problem solving worksheet

Get your free ratio problem solving worksheet of 20+ questions and answers. Includes reasoning and applied questions.

Related lessons on ratio

Ratio problem solving is part of our series of lessons to support revision on ratio . You may find it helpful to start with the main ratio lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:

  • How to work out ratio  
  • Ratio to fraction
  • Ratio scale
  • Ratio to percentage

Ratio problem solving examples

Example 1: part:part ratio.

Within a school, the number of students who have school dinners to packed lunches is 5:7. If 465 students have a school dinner, how many students have a packed lunch?

Within a school, the number of students who have school dinners to packed lunches is \bf{5:7.} If \bf{465} students have a school dinner , how many students have a packed lunch ?

Here we can see that the ratio is 5:7 where the first part of the ratio represents school dinners (S) and the second part of the ratio represents packed lunches (P).

We could write this as

Ratio problem solving example 1 step 1

Where the letter above each part of the ratio links to the question.

We know that 465 students have school dinner.

2 Know what you are trying to calculate.

From the question, we need to calculate the number of students that have a packed lunch, so we can now write a ratio below the ratio 5:7 that shows that we have 465 students who have school dinners, and p students who have a packed lunch.

Ratio problem solving example 1 step 2

We need to find the value of p.

3 Use prior knowledge to structure a solution.

We are looking for an equivalent ratio to 5:7. So we need to calculate the multiplier. We do this by dividing the known values on the same side of the ratio by each other.

So the value of p is equal to 7 \times 93=651.

There are 651 students that have a packed lunch.

Example 2: unit conversions

The table below shows the currency conversions on one day.

Ratio problem solving example 2

Use the table above to convert £520 (GBP) to Euros € (EUR).

Ratio problem solving example 2

Use the table above to convert \bf{£520} (GBP) to Euros \bf{€} (EUR).

The two values in the table that are important are GBP and EUR. Writing this as a ratio, we can state

Ratio problem solving example 2 step 1 image 2

We know that we have £520.

We need to convert GBP to EUR and so we are looking for an equivalent ratio with GBP = £520 and EUR = E.

Ratio problem solving example 2 step 2

To get from 1 to 520, we multiply by 520 and so to calculate the number of Euros for £520, we need to multiply 1.17 by 520.

1.17 \times 520=608.4

So £520 = €608.40.

Example 3: writing a ratio 1:n

Liquid plant food is sold in concentrated bottles. The instructions on the bottle state that the 500ml of concentrated plant food must be diluted into 2l of water. Express the ratio of plant food to water respectively in the ratio 1:n.

Liquid plant food is sold in concentrated bottles. The instructions on the bottle state that the \bf{500ml} of concentrated plant food must be diluted into \bf{2l} of water . Express the ratio of plant food to water respectively as a ratio in the form 1:n.

Using the information in the question, we can now state the ratio of plant food to water as 500ml:2l. As we can convert litres into millilitres, we could convert 2l into millilitres by multiplying it by 1000.

2l = 2000ml

So we can also express the ratio as 500:2000 which will help us in later steps.

We want to simplify the ratio 500:2000 into the form 1:n.

We need to find an equivalent ratio where the first part of the ratio is equal to 1. We can only do this by dividing both parts of the ratio by 500 (as 500 \div 500=1 ).

Ratio problem solving example 3 step 3

So the ratio of plant food to water in the form 1:n is 1:4.

Example 4: forming and solving an equation

Three siblings, Josh, Kieran and Luke, receive pocket money per week proportional to their age. Kieran is 3 years older than Josh. Luke is twice Josh’s age. If Josh receives £8 pocket money, how much money do the three siblings receive in total?

Three siblings, Josh, Kieran and Luke, receive pocket money per week proportional to their ages. Kieran is \bf{3} years older than Josh . Luke is twice Josh’s age. If Luke receives \bf{£8} pocket money, how much money do the three siblings receive in total ?

We can represent the ages of the three siblings as a ratio. Taking Josh as x years old, Kieran would therefore be x+3 years old, and Luke would be 2x years old. As a ratio, we have

Ratio problem solving example 4 step 1

We also know that Luke receives £8.

We want to calculate the total amount of pocket money for the three siblings.

We need to find the value of x first. As Luke receives £8, we can state the equation 2x=8 and so x=4.

Now we know the value of x, we can substitute this value into the other parts of the ratio to obtain how much money the siblings each receive.

Ratio problem solving example 4 step 3

The total amount of pocket money is therefore 4+7+8=£19.

Example 5: simplifying ratios

Below is a bar chart showing the results for the colours of counters in a bag.

Ratio problem solving example 5

Express this data as a ratio in its simplest form.

From the bar chart, we can read the frequencies to create the ratio.

Ratio problem solving example 5 step 1

We need to simplify this ratio.

To simplify a ratio, we need to find the highest common factor of all the parts of the ratio. By listing the factors of each number, you can quickly see that the highest common factor is 2.

\begin{aligned} &12 = 1, {\color{red} 2}, 3, 4, 6, 12 \\\\ &16 = 1, {\color{red} 2}, 4, 8, 16 \\\\ &10 = 1, {\color{red} 2}, 5, 10 \end{aligned}

HCF (12,16,10) = 2

Dividing all the parts of the ratio by 2 , we get

Ratio problem solving example 5 step 3

Our solution is 6:8:5 .

Example 6: combining two ratios

Glass is made from silica, lime and soda. The ratio of silica to lime is 15:2. The ratio of silica to soda is 5:1. State the ratio of silica:lime:soda.

Glass is made from silica, lime and soda. The ratio of silica to lime is \bf{15:2.} The ratio of silica to soda is \bf{5:1.} State the ratio of silica:lime:soda .

We know the two ratios

Ratio problem solving example 6 step 1

We are trying to find the ratio of all 3 components: silica, lime and soda.

Using equivalent ratios we can say that the ratio of silica:soda is equivalent to 15:3 by multiplying the ratio by 3.

Ratio problem solving example 6 step 3 image 1

We now have the same amount of silica in both ratios and so we can now combine them to get the ratio 15:2:3.

Ratio problem solving example 6 step 3 image 2

Example 7: using bar modelling

India and Beau share some popcorn in the ratio of 5:2. If India has 75g more popcorn than Beau, what was the original quantity?

India and Beau share some popcorn in the ratio of \bf{5:2.} If India has \bf{75g} more popcorn than Beau , what was the original quantity?

We know that the initial ratio is 5:2 and that India has three more parts than Beau.

We want to find the original quantity.

Drawing a bar model of this problem, we have

Ratio problem solving example 7 step 1

Where India has 5 equal shares, and Beau has 2 equal shares.

Each share is the same value and so if we can find out this value, we can then find the total quantity.

From the question, India’s share is 75g more than Beau’s share so we can write this on the bar model.

Ratio problem solving example 7 step 3 image 1

We can find the value of one share by working out 75 \div 3=25g.

Ratio problem solving example 7 step 3 image 2

We can fill in each share to be 25g.

Ratio problem solving example 7 step 3 image 3

Adding up each share, we get

India = 5 \times 25=125g

Beau = 2 \times 25=50g

The total amount of popcorn was 125+50=175g.

Common misconceptions

  • Mixing units

Make sure that all the units in the ratio are the same. For example, in example 6 , all the units in the ratio were in millilitres. We did not mix ml and l in the ratio.

  • Ratio written in the wrong order

For example the number of dogs to cats is given as the ratio 12:13 but the solution is written as 13:12.

  • Ratios and fractions confusion

Take care when writing ratios as fractions and vice-versa. Most ratios we come across are part:part. The ratio here of red:yellow is 1:2. So the fraction which is red is \frac{1}{3} (not \frac{1}{2} ).

Ratio problem solving common misconceptions

  • Counting the number of parts in the ratio, not the total number of shares

For example, the ratio 5:4 has 9 shares, and 2 parts. This is because the ratio contains 2 numbers but the sum of these parts (the number of shares) is 5+4=9. You need to find the value per share, so you need to use the 9 shares in your next line of working.

  • Ratios of the form \bf{1:n}

The assumption can be incorrectly made that n must be greater than 1 , but n can be any number, including a decimal.

Practice ratio problem solving questions

1. An online shop sells board games and computer games. The ratio of board games to the total number of games sold in one month is 3:8. What is the ratio of board games to computer games?

GCSE Quiz True

8-3=5 computer games sold for every 3 board games.

2. The volume of gas is directly proportional to the temperature (in degrees Kelvin). A balloon contains 2.75l of gas and has a temperature of 18^{\circ}K. What is the volume of gas if the temperature increases to 45^{\circ}K?

3. The ratio of prime numbers to non-prime numbers from 1-200 is 45:155. Express this as a ratio in the form 1:n.

4. The angles in a triangle are written as the ratio x:2x:3x. Calculate the size of each angle.

5. A clothing company has a sale on tops, dresses and shoes. \frac{1}{3} of sales were for tops, \frac{1}{5} of sales were for dresses, and the rest were for shoes. Write a ratio of tops to dresses to shoes sold in its simplest form.

6. During one month, the weather was recorded into 3 categories: sunshine, cloud and rain. The ratio of sunshine to cloud was 2:3 and the ratio of cloud to rain was 9:11. State the ratio that compares sunshine:cloud:rain for the month.

Ratio problem solving GCSE questions

1. One mole of water weighs 18 grams and contains 6.02 \times 10^{23} water molecules.

Write this in the form 1gram:n where n represents the number of water molecules in standard form.

2. A plank of wood is sawn into three pieces in the ratio 3:2:5. The first piece is 36cm shorter than the third piece.

Calculate the length of the plank of wood.

5-3=2 \ parts = 36cm so 1 \ part = 18cm

3. (a) Jenny is x years old. Sally is 4 years older than Jenny. Kim is twice Jenny’s age. Write their ages in a ratio J:S:K.

(b) Sally is 16 years younger than Kim. Calculate the sum of their ages.

Learning checklist

You have now learned how to:

  • Relate the language of ratios and the associated calculations to the arithmetic of fractions and to linear functions
  • Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multi-step problems
  • Make and use connections between different parts of mathematics to solve problems

The next lessons are

  • Compound measures
  • Best buy maths

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Algebra: Ratio Word Problems

Related Pages Two-Term Ratio Word Problems More Ratio Word Problems Algebra Lessons

In these lessons, we will learn how to solve ratio word problems that have two-term ratios or three-term ratios.

Ratio problems are word problems that use ratios to relate the different items in the question.

The main things to be aware about for ratio problems are:

  • Change the quantities to the same unit if necessary.
  • Write the items in the ratio as a fraction .
  • Make sure that you have the same items in the numerator and denominator.

Ratio Problems: Two-Term Ratios

Example 1: In a bag of red and green sweets, the ratio of red sweets to green sweets is 3:4. If the bag contains 120 green sweets, how many red sweets are there?

Solution: Step 1: Assign variables: Let x = number of red sweets.

Step 2: Solve the equation. Cross Multiply 3 × 120 = 4 × x 360 = 4 x

Answer: There are 90 red sweets.

Example 2: John has 30 marbles, 18 of which are red and 12 of which are blue. Jane has 20 marbles, all of them either red or blue. If the ratio of the red marbles to the blue marbles is the same for both John and Jane, then John has how many more blue marbles than Jane?

Solution: Step 1: Sentence: Jane has 20 marbles, all of them either red or blue. Assign variables: Let x = number of blue marbles for Jane 20 – x = number red marbles for Jane

Step 2: Solve the equation

Cross Multiply 3 × x = 2 × (20 – x ) 3 x = 40 – 2 x

John has 12 blue marbles. So, he has 12 – 8 = 4 more blue marbles than Jane.

Answer: John has 4 more blue marbles than Jane.

How To Solve Word Problems Using Proportions?

This is another word problem that involves ratio or proportion.

Example: A recipe uses 5 cups of flour for every 2 cups of sugar. If I want to make a recipe using 8 cups of flour. How much sugar should I use?

How To Solve Proportion Word Problems?

When solving proportion word problems remember to have like units in the numerator and denominator of each ratio in the proportion.

  • Biologist tagged 900 rabbits in Bryer Lake National Park. At a later date, they found 6 tagged rabbits in a sample of 2000. Estimate the total number of rabbits in Bryer Lake National Park.
  • Mel fills his gas tank up with 6 gallons of premium unleaded gas for a cost of $26.58. How much would it costs to fill an 18 gallon tank? 3 If 4 US dollars can be exchanged for 1.75 Euros, how many Euros can be obtained for 144 US dollars?

Ratio problems: Three-term Ratios

Example 1: A special cereal mixture contains rice, wheat and corn in the ratio of 2:3:5. If a bag of the mixture contains 3 pounds of rice, how much corn does it contain?

Solution: Step 1: Assign variables: Let x = amount of corn

Step 2: Solve the equation Cross Multiply 2 × x = 3 × 5 2 x = 15

Answer: The mixture contains 7.5 pounds of corn.

Example 2: Clothing store A sells T-shirts in only three colors: red, blue and green. The colors are in the ratio of 3 to 4 to 5. If the store has 20 blue T-shirts, how many T-shirts does it have altogether?

Solution: Step 1: Assign variables: Let x = number of red shirts and y = number of green shirts

Step 2: Solve the equation Cross Multiply 3 × 20 = x × 4 60 = 4 x x = 15

5 × 20 = y × 4 100 = 4 y y = 25

The total number of shirts would be 15 + 25 + 20 = 60

Answer: There are 60 shirts.

Algebra And Ratios With Three Terms

Let’s study how algebra can help us think about ratios with more than two terms.

Example: There are a total of 42 computers. Each computer runs one of three operating systems: OSX, Windows, Linux. The ratio of the computers running OSX, Windows, Linux is 2:5:7. Find the number of computers that are running each of the operating systems.

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Solving Ratio Problems

videolesson.JPG

  • We add the parts of the ratio to find the total number of parts.
  • There are 2 + 3 = 5 parts in the ratio in total.
  • To find the value of one part we divide the total amount by the total number of parts.
  • 50 ÷ 5 = 10.
  • We multiply the ratio by the value of each part.
  • 2:3 multiplied by 10 gives us 20:30.
  • The 50 counters are shared into 20 counters to 30 counters.

videolesson.JPG

  • 2 + 3 = 5 and so there are 5 parts in the ratio in total.
  • We divide by this total number of parts to find the value of each part.
  • We multiply the original ratio by the value of each part.
  • We have 20:30.

videolesson.JPG

  • Sharing in a Ratio: Part 1

practiseqs.JPG

Ratio Problems: Worksheets and Answers

ratio problems worksheet pdf

How to Solve Ratio Problems

Share £50 in the ratio 2:3

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  • 6.5 Solve Proportions and their Applications
  • Introduction
  • 1.1 Introduction to Whole Numbers
  • 1.2 Add Whole Numbers
  • 1.3 Subtract Whole Numbers
  • 1.4 Multiply Whole Numbers
  • 1.5 Divide Whole Numbers
  • Key Concepts
  • Review Exercises
  • Practice Test
  • Introduction to the Language of Algebra
  • 2.1 Use the Language of Algebra
  • 2.2 Evaluate, Simplify, and Translate Expressions
  • 2.3 Solving Equations Using the Subtraction and Addition Properties of Equality
  • 2.4 Find Multiples and Factors
  • 2.5 Prime Factorization and the Least Common Multiple
  • Introduction to Integers
  • 3.1 Introduction to Integers
  • 3.2 Add Integers
  • 3.3 Subtract Integers
  • 3.4 Multiply and Divide Integers
  • 3.5 Solve Equations Using Integers; The Division Property of Equality
  • Introduction to Fractions
  • 4.1 Visualize Fractions
  • 4.2 Multiply and Divide Fractions
  • 4.3 Multiply and Divide Mixed Numbers and Complex Fractions
  • 4.4 Add and Subtract Fractions with Common Denominators
  • 4.5 Add and Subtract Fractions with Different Denominators
  • 4.6 Add and Subtract Mixed Numbers
  • 4.7 Solve Equations with Fractions
  • Introduction to Decimals
  • 5.1 Decimals
  • 5.2 Decimal Operations
  • 5.3 Decimals and Fractions
  • 5.4 Solve Equations with Decimals
  • 5.5 Averages and Probability
  • 5.6 Ratios and Rate
  • 5.7 Simplify and Use Square Roots
  • Introduction to Percents
  • 6.1 Understand Percent
  • 6.2 Solve General Applications of Percent
  • 6.3 Solve Sales Tax, Commission, and Discount Applications
  • 6.4 Solve Simple Interest Applications
  • Introduction to the Properties of Real Numbers
  • 7.1 Rational and Irrational Numbers
  • 7.2 Commutative and Associative Properties
  • 7.3 Distributive Property
  • 7.4 Properties of Identity, Inverses, and Zero
  • 7.5 Systems of Measurement
  • Introduction to Solving Linear Equations
  • 8.1 Solve Equations Using the Subtraction and Addition Properties of Equality
  • 8.2 Solve Equations Using the Division and Multiplication Properties of Equality
  • 8.3 Solve Equations with Variables and Constants on Both Sides
  • 8.4 Solve Equations with Fraction or Decimal Coefficients
  • 9.1 Use a Problem Solving Strategy
  • 9.2 Solve Money Applications
  • 9.3 Use Properties of Angles, Triangles, and the Pythagorean Theorem
  • 9.4 Use Properties of Rectangles, Triangles, and Trapezoids
  • 9.5 Solve Geometry Applications: Circles and Irregular Figures
  • 9.6 Solve Geometry Applications: Volume and Surface Area
  • 9.7 Solve a Formula for a Specific Variable
  • Introduction to Polynomials
  • 10.1 Add and Subtract Polynomials
  • 10.2 Use Multiplication Properties of Exponents
  • 10.3 Multiply Polynomials
  • 10.4 Divide Monomials
  • 10.5 Integer Exponents and Scientific Notation
  • 10.6 Introduction to Factoring Polynomials
  • 11.1 Use the Rectangular Coordinate System
  • 11.2 Graphing Linear Equations
  • 11.3 Graphing with Intercepts
  • 11.4 Understand Slope of a Line
  • A | Cumulative Review
  • B | Powers and Roots Tables
  • C | Geometric Formulas

Learning Objectives

By the end of this section, you will be able to:

  • Use the definition of proportion
  • Solve proportions
  • Solve applications using proportions
  • Write percent equations as proportions
  • Translate and solve percent proportions

Be Prepared 6.11

Before you get started, take this readiness quiz.

Simplify: 1 3 4 . 1 3 4 . If you missed this problem, review Example 4.44 .

Be Prepared 6.12

Solve: x 4 = 20 . x 4 = 20 . If you missed this problem, review Example 4.99 .

Be Prepared 6.13

Write as a rate: Sale rode his bike 24 24 miles in 2 2 hours. If you missed this problem, review Example 5.63 .

Use the Definition of Proportion

In the section on Ratios and Rates we saw some ways they are used in our daily lives. When two ratios or rates are equal, the equation relating them is called a proportion .

A proportion is an equation of the form a b = c d , a b = c d , where b ≠ 0 , d ≠ 0 . b ≠ 0 , d ≠ 0 .

The proportion states two ratios or rates are equal. The proportion is read “ a “ a is to b , b , as c c is to d ”. d ”.

The equation 1 2 = 4 8 1 2 = 4 8 is a proportion because the two fractions are equal. The proportion 1 2 = 4 8 1 2 = 4 8 is read “ 1 “ 1 is to 2 2 as 4 4 is to 8 ”. 8 ”.

If we compare quantities with units, we have to be sure we are comparing them in the right order. For example, in the proportion 20 students 1 teacher = 60 students 3 teachers 20 students 1 teacher = 60 students 3 teachers we compare the number of students to the number of teachers. We put students in the numerators and teachers in the denominators.

Example 6.40

Write each sentence as a proportion:

  • ⓐ 3 3 is to 7 7 as 15 15 is to 35 . 35 .
  • ⓑ 5 5 hits in 8 8 at bats is the same as 30 30 hits in 48 48 at-bats.
  • ⓒ $1.50 $1.50 for 6 6 ounces is equivalent to $2.25 $2.25 for 9 9 ounces.

Try It 6.79

  • ⓐ 5 5 is to 9 9 as 20 20 is to 36 . 36 .
  • ⓑ 7 7 hits in 11 11 at-bats is the same as 28 28 hits in 44 44 at-bats.
  • ⓒ $2.50 $2.50 for 8 8 ounces is equivalent to $3.75 $3.75 for 12 12 ounces.

Try It 6.80

  • ⓐ 6 6 is to 7 7 as 36 36 is to 42 . 42 .
  • ⓑ 8 8 adults for 36 36 children is the same as 12 12 adults for 54 54 children.
  • ⓒ $3.75 $3.75 for 6 6 ounces is equivalent to $2.50 $2.50 for 4 4 ounces.

Look at the proportions 1 2 = 4 8 1 2 = 4 8 and 2 3 = 6 9 . 2 3 = 6 9 . From our work with equivalent fractions we know these equations are true. But how do we know if an equation is a proportion with equivalent fractions if it contains fractions with larger numbers?

To determine if a proportion is true, we find the cross products of each proportion. To find the cross products, we multiply each denominator with the opposite numerator (diagonally across the equal sign). The results are called a cross product because of the cross formed. If, and only if, the given proportion is true, that is, the two sides are equal, then the cross products of a proportion will be equal.

Cross Products of a Proportion

For any proportion of the form a b = c d , a b = c d , where b ≠ 0 , d ≠ 0 , b ≠ 0 , d ≠ 0 , its cross products are equal.

Cross products can be used to test whether a proportion is true. To test whether an equation makes a proportion, we find the cross products. If they are both equal, we have a proportion.

Example 6.41

Determine whether each equation is a proportion:

  • ⓐ 4 9 = 12 28 4 9 = 12 28
  • ⓑ 17.5 37.5 = 7 15 17.5 37.5 = 7 15

To determine if the equation is a proportion, we find the cross products. If they are equal, the equation is a proportion.

Since the cross products are not equal, 28 · 4 ≠ 9 · 12 , 28 · 4 ≠ 9 · 12 , the equation is not a proportion.

Since the cross products are equal, 15 · 17.5 = 37.5 · 7 , 15 · 17.5 = 37.5 · 7 , the equation is a proportion.

Try It 6.81

  • ⓐ 7 9 = 54 72 7 9 = 54 72
  • ⓑ 24.5 45.5 = 7 13 24.5 45.5 = 7 13

Try It 6.82

  • ⓐ 8 9 = 56 73 8 9 = 56 73
  • ⓑ 28.5 52.5 = 8 15 28.5 52.5 = 8 15

Solve Proportions

To solve a proportion containing a variable, we remember that the proportion is an equation. All of the techniques we have used so far to solve equations still apply. In the next example, we will solve a proportion by multiplying by the Least Common Denominator (LCD) using the Multiplication Property of Equality .

Example 6.42

Solve: x 63 = 4 7 . x 63 = 4 7 .

Try It 6.83

Solve the proportion: n 84 = 11 12 . n 84 = 11 12 .

Try It 6.84

Solve the proportion: y 96 = 13 12 . y 96 = 13 12 .

When the variable is in a denominator, we’ll use the fact that the cross products of a proportion are equal to solve the proportions.

We can find the cross products of the proportion and then set them equal. Then we solve the resulting equation using our familiar techniques.

Example 6.43

Solve: 144 a = 9 4 . 144 a = 9 4 .

Notice that the variable is in the denominator, so we will solve by finding the cross products and setting them equal.

Another method to solve this would be to multiply both sides by the LCD, 4 a . 4 a . Try it and verify that you get the same solution.

Try It 6.85

Solve the proportion: 91 b = 7 5 . 91 b = 7 5 .

Try It 6.86

Solve the proportion: 39 c = 13 8 . 39 c = 13 8 .

Example 6.44

Solve: 52 91 = −4 y . 52 91 = −4 y .

Try It 6.87

Solve the proportion: 84 98 = −6 x . 84 98 = −6 x .

Try It 6.88

Solve the proportion: −7 y = 105 135 . −7 y = 105 135 .

Solve Applications Using Proportions

The strategy for solving applications that we have used earlier in this chapter, also works for proportions, since proportions are equations. When we set up the proportion , we must make sure the units are correct—the units in the numerators match and the units in the denominators match.

Example 6.45

When pediatricians prescribe acetaminophen to children, they prescribe 5 5 milliliters (ml) of acetaminophen for every 25 25 pounds of the child’s weight. If Zoe weighs 80 80 pounds, how many milliliters of acetaminophen will her doctor prescribe?

You could also solve this proportion by setting the cross products equal.

Try It 6.89

Pediatricians prescribe 5 5 milliliters (ml) of acetaminophen for every 25 25 pounds of a child’s weight. How many milliliters of acetaminophen will the doctor prescribe for Emilia, who weighs 60 60 pounds?

Try It 6.90

For every 1 1 kilogram (kg) of a child’s weight, pediatricians prescribe 15 15 milligrams (mg) of a fever reducer. If Isabella weighs 12 12 kg, how many milligrams of the fever reducer will the pediatrician prescribe?

Example 6.46

One brand of microwave popcorn has 120 120 calories per serving. A whole bag of this popcorn has 3.5 3.5 servings. How many calories are in a whole bag of this microwave popcorn?

Try It 6.91

Marissa loves the Caramel Macchiato at the coffee shop. The 16 16 oz. medium size has 240 240 calories. How many calories will she get if she drinks the large 20 20 oz. size?

Try It 6.92

Yaneli loves Starburst candies, but wants to keep her snacks to 100 100 calories. If the candies have 160 160 calories for 8 8 pieces, how many pieces can she have in her snack?

Example 6.47

Josiah went to Mexico for spring break and changed $325 $325 dollars into Mexican pesos. At that time, the exchange rate had $1 $1 U.S. is equal to 12.54 12.54 Mexican pesos. How many Mexican pesos did he get for his trip?

Try It 6.93

Yurianna is going to Europe and wants to change $800 $800 dollars into Euros. At the current exchange rate, $1 $1 US is equal to 0.738 0.738 Euro. How many Euros will she have for her trip?

Try It 6.94

Corey and Nicole are traveling to Japan and need to exchange $600 $600 into Japanese yen. If each dollar is 94.1 94.1 yen, how many yen will they get?

Write Percent Equations As Proportions

Previously, we solved percent equations by applying the properties of equality we have used to solve equations throughout this text. Some people prefer to solve percent equations by using the proportion method. The proportion method for solving percent problems involves a percent proportion. A percent proportion is an equation where a percent is equal to an equivalent ratio.

For example, 60% = 60 100 60% = 60 100 and we can simplify 60 100 = 3 5 . 60 100 = 3 5 . Since the equation 60 100 = 3 5 60 100 = 3 5 shows a percent equal to an equivalent ratio, we call it a percent proportion . Using the vocabulary we used earlier:

Percent Proportion

The amount is to the base as the percent is to 100 . 100 .

If we restate the problem in the words of a proportion, it may be easier to set up the proportion:

We could also say:

First we will practice translating into a percent proportion. Later, we’ll solve the proportion.

Example 6.48

Translate to a proportion. What number is 75% 75% of 90 ? 90 ?

If you look for the word "of", it may help you identify the base.

Try It 6.95

Translate to a proportion: What number is 60% 60% of 105 ? 105 ?

Try It 6.96

Translate to a proportion: What number is 40% 40% of 85 ? 85 ?

Example 6.49

Translate to a proportion. 19 19 is 25% 25% of what number?

Try It 6.97

Translate to a proportion: 36 36 is 25% 25% of what number?

Try It 6.98

Translate to a proportion: 27 27 is 36% 36% of what number?

Example 6.50

Translate to a proportion. What percent of 27 27 is 9 ? 9 ?

Try It 6.99

Translate to a proportion: What percent of 52 52 is 39 ? 39 ?

Try It 6.100

Translate to a proportion: What percent of 92 92 is 23 ? 23 ?

Translate and Solve Percent Proportions

Now that we have written percent equations as proportions, we are ready to solve the equations.

Example 6.51

Translate and solve using proportions: What number is 45% 45% of 80 ? 80 ?

Try It 6.101

Translate and solve using proportions: What number is 65% 65% of 40 ? 40 ?

Try It 6.102

Translate and solve using proportions: What number is 85% 85% of 40 ? 40 ?

In the next example, the percent is more than 100 , 100 , which is more than one whole. So the unknown number will be more than the base.

Example 6.52

Translate and solve using proportions: 125% 125% of 25 25 is what number?

Try It 6.103

Translate and solve using proportions: 125% 125% of 64 64 is what number?

Try It 6.104

Translate and solve using proportions: 175% 175% of 84 84 is what number?

Percents with decimals and money are also used in proportions.

Example 6.53

Translate and solve: 6.5% 6.5% of what number is $1.56 ? $1.56 ?

Try It 6.105

Translate and solve using proportions: 8.5% 8.5% of what number is $3.23 ? $3.23 ?

Try It 6.106

Translate and solve using proportions: 7.25% 7.25% of what number is $4.64 ? $4.64 ?

Example 6.54

Translate and solve using proportions: What percent of 72 72 is 9 ? 9 ?

Try It 6.107

Translate and solve using proportions: What percent of 72 72 is 27 ? 27 ?

Try It 6.108

Translate and solve using proportions: What percent of 92 92 is 23 ? 23 ?

Section 6.5 Exercises

Practice makes perfect.

In the following exercises, write each sentence as a proportion.

4 4 is to 15 15 as 36 36 is to 135 . 135 .

7 7 is to 9 9 as 35 35 is to 45 . 45 .

12 12 is to 5 5 as 96 96 is to 40 . 40 .

15 15 is to 8 8 as 75 75 is to 40 . 40 .

5 5 wins in 7 7 games is the same as 115 115 wins in 161 161 games.

4 4 wins in 9 9 games is the same as 36 36 wins in 81 81 games.

8 8 campers to 1 1 counselor is the same as 48 48 campers to 6 6 counselors.

6 6 campers to 1 1 counselor is the same as 48 48 campers to 8 8 counselors.

$9.36 $9.36 for 18 18 ounces is the same as $2.60 $2.60 for 5 5 ounces.

$3.92 $3.92 for 8 8 ounces is the same as $1.47 $1.47 for 3 3 ounces.

$18.04 $18.04 for 11 11 pounds is the same as $4.92 $4.92 for 3 3 pounds.

$12.42 $12.42 for 27 27 pounds is the same as $5.52 $5.52 for 12 12 pounds.

In the following exercises, determine whether each equation is a proportion.

7 15 = 56 120 7 15 = 56 120

5 12 = 45 108 5 12 = 45 108

11 6 = 21 16 11 6 = 21 16

9 4 = 39 34 9 4 = 39 34

12 18 = 4.99 7.56 12 18 = 4.99 7.56

9 16 = 2.16 3.89 9 16 = 2.16 3.89

13.5 8.5 = 31.05 19.55 13.5 8.5 = 31.05 19.55

10.1 8.4 = 3.03 2.52 10.1 8.4 = 3.03 2.52

In the following exercises, solve each proportion.

x 56 = 7 8 x 56 = 7 8

n 91 = 8 13 n 91 = 8 13

49 63 = z 9 49 63 = z 9

56 72 = y 9 56 72 = y 9

5 a = 65 117 5 a = 65 117

4 b = 64 144 4 b = 64 144

98 154 = −7 p 98 154 = −7 p

72 156 = −6 q 72 156 = −6 q

a −8 = −42 48 a −8 = −42 48

b −7 = −30 42 b −7 = −30 42

2.6 3.9 = c 3 2.6 3.9 = c 3

2.7 3.6 = d 4 2.7 3.6 = d 4

2.7 j = 0.9 0.2 2.7 j = 0.9 0.2

2.8 k = 2.1 1.5 2.8 k = 2.1 1.5

1 2 1 = m 8 1 2 1 = m 8

1 3 3 = 9 n 1 3 3 = 9 n

In the following exercises, solve the proportion problem.

Pediatricians prescribe 5 5 milliliters (ml) of acetaminophen for every 25 25 pounds of a child’s weight. How many milliliters of acetaminophen will the doctor prescribe for Jocelyn, who weighs 45 45 pounds?

Brianna, who weighs 6 6 kg, just received her shots and needs a pain killer. The pain killer is prescribed for children at 15 15 milligrams (mg) for every 1 1 kilogram (kg) of the child’s weight. How many milligrams will the doctor prescribe?

At the gym, Carol takes her pulse for 10 10 sec and counts 19 19 beats. How many beats per minute is this? Has Carol met her target heart rate of 140 140 beats per minute?

Kevin wants to keep his heart rate at 160 160 beats per minute while training. During his workout he counts 27 27 beats in 10 10 seconds. How many beats per minute is this? Has Kevin met his target heart rate?

A new energy drink advertises 106 106 calories for 8 8 ounces. How many calories are in 12 12 ounces of the drink?

One 12 12 ounce can of soda has 150 150 calories. If Josiah drinks the big 32 32 ounce size from the local mini-mart, how many calories does he get?

Karen eats 1 2 1 2 cup of oatmeal that counts for 2 2 points on her weight loss program. Her husband, Joe, can have 3 3 points of oatmeal for breakfast. How much oatmeal can he have?

An oatmeal cookie recipe calls for 1 2 1 2 cup of butter to make 4 4 dozen cookies. Hilda needs to make 10 10 dozen cookies for the bake sale. How many cups of butter will she need?

Janice is traveling to Canada and will change $250 $250 US dollars into Canadian dollars. At the current exchange rate, $1 $1 US is equal to $1.01 $1.01 Canadian. How many Canadian dollars will she get for her trip?

Todd is traveling to Mexico and needs to exchange $450 $450 into Mexican pesos. If each dollar is worth 12.29 12.29 pesos, how many pesos will he get for his trip?

Steve changed $600 $600 into 480 480 Euros. How many Euros did he receive per US dollar?

Martha changed $350 $350 US into 385 385 Australian dollars. How many Australian dollars did she receive per US dollar?

At the laundromat, Lucy changed $12.00 $12.00 into quarters. How many quarters did she get?

When she arrived at a casino, Gerty changed $20 $20 into nickels. How many nickels did she get?

Jesse’s car gets 30 30 miles per gallon of gas. If Las Vegas is 285 285 miles away, how many gallons of gas are needed to get there and then home? If gas is $3.09 $3.09 per gallon, what is the total cost of the gas for the trip?

Danny wants to drive to Phoenix to see his grandfather. Phoenix is 370 370 miles from Danny’s home and his car gets 18.5 18.5 miles per gallon. How many gallons of gas will Danny need to get to and from Phoenix? If gas is $3.19 $3.19 per gallon, what is the total cost for the gas to drive to see his grandfather?

Hugh leaves early one morning to drive from his home in Chicago to go to Mount Rushmore, 812 812 miles away. After 3 3 hours, he has gone 190 190 miles. At that rate, how long will the whole drive take?

Kelly leaves her home in Seattle to drive to Spokane, a distance of 280 280 miles. After 2 2 hours, she has gone 152 152 miles. At that rate, how long will the whole drive take?

Phil wants to fertilize his lawn. Each bag of fertilizer covers about 4,000 4,000 square feet of lawn. Phil’s lawn is approximately 13,500 13,500 square feet. How many bags of fertilizer will he have to buy?

April wants to paint the exterior of her house. One gallon of paint covers about 350 350 square feet, and the exterior of the house measures approximately 2000 2000 square feet. How many gallons of paint will she have to buy?

Write Percent Equations as Proportions

In the following exercises, translate to a proportion.

What number is 35% 35% of 250 ? 250 ?

What number is 75% 75% of 920 ? 920 ?

What number is 110% 110% of 47 ? 47 ?

What number is 150% 150% of 64 ? 64 ?

45 45 is 30% 30% of what number?

25 25 is 80% 80% of what number?

90 90 is 150% 150% of what number?

77 77 is 110% 110% of what number?

What percent of 85 85 is 17 ? 17 ?

What percent of 92 92 is 46 ? 46 ?

What percent of 260 260 is 340 ? 340 ?

What percent of 180 180 is 220 ? 220 ?

In the following exercises, translate and solve using proportions.

What number is 65% 65% of 180 ? 180 ?

What number is 55% 55% of 300 ? 300 ?

18% 18% of 92 92 is what number?

22% 22% of 74 74 is what number?

175% 175% of 26 26 is what number?

250% 250% of 61 61 is what number?

What is 300% 300% of 488 ? 488 ?

What is 500% 500% of 315 ? 315 ?

17% 17% of what number is $7.65 ? $7.65 ?

19% 19% of what number is $6.46 ? $6.46 ?

$13.53 $13.53 is 8.25% 8.25% of what number?

$18.12 $18.12 is 7.55% 7.55% of what number?

What percent of 56 56 is 14 ? 14 ?

What percent of 80 80 is 28 ? 28 ?

What percent of 96 96 is 12 ? 12 ?

What percent of 120 120 is 27 ? 27 ?

Everyday Math

Mixing a concentrate Sam bought a large bottle of concentrated cleaning solution at the warehouse store. He must mix the concentrate with water to make a solution for washing his windows. The directions tell him to mix 3 3 ounces of concentrate with 5 5 ounces of water. If he puts 12 12 ounces of concentrate in a bucket, how many ounces of water should he add? How many ounces of the solution will he have altogether?

Mixing a concentrate Travis is going to wash his car. The directions on the bottle of car wash concentrate say to mix 2 2 ounces of concentrate with 15 15 ounces of water. If Travis puts 6 6 ounces of concentrate in a bucket, how much water must he mix with the concentrate?

Writing Exercises

To solve “what number is 45% 45% of 350 ” 350 ” do you prefer to use an equation like you did in the section on Decimal Operations or a proportion like you did in this section? Explain your reason.

To solve “what percent of 125 125 is 25 ” 25 ” do you prefer to use an equation like you did in the section on Decimal Operations or a proportion like you did in this section? Explain your reason.

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

ⓑ Overall, after looking at the checklist, do you think you are well-prepared for the next Chapter? Why or why not?

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How to Calculate Ratios

Last Updated: January 29, 2024 References

This article was co-authored by Grace Imson, MA . Grace Imson is a math teacher with over 40 years of teaching experience. Grace is currently a math instructor at the City College of San Francisco and was previously in the Math Department at Saint Louis University. She has taught math at the elementary, middle, high school, and college levels. She has an MA in Education, specializing in Administration and Supervision from Saint Louis University. This article has been viewed 3,083,046 times.

Ratios are mathematical expressions that compare two or more numbers. They can compare absolute quantities and amounts or can be used to compare portions of a larger whole. Ratios can be calculated and written in several different ways, but the principles guiding the use of ratios are universal to all.

Practice Problems

problem solve ratio

Understanding Ratios

Step 1 Be aware of how ratios are used.

  • Ratios can be used to show the relation between any quantities, even if one is not directly tied to the other (as they would be in a recipe). For example, if there are five girls and ten boys in a class, the ratio of girls to boys is 5 to 10. Neither quantity is dependent on or tied to the other, and would change if anyone left or new students came in. The ratio merely compares the quantities.

Step 3 Notice the different ways in which ratios are expressed.

  • You will commonly see ratios represented using words (as above). Because they are used so commonly and in such a variety of ways, if you find yourself working outside of mathematic or scientific fields, this may the most common form of ratio you will see.
  • Ratios are frequently expressed using a colon. When comparing two numbers in a ratio, you'll use one colon (as in 7 : 13). When you're comparing more than two numbers, you'll put a colon between each set of numbers in succession (as in 10 : 2 : 23). In our classroom example, we might compare the number of boys to the number of girls with the ratio 5 girls : 10 boys. We can simply express the ratio as 5 : 10.
  • Ratios are also sometimes expressed using fractional notation. In the case of the classroom, the 5 girls and 10 boys would be shown simply as 5/10. That said, it shouldn't be read out loud the same as a fraction, and you need to keep in mind that the numbers do not represent a portion of a whole.

Using Ratios

Step 1 Reduce a ratio...

  • In the classroom example above, 5 girls to 10 boys (5 : 10), both sides of the ratio have a factor of 5. Divide both sides by 5 (the greatest common factor) to get 1 girl to 2 boys (or 1 : 2). However, we should keep the original quantities in mind, even when using this reduced ratio. There are not 3 total students in the class, but 15. The reduced ratio just compares the relationship between the number of boys and girls. There are 2 boys for every girl, not exactly 2 boys and 1 girl.
  • Some ratios cannot be reduced. For example, 3 : 56 cannot be reduced because the two numbers share no common factors - 3 is a prime number, and 56 is not divisible by 3.

Step 2 Use multiplication or...

  • For example, a baker needs to triple the size of a cake recipe. If the normal ratio of flour to sugar is 2 to 1 (2 : 1), then both numbers must be increased by a factor of three. The appropriate quantities for the recipe are now 6 cups of flour to 3 cups of sugar (6 : 3).
  • The same process can be reversed. If the baker needed only one-half of the normal recipe, both quantities could be multiplied by 1/2 (or divided by two). The result would be 1 cup of flour to 1/2 (0.5) cup of sugar.

Step 3 Find unknown variables when given two equivalent ratios.

  • For example, let's say we have a small group of students containing 2 boys and 5 girls. If we were to maintain this proportion of boys to girls, how many boys would be in a class that contained 20 girls? To solve, first, let's make two ratios, one with our unknown variables: 2 boys : 5 girls = x boys : 20 girls. If we convert these ratios to their fraction forms, we get 2/5 and x/20. If you cross multiply, you are left with 5x=40, and you can solve by dividing both figures by 5. The final solution is x=8.

Grace Imson, MA

Grace Imson, MA

Look at the order of terms to figure out the numerator and denominator in a word problem. The first term is usually the numerator, and the second is usually the denominator. For example, if a problem asks for the ratio of the length of an item to its width, the length will be the numerator, and width will be the denominator.

Catching Mistakes

Step 1 Avoid addition or subtraction in ratio word problems.

  • Wrong method: "8 - 4 = 4, so I added 4 potatoes to the recipe. That means I should take the 5 carrots and add 4 to that too... wait! That's not how ratios work. I'll try again."
  • Right method: "8 ÷ 4 = 2, so I multiplied the number of potatoes by 2. That means I should multiply the 5 carrots by 2 as well. 5 x 2 = 10, so I want 10 carrots total in the new recipe."

Step 2 Convert...

  • A dragon has 500 grams of gold and 10 kilograms of silver. What is the ratio of gold to silver in the dragon's hoard?

{\frac  {1,000grams}{1kilogram}}

  • The dragon has 500 grams of gold and 10,000 grams of silver.

{\frac  {500gramsGold}{10,000gramsSilver}}={\frac  {5}{100}}={\frac  {1}{20}}

  • Example problem: If you have six boxes, and in every three boxes there are nine marbles, how many marbles do you have?

6boxes*{\frac  {3boxes}{9marbles}}=...

One common problem is knowing which number to use as a numerator. In a word problem, the first term stated is usually the numerator and the second term stated is usually the denominator. If you want the ratio of the length of an item to the width, length becomes your numerator and width becomes your denominator.

Community Q&A

Community Answer

You Might Also Like

Calculate Compression Ratio

  • ↑ http://www.virtualnerd.com/common-core/grade-6/6_RP-ratios-proportional-relationships/A
  • ↑ http://www.purplemath.com/modules/ratio.htm
  • ↑ http://www.helpwithfractions.com/math-homework-helper/least-common-denominator/
  • ↑ http://www.mathplanet.com/education/algebra-1/how-to-solve-linear-equations/ratios-and-proportions-and-how-to-solve-them
  • ↑ http://www.math.com/school/subject1/lessons/S1U2L2DP.html

About This Article

Grace Imson, MA

To calculate a ratio, start by determining which 2 quantities are being compared to each other. For example, if you wanted to know the ratio of girls to boys in a class where there are 5 girls and 10 boys, 5 and 10 would be the quantities you're comparing. Then, put a colon or the word "to" between the numbers to express them as a ratio. In this example, you'd write "5 to 10" or "5:10." Finally, simplify the ratio if possible by dividing both numbers by the greatest common factor. To learn how to solve equations and word problems with ratios, scroll down! Did this summary help you? Yes No

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Primary Grade Challenge Math by Edward Zaccaro

A good book on problem solving with very varied word problems and strategies on how to solve problems. Includes chapters on: Sequences, Problem-solving, Money, Percents, Algebraic Thinking, Negative Numbers, Logic, Ratios, Probability, Measurements, Fractions, Division. Each chapter’s questions are broken down into four levels: easy, somewhat challenging, challenging, and very challenging.

Practice makes perfect. Practice math at IXL.com

A ratio compares values .

A ratio says how much of one thing there is compared to another thing.

Ratios can be shown in different ways:

A ratio can be scaled up:

Try it Yourself

Using ratios.

The trick with ratios is to always multiply or divide the numbers by the same value .

Example: A Recipe for pancakes uses 3 cups of flour and 2 cups of milk.

So the ratio of flour to milk is 3 : 2

To make pancakes for a LOT of people we might need 4 times the quantity, so we multiply the numbers by 4:

3 ×4 : 2 ×4 = 12 : 8

In other words, 12 cups of flour and 8 cups of milk .

The ratio is still the same, so the pancakes should be just as yummy.

"Part-to-Part" and "Part-to-Whole" Ratios

The examples so far have been "part-to-part" (comparing one part to another part).

But a ratio can also show a part compared to the whole lot .

Example: There are 5 pups, 2 are boys, and 3 are girls

Part-to-Part:

The ratio of boys to girls is 2:3 or 2 / 3

The ratio of girls to boys is 3:2 or 3 / 2

Part-to-Whole:

The ratio of boys to all pups is 2:5 or 2 / 5

The ratio of girls to all pups is 3:5 or 3 / 5

Try It Yourself

We can use ratios to scale drawings up or down (by multiplying or dividing).

Example: To draw a horse at 1/10th normal size, multiply all sizes by 1/10th

This horse in real life is 1500 mm high and 2000 mm long, so the ratio of its height to length is

1500 : 2000

What is that ratio when we draw it at 1/10th normal size?

We can make any reduction/enlargement we want that way.

"I must have big feet, my foot is nearly as long as my Mom's!"

But then she thought to measure heights, and found she is 133cm tall, and her Mom is 152cm tall.

In a table this is:

The "foot-to-height" ratio in fraction style is:

We can simplify those fractions like this:

And we get this (please check that the calcs are correct):

"Oh!" she said, "the Ratios are the same".

"So my foot is only as big as it should be for my height, and is not really too big."

You can practice your ratio skills by Making Some Chocolate Crispies

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Mathematics LibreTexts

8.7: Solve Proportion and Similar Figure Applications

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  • Page ID 15179

Learning Objectives

By the end of this section, you will be able to:

  • Solve proportions
  • Solve similar figure applications

Before you get started, take this readiness quiz.

If you miss a problem, go back to the section listed and review the material.

  • Solve \(\dfrac{n}{3}=30\). If you missed this problem, review Exercise 2.2.25 .
  • The perimeter of a triangular window is 23 feet. The lengths of two sides are ten feet and six feet. How long is the third side? If you missed this problem, review Example 3.4.2

Solve Proportions

When two rational expressions are equal, the equation relating them is called a proportion .

Definition: PROPORTION

A proportion is an equation of the form \(\dfrac{a}{b}=\dfrac{c}{d}\), where \(b \ne 0\), \(d \ne 0\).

The proportion is read “a is to b, as c is to d"

The equation \(\dfrac{1}{2}=\dfrac{4}{8}\) is a proportion because the two fractions are equal.

The proportion \(\dfrac{1}{2}=\dfrac{4}{8}\) is read “1 is to 2 as 4 is to 8.”

Proportions are used in many applications to ‘scale up’ quantities. We’ll start with a very simple example so you can see how proportions work. Even if you can figure out the answer to the example right away, make sure you also learn to solve it using proportions.

Suppose a school principal wants to have 1 teacher for 20 students. She could use proportions to find the number of teachers for 60 students. We let x be the number of teachers for 60 students and then set up the proportion:

\[\dfrac{1\,\text{teacher}}{20\,\text{students}}=\dfrac{x\,\text{teachers}}{60\,\text{students}}\nonumber\]

We are careful to match the units of the numerators and the units of the denominators—teachers in the numerators, students in the denominators.

Since a proportion is an equation with rational expressions, we will solve proportions the same way we solved equations in Solve Rational Equations . We’ll multiply both sides of the equation by the LCD to clear the fractions and then solve the resulting equation.

Now we’ll do a few examples of solving numerical proportions without any units. Then we will solve applications using proportions.

Example \(\PageIndex{1}\)

\(\dfrac{x}{63}=\dfrac{4}{7}\).

Try It \(\PageIndex{1}\)

\(\dfrac{n}{84}=\dfrac{11}{12}\).

Try It \(\PageIndex{2}\)

\(\dfrac{y}{96}=\dfrac{13}{12}\).

Example \(\PageIndex{2}\)

\(\dfrac{144}{a}=\dfrac{9}{4}\).

Try It \(\PageIndex{3}\)

\(\dfrac{91}{b}=\dfrac{7}{5}\).

Try It \(\PageIndex{4}\)

\(\dfrac{39}{c}=\dfrac{13}{8}\).

Example \(\PageIndex{3}\)

\(\dfrac{n}{n+14}=\dfrac{5}{7}.\)

Try It \(\PageIndex{5}\)

\(\dfrac{y}{y+55}=\dfrac{3}{8}\).

Try It \(\PageIndex{6}\)

\(\dfrac{z}{z−84}=−\dfrac{1}{5}\).

Example \(\PageIndex{4}\)

\(\dfrac{p+12}{9}=\dfrac{p−12}{6}\).

Try It \(\PageIndex{7}\)

\(\dfrac{v+30}{8}=\dfrac{v+66}{12}\).

Try It \(\PageIndex{8}\)

\(\dfrac{2x+15}{9}=\dfrac{7x+3}{15}\).

To solve applications with proportions, we will follow our usual strategy for solving applications. But when we set up the proportion, we must make sure to have the units correct—the units in the numerators must match and the units in the denominators must match.

Example \(\PageIndex{5}\)

When pediatricians prescribe acetaminophen to children, they prescribe 5 milliliters (ml) of acetaminophen for every 25 pounds of the child’s weight. If Zoe weighs 80 pounds, how many milliliters of acetaminophen will her doctor prescribe?

Try It \(\PageIndex{9}\)

Pediatricians prescribe 5 milliliters (ml) of acetaminophen for every 25 pounds of a child’s weight. How many milliliters of acetaminophen will the doctor prescribe for Emilia, who weighs 60 pounds?

Try It \(\PageIndex{10}\)

For every 1 kilogram (kg) of a child’s weight, pediatricians prescribe 15 milligrams (mg) of a fever reducer. If Isabella weighs 12 kg, how many milligrams of the fever reducer will the pediatrician prescribe?

Example \(\PageIndex{6}\)

A 16-ounce iced caramel macchiato has 230 calories. How many calories are there in a 24-ounce iced caramel macchiato?

Try It \(\PageIndex{11}\)

At a fast-food restaurant, a 22-ounce chocolate shake has 850 calories. How many calories are in their 12-ounce chocolate shake? Round your answer to nearest whole number.

464 calories

Try It \(\PageIndex{12}\)

Yaneli loves Starburst candies, but wants to keep her snacks to 100 calories. If the candies have 160 calories for 8 pieces, how many pieces can she have in her snack?

Example \(\PageIndex{7}\)

Josiah went to Mexico for spring break and changed $325 dollars into Mexican pesos. At that time, the exchange rate had $1 US is equal to 12.54 Mexican pesos. How many Mexican pesos did he get for his trip?

Try It \(\PageIndex{13}\)

Yurianna is going to Europe and wants to change $800 dollars into Euros. At the current exchange rate, $1 US is equal to 0.738 Euro. How many Euros will she have for her trip?

590.4 Euros

Try It \(\PageIndex{14}\)

Corey and Nicole are traveling to Japan and need to exchange $600 into Japanese yen. If each dollar is 94.1 yen, how many yen will they get?

In the example above, we related the number of pesos to the number of dollars by using a proportion. We could say the number of pesos is proportional to the number of dollars. If two quantities are related by a proportion, we say that they are proportional.

Solve Similar Figure Applications

When you shrink or enlarge a photo on a phone or tablet, figure out a distance on a map, or use a pattern to build a bookcase or sew a dress, you are working with similar figures . If two figures have exactly the same shape, but different sizes, they are said to be similar. One is a scale model of the other. All their corresponding angles have the same measures and their corresponding sides are in the same ratio.

Definition: SIMILAR FIGURES

Two figures are similar if the measures of their corresponding angles are equal and their corresponding sides are in the same ratio.

For example, the two triangles in Figure are similar. Each side of ΔABC is 4 times the length of the corresponding side of ΔXYZ.

The above image shows the steps to solve the proportion 1 divided by 12.54 equals 325 divided by p. What are you asked to find? How many Mexican pesos did he get? Assign a variable. Let p equal the number of pesos. Write a sentence that gives the information to find it. If one dollar US is equal to 12.54 pesos, then 325 dollars is how many pesos. Translate into a proportion, be careful of the units. Dollars divided pesos equals dollars divided by pesos to get 1 divided by 12.54 equals 325 divided by p. Multiply both sides by the LCD, 12.54 p to get 1 divided by 12.54 p times 1 divided by 12.54 equals 12.54 p times 325 divided by p. Remove common factors from both sides. Cross out 12.54 from the left side of the equation. Cross out p from the right side of the equation. Simplify to get p equals 4075.5 in the original proportion. Check. Is the answer reasonable? Yes, $100 would be $1254 pesos. $325 is a little more than 3 times this amount, so our answer of 4075.5 pesos makes sense. Substitute p equals 4075.5 in the original proportion. Use a calculator. We now have 1 divided by 12.54 equals 325 divided by p. Next, 1 divided by 12.54 equals 325 divided by 4075.5 to get 0.07874 equals 0.07874. The answer checks.

This is summed up in the Property of Similar Triangles.

Definition: PROPERTY OF SIMILAR TRIANGLES

  • If ΔABC is similar to ΔXYZ

The above figure shows to similar triangles. The larger triangle labeled A B C. The length of A to B is c, The length of B to C is a. The length of C to A is b. The larger triangle is labeled X Y Z. The length of X to Y is z. The length of Y to Z is x. The length of X to Z is y. To the right of the triangles, it states that measure of corresponding angle A is equal to the measure of corresponding angle X, measure of corresponding angle B is equal to the measure of corresponding angle Y, and measure of corresponding angle C is equal to the measure of corresponding angle Z. Therefore, a divided by x equals b divided by y equals c divided by z.

To solve applications with similar figures we will follow the Problem-Solving Strategy for Geometry Applications we used earlier.

Definition: SOLVE GEOMETRY APPLICATIONS.

  • Read the problem and make all the words and ideas are understood. Draw the figure and label it with the given information.
  • Identify what we are looking for.
  • Name what we are looking for by choosing a variable to represent it.
  • Translate into an equation by writing the appropriate formula or model for the situation. Substitute in the given information.
  • Solve the equation using good algebra techniques.
  • Check the answer in the problem and make sure it makes sense.
  • Answer the question with a complete sentence.

Example \(\PageIndex{8}\)

ΔABC is similar to ΔXYZ. The lengths of two sides of each triangle are given in the figure.

The above image shows two similar triangles. Two sides are given for each triangle. The larger triangle is labeled A B C. The length of A to B is 4. The length from B to C is a. The length from C to A is 3.2. The smaller triangle is labeled X Y Z. The length from X to Y is 3. The length from Y to Z is 4.5. The length from Z to X is y.

Find the length of the sides of the similar triangles.

Try It \(\PageIndex{15}\)

ΔABC is similar to ΔXYZ. The lengths of two sides of each triangle are given in the figure.

The above image shows two similar triangles. The smaller triangle is labeled A B C. The length of two sides is given for the smaller triangle A B C. The length from A to B is 17. The length from B to C is a. The length from C to D is 15. The larger triangle is labeled X Y Z. The length is given for two sides. The length from X to Y is 25.5. The length from Y to Z is 12. The length from Z to X is y.

Find the length of side a

Try It \(\PageIndex{16}\)

The next example shows how similar triangles are used with maps.

Example \(\PageIndex{9}\)

On a map, San Francisco, Las Vegas, and Los Angeles form a triangle whose sides are shown in the figure below. If the actual distance from Los Angeles to Las Vegas is 270 miles find the distance from Los Angeles to San Francisco.

The above image shows two similar triangles and how they are used with maps. The smaller triangle on the left shows San Francisco, Las Vegas and Los Angeles on the three points. San Francisco to Los Angeles is 1.3 inches. Los Angeles to Las Vegas is 1 inch. Las Vegas to San Francisco is 2.1 inches. The second larger triangle shows the same points. The distance from San Francisco to Los Angeles is x. The distance from Los Angeles to Las Vegas is 270 miles. The distance from Las Vegas to San Francisco is not noted.

Try It \(\PageIndex{17}\)

On the map, Seattle, Portland, and Boise form a triangle whose sides are shown in the figure below. If the actual distance from Seattle to Boise is 400 miles, find the distance from Seattle to Portland.

The above image is a triangle with one side labeled “Seattle, 4.5 inches”. The other side is labeled “Portland 3.5 inches”. The third side is labeled 1.5 inches. The vertex is labeled “Boise.”

Try It \(\PageIndex{18}\)

Using the map above, find the distance from Portland to Boise.

We can use similar figures to find heights that we cannot directly measure.

Example \(\PageIndex{10}\)

Tyler is 6 feet tall. Late one afternoon, his shadow was 8 feet long. At the same time, the shadow of a tree was 24 feet long. Find the height of the tree.

Try It \(\PageIndex{19}\)

A telephone pole casts a shadow that is 50 feet long. Nearby, an 8 foot tall traffic sign casts a shadow that is 10 feet long. How tall is the telephone pole?

Try It \(\PageIndex{20}\)

A pine tree casts a shadow of 80 feet next to a 30-foot tall building which casts a 40 feet shadow. How tall is the pine tree?

Key Concepts

  • Read the problem and make sure all the words and ideas are understood. Draw the figure and label it with the given information.

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Step by Step tutorial on How to Solve Ratios In Mathematics

When we have to compare two or more than two numbers in mathematics then we can use ratios for the same as ratios can compare two or more quantitative numbers or amount or you can compare the portions of numbers of the larger numbers. Ratio is one of the tools of data analysts. This is why many people face difficulty in solving ratios so they are always in search of methods on how to solve ratios. If you are also stuck with solving ratios then this article will help you to understand the concept of ratios and methods on how to solve ratios.

Assignment help

Concept of ratio

Before learning the steps on how to solve ratios one must be well versed with ratios. As you can’t mug up mathematics you have to understand the concepts then only you can solve ratios. 

First thing to learn is that ratios are used only in academics but also by data analysts for analysing the data in the form of comparison. Generally we think ratio compares only two numbers rather you can compare more than two numbers such as 3 or 4 through ratios. 

Second thing to learn on how to solve ratios is that ratio basically states the relation of two or more numbers with each other. 

Thirdly the sign of ratio is “:”. So if you want to tell someone that you got 75 marks in maths and your friend got 50 marks in maths then you can write it in the form of ratio as 75:50 that is 3:2.

Likewise you can write sex ratio of your class like 15 males and 10 females then you can write it as 15:10 that is 3:2.  And we read the ratio as “isto”. So you will read it as 3 isto 2. 

You can also write it in division form like 3/2. 

Thus there are 3 ways to write ratios. 

Steps – How to solve Ratios 

The first step on how to solve the ratio is to write the values you want to compare and you can write such values in any given form like using colon or through division sign or by writing isto. Let’s understand the steps through an example. Suppose you want to take out the ratio of your maths and physics marks. You have got 90 marks in maths and 70 marks in physics. So firstly I will write it in the form of a ratio. 

90 isto 70 or 90:70 or 90/70.

Second step on how to solve the problem is to reduce the values into their simplest way. So for that you can take out the common factors from the numbers. And then we can divide both of the numbers from such a common factor so that we can get the numbers in their simplest form. For example we have a number 90 : 70 then after writing it in the format of ratios now you have to bring out the common factors between the terms of ratios. So in this example we have 10 as a common factor. Thus you will divide both the numbers 90 and 70 by 10 so that you get the numbers in their simplest form so you will get 90/10:70/10 = 9:7.

Thus the ratio is 9:7.

Let’s take another example of three digits and three digits are 75 marks in biology, 25 marks in physics and 100 marks in maths. So let’s first write it in the form of ratio that is 

75 : 25 : 100

Now we need to follow the next step of how to solve ratios. That is to find out the common factor from all the numbers thus we can clearly see that 25 is the common factor so you will have to divide each number with 25. 

75/25 : 25/25 : 100/25 

= 3 : 1 : 4

Thus the answer is 3:1:4.

The important point to learn in ratio is that it does not change with the multiplication or division of same numbers. It will remain the same. For example if you multiply the above number with 2 then they will become 75 x 2 : 25 x 2 : 100 x 2 = 150 : 50 : 200. Now also the ratio is same if you convert it to the smallest form then like first you have to divide it by 50 then you will find get the same ratio that is 3:1:2. 

You can also find the value of variables if two ratios are equal. Let’s take an example to understand it better. Suppose you have one ratio 3:2 and other ratio 5:x and these two ratios are equal and now you are required to find the value of x song the equation will be 

3 / 4 = 3/X

3 x X = 3 x 2 

Ratios are the mathematical expressions used to compare two or more numbers having common factors. We also use ratios one daily basis. Although ratio is a simple mathematical concept still many people ask how to solve ratios . So we have written this article in the simplest language and steps wise with examples to solve ratios. Get the best help for math homework from the leading experts.

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How to Find Molar Ratio: Examples and Practice

  • The Albert Team
  • Last Updated On: February 12, 2024

How to find molar ratio: examples and practice problems

Chemistry isn’t just about mixing colorful liquids in beakers and waiting for an explosion—it’s a world of ratios, reactions, and relationships. At the heart of understanding this fascinating world lies the concept of the molar ratio, a key player in predicting the outcomes of chemical reactions. But what exactly is a molar ratio, and why is it so important? Simply put, it quantifies the proportions of reactants and products in a chemical equation, and accounts for every atom according to the law of conservation of mass. Remember learning about balanced equations? It’s time to put that knowledge into action. In this blog post, we’ll dive deep into the world of molar ratios, from what they are to how to find them using balanced equations. Whether you’re a budding chemist or just curious about the science behind the reactions, you’re in the right place to uncover the secrets of how to find the molar ratio.

What We Review

What is Molar Ratio?

Imagine you’re following a recipe to bake a cake. You wouldn’t just throw in random amounts of flour, sugar, and eggs, right? Just like in baking, chemistry requires precise measurements to get the desired outcome. This is where the concept of the molar ratio comes into play, acting as the “recipe” for chemical reactions.

In order to determine how much reactant must be used in an equation or how much product will be produced, molar ratio calculations are used. They are all based on the balanced equation.

A molar ratio is the proportion of moles of one substance to the moles of another substance in a chemical reaction. The coefficients of the substances in a balanced chemical equation show the molar ratio relationship. For example, in the reaction to produce water ( 2H_2 + O_2 \rightarrow 2H_2O ), the molar ratio of H_2 to O_2 is 2:1. This means that two moles of hydrogen gas react with one mole of oxygen gas to produce water.

So, why is this important? Chemists predict how much of each reactant they need to produce a certain amount of product without any waste by using molar ratio. It ensures that every atom of the reactants has a place in the products, adhering to the law of conservation of mass, which states that matter cannot be created or destroyed in a chemical reaction.

Understanding molar ratios is crucial for anyone looking to delve into the world of chemistry, whether it’s synthesizing a new compound in a research lab or figuring out the right amount of baking soda to add to your volcano science project. By mastering this concept, you’ll unlock the ability to navigate through chemical equations with ease, paving the way for exciting experiments and discoveries.

Chemical plants and other factories use balanced equations and molar ratios to determine reactant amounts to create a certain amount of product.

How to Find Molar Ratio

In order to truly grasp the concept of molar ratio, let’s dive into some example problems that highlight how to use this tool in real chemical equations. Curious about how to find the molar ratio? These examples will show you step-by-step how to calculate molar ratios and apply them to predict the amounts of reactants and products in a chemical reaction.

Example 1: Combustion of Propane

The combustion of propane ( C_3H_8 ) in oxygen ( O_2 ) is a common reaction that produces carbon dioxide ( CO_2 ) and water ( H_2O ). The balanced chemical equation for this reaction is:

Question: What is the molar ratio of O_2 to CO_2 in the combustion of propane?

Solution: To find molar ratio, look at the coefficients in your balanced equation. By looking at the balanced equation, we can see that 5 moles of O_2 produce 3 moles of CO_2 . Therefore, the molar ratio of O_2 to CO_2 is 5:3.

Example 2: Formation of Ammonia

The Haber process combines nitrogen ( N_2 ) and hydrogen ( H_2 ) gas to form ammonia ( NH_3 ), a crucial component in fertilizers. The balanced equation for this reaction is:

Question: If you start with 4 moles of N_2 how many moles of H_2 are needed to react completely based on the molar ratio?

Solution: From the balanced equation, the molar ratio of N_2 to H_2 is 1:3. This means for every mole of N_2 , they require 3 moles of H_2 to react. For 4 moles of N_2 , we need:

Therefore, 12 moles of H_2 completely react with 4 moles of N_2 .

Practice Problems: Finding and Applying Molar Ratio

Now that you’ve seen how to find molar ratio and how to use them through example problems, it’s your turn to try solving some on your own. These practice problems will test your understanding of molar ratios and how to apply them to different chemical reactions. Work through these on your own, then scroll down for solutions.

Problem 1: Synthesis of Water

When hydrogen gas ( H_2 ) reacts with oxygen gas ( O_2 ) water ( H_2O ) forms. The balanced equation for this reaction is: 

If you have 6 moles of H_2 , how many moles of O_2 are needed to react completely, and how many moles of H_2O will be produced?

Problem 2: Decomposition of Potassium Chlorate

Potassium chlorate ( KClO_3 ) decomposes upon heating to produce potassium chloride ( KCl ). The balanced equation for this reaction is:

How many moles of O_2 can be produced from the decomposition of 4 moles of KClO_3 ?

Problem 3: Combustion of Ethanol

Ethanol ( C_2H_5OH ) combusts in oxygen to produce carbon dioxide and water. The balanced chemical equation is:

If 2 moles of C_2H_5OH are combusted, how many moles of O_2 are required, and what amounts of CO_2 and H_2O are produced?

Problem 4: Production of Ammonium Nitrate

Ammonium nitrate ( NH_4NH_3 )is produced by the reaction of ammonia ( NH_4 ) with nitric acid ( HNO_3 ). The balanced chemical equation for this reaction is:

If a fertilizer company needs 5 moles of ammonium nitrate, how many moles of ammonia and nitric acid are required to achieve this?

Problem 5: Synthesis of Magnesium Oxide

Magnesium ( Mg ) reacts with oxygen ( O_2 ) to form magnesium oxide ( MgO ). The balanced equation for this reaction is:

During a lab experiment, a student reacts 6 moles of magnesium with excess oxygen. How many moles of magnesium oxide does the reaction produce, and how many moles of oxygen are consumed in the reaction?

Tips for Solving:

  • Start by identifying the molar ratios between the reactants and products from the balanced chemical equations.
  • Use the molar ratios to calculate the amounts of reactants or products as needed.
  • Remember to check your work and ensure that the law of conservation of mass is satisfied in your calculations.

Molar Ratio Practice Problem Solutions

Are you ready to see how you did? Review below to see the solutions for the molar ratio practice problems.

Remember, to find molar ratio, use the coefficients in the balanced equation. The molar ratio of H_2 to O_2 is 2:1, meaning 2 moles of H_2 react with 1 mole of O_2 . You will use this ratio to determine how many moles of O_2 are needed to react completely.

The molar ratio of H_2 to H_2O is 2:2, which can be simplified to 1:1. Therefore, if 6 moles of H_2 reacts, it produces 6 moles of H_2O .

The molar ratio of KClO_3 to O_2 is 2:3. Hence, 2 moles of KClO_3 react with 3 moles of O_2 . You will use this to determine how many moles of O_2 will be produced.

This question has three different parts. The first is determining how many moles of O_2 are needed to react completely with 2 moles of C_2H_5OH . Initially, you must find the molar ratio. The ratio of O_2 to  C_2H_5OH is 3:1.

The second part asks how much CO_2 is produced from 2 moles of C_2H_5OH . The ratio of CO_2 to C_2H_5OH is 2:1.

The third part asks how much H_2O the reaction produces from 2 moles of C_2H_5OH . The ratio of H_2O to  C_2H_5OH is 3:1.

If a fertilizer company needs to produce 5 moles of ammonium nitrate, how many moles of ammonia and nitric acid are required to achieve this?

This is a two-part problem, but solved the same way. This is because the balanced equation has a molar ratio of 1:1 for all reactants and products in the equation. Therefore, however many moles you put into the reaction, produces the same amount of moles as products. Therefore, if we want to produce 5 moles of NH_4NH_3 , we would need to put in 5 moles of NH_3 and 5 moles of HNO_3 .

During a lab experiment, a student reacts 6 moles of magnesium with excess oxygen. How many moles of magnesium oxide will be produced, and how many moles of oxygen are consumed in the reaction?

This is a two-part problem. The first part asks how many moles of Mg the reaction makes if 6 moles of Mg reacts. The molar ratio of MgO to Mg is 2:2, which can be simplified to 1:1. Therefore, if 6 moles of Mg reacts, 6 moles of MgO will be produced.

The second part of the problem asks how much excess O_2 the reaction uses if 6 moles of Mg reacted. The molar ratio of Mg to O_2 is 2:1. We use this to determine our answer.

Molar ratios aren't just something learned in chemistry class; they are used by companies across the world to make commercial products.

Embarking on the journey through the world of chemistry reveals the intricate dance of atoms and molecules, governed by fundamental principles such as the molar ratio. This concept, akin to the precise measurements in a recipe, ensures that chemical reactions proceed smoothly, with each reactant and product playing its part in the grand scheme of matter transformation.

Understanding molar ratios not only demystifies how substances react in specific proportions but also empowers us with the ability to predict the outcomes of these reactions. Whether it’s synthesizing a new compound in the lab, analyzing environmental samples, or simply marveling at the chemical reactions in everyday life, the knowledge of molar ratios serves as a crucial tool in the arsenal of any budding chemist.

In conclusion, we’ve explored how to find molar ratio and tackled practice problems to solidify our understanding. Remember, the beauty of chemistry lies not just in theoretical knowledge but in applying these concepts to solve real-world problems. So, I encourage you to continue exploring, questioning, and experimenting with the fascinating reactions that make up our world.

Chemistry continually challenges and inspires, and with tools like molar ratios, you can uncover the mysteries that lie in molecules and reactions. So, keep your curiosity alive, and let the molar ratio guide you as you journey through the incredible landscape of chemistry.

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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 ‍  

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  3. How to Solve Ratio Problems Easily: Try These Tricks!

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  4. 😱 Solve ratio problems. Proportions: Simple Exercises. 2019-02-03

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COMMENTS

  1. Ratio Problem Solving

    What is ratio problem solving? Ratio problem solving is a collection of ratio and proportion word problems that link together aspects of ratio and proportion into more real life questions. This requires you to be able to take key information from a question and use your knowledge of ratios (and other areas of the curriculum) to solve the problem.

  2. Ratios and proportions

    Solving word problems using proportions How do we write ratios? Two common types of ratios we'll see are part to part and part to whole. For example, when we make lemonade: The ratio of lemon juice to sugar is a part-to-part ratio. It compares the amount of two ingredients. The ratio of lemon juice to lemonade is a part-to-whole ratio.

  3. Ratio Problem Solving

    Ratio problem solving is a collection of word problems that link together aspects of ratio and proportion into more real life questions. This requires you to be able to take key information from a question and use your knowledge of ratios (and other areas of the curriculum) to solve the problem.

  4. Ratio Word Problems (video lessons, examples and solutions)

    Solution: Step 1: Assign variables: Let x = number of red sweets. Write the items in the ratio as a fraction. Step 2: Solve the equation. Cross Multiply 3 × 120 = 4 × x 360 = 4 x Isolate variable x Answer: There are 90 red sweets. Example 2: John has 30 marbles, 18 of which are red and 12 of which are blue.

  5. Ratios and rates

    What types of word problems can we solve with proportions? Intro to ratios Learn Intro to ratios Basic ratios

  6. Solving ratio problems with tables (video)

    Solving ratio problems with tables Google Classroom About Transcript Equivalent ratios have the same relationship between their numerators and denominators. To find missing values in tables, maintain the same ratio. Comparing fractions is easier with common numerators or denominators.

  7. Solving Ratio Problems

    Solving Ratio Problems We add the parts of the ratio to find the total number of parts. There are 2 + 3 = 5 parts in the ratio in total. To find the value of one part we divide the total amount by the total number of parts. 50 ÷ 5 = 10. We multiply the ratio by the value of each part. 2:3 multiplied by 10 gives us 20:30.

  8. Solving ratio problems

    Question Practise solving ratio problems Quiz Real-world maths Game - Divided Islands Key points Ratio problems take different forms, which may include: linking ratios and fractions...

  9. 6.5 Solve Proportions and their Applications

    Proportion A proportion is an equation of the form a b = c d, where b ≠ 0, d ≠ 0. The proportion states two ratios or rates are equal. The proportion is read "a is to b, as c is to d". The equation 1 2 = 4 8 is a proportion because the two fractions are equal. The proportion 1 2 = 4 8 is read "1 is to 2 as 4 is to 8".

  10. Ratio Calculator

    Ratio Solver A : B = C : D : = : Answer: Get a Widget for this Calculator © Calculator Soup Calculator Use The ratio calculator performs three types of operations and shows the steps to solve: Simplify ratios or create an equivalent ratio when one side of the ratio is empty.

  11. Ratio: Problem Solving Textbook Exercise

    The Corbettmaths Textbook Exercise on Ratio: Problem Solving. Previous: Ratio: Difference Between Textbook Exercise

  12. How to Calculate Ratios: 9 Steps (with Pictures)

    1 Be aware of how ratios are used. Ratios are used in both academic settings and in the real world to compare multiple amounts or quantities to each other. The simplest ratios compare only two values, but ratios comparing three or more values are also possible.

  13. Solving Ratio Problems Involving Totals

    To solve ratio problems involving totals, we take these steps: Name the unknowns using variables. Set up a ratio box with totals using the given information. Use the ratio box to set up a...

  14. Free worksheets for ratio word problems

    Find here an unlimited supply of worksheets with simple word problems involving ratios, meant for 6th-8th grade math. In level 1, the problems ask for a specific ratio (such as, "Noah drew 9 hearts, 6 stars, and 12 circles. What is the ratio of circles to hearts?"). In level 2, the problems are the same but the ratios are supposed to be simplified.

  15. Ratios

    We can use ratios to scale drawings up or down (by multiplying or dividing). The height to width ratio of the Indian Flag is 2:3. So for every 2 (inches, meters, whatever) of height. there should be 3 of width. If we made the flag 20 inches high, it should be 30 inches wide. If we made the flag 40 cm high, it should be 60 cm wide (which is ...

  16. Ratio Practice Questions

    Practice Questions. Previous: Percentages of an Amount (Non Calculator) Practice Questions. Next: Rotations Practice Questions. The Corbettmaths Practice Questions on Ratio.

  17. Part to whole ratio word problem using tables

    4 years ago Hi Annet. You need to find the sum to be able to find the ratio. Example: The ratio of girls to boys in a school is (5:6). If there are 33 students, how many boys are there and girls are there? 1. 5 + 6 = 11 2. 6/11 = boy part of the school/total students 3. 11 x ? = 33, so 6 x ? = ? boys 4. 11 x 3 = 33, so 6 x 3 = ? 5. 6 x 3 = 18

  18. Ratio and Proportion Word Problems

    Ratio and Proportion Word Problems - Math The Organic Chemistry Tutor 7.42M subscribers Subscribe Subscribed 24K 1.8M views 4 years ago GED Math Playlist This math video tutorial provides a basic...

  19. 8.7: Solve Proportion and Similar Figure Applications

    Try It 8.7.8 8.7. 8. 2x + 15 9 = 7x + 3 15 2 x + 15 9 = 7 x + 3 15. Answer. To solve applications with proportions, we will follow our usual strategy for solving applications. But when we set up the proportion, we must make sure to have the units correct—the units in the numerators must match and the units in the denominators must match.

  20. Step by Step tutorial on How to Solve Ratios In Mathematics

    75/25 : 25/25 : 100/25. = 3 : 1 : 4. Thus the answer is 3:1:4. The important point to learn in ratio is that it does not change with the multiplication or division of same numbers. It will remain the same. For example if you multiply the above number with 2 then they will become 75 x 2 : 25 x 2 : 100 x 2 = 150 : 50 : 200.

  21. Ratio Word Problems Calculator

    Free Ratio Word Problems Calculator - Solves a ratio word problem using a given ratio of 2 items in proportion to a whole number. This calculator has 1 input. What 3 formulas are used for the Ratio Word Problems Calculator? a:b ratio means a + b = c total options Expected Number of A = a * n/c Expected Number of B = b * n/c

  22. How to Find Molar Ratio: Examples and Practice

    Review below to see the solutions for the molar ratio practice problems. Problem 1: Synthesis of Water. When hydrogen gas ... Remember, the beauty of chemistry lies not just in theoretical knowledge but in applying these concepts to solve real-world problems. So, I encourage you to continue exploring, questioning, and experimenting with the ...

  23. Proportion word problems (practice)

    Proportion word problem: hot dogs. Proportion word problems. Math > 7th grade > Proportional relationships > Writing & solving proportions ... Lesson 5: Writing & solving proportions. Worked example: Solving proportions. Solving proportions. Writing proportions example. Writing proportions.