Ratio and proportions worksheets: Proportions Worksheets — free & printable

Ratio Worksheets

Advertisement

Are you looking for the best ratio worksheets on the internet? Look no further — we have the perfect set of free ratio worksheets for you. Our ratio worksheets give students the opportunity to practice and reinforce their understanding of how to use ratios in real-world situations. Our worksheet includes examples, visual diagrams, and practice problems that will help your students gain a better understanding of how to properly work with ratios. With our ratio worksheets, you can be sure that your students are learning the concepts they need to succeed. So don’t hesitate and try our free ratio worksheets today!

Browse Sheets By Problem Type

Wordvisualnumericshort sentencehorizontaltablesgraphing

Grid View (new)

×
Finding Ratios
Link

Finding Ratios Visual

6rp1

Each worksheet has 11 problems finding the ratio of shapes.

One Atta Time

Flash Cards

Distance Learning

Create New Sheet

Select a Worksheet >

Version 1

Version 2

Version 3

Version 4

Version 5

Version 6

Version 7

Version 8

Version 9

Version 10

Grab ’em All

Create New Sheet

Ratio Wording

6rp1

Each worksheet has 15 problems interpreting the ratio described.

One Atta Time

Flash Cards

Distance Learning

Create New Sheet

Select a Worksheet >

Version 1

Version 2

Version 3

Version 4

Version 5

Version 6

Version 7

Version 8

Version 9

Version 10

Grab ’em All

Create New Sheet

Rate Language

6rp2

Each worksheet has 15 problems using and finding rate terminology.

One Atta Time

Flash Cards

Distance Learning

Create New Sheet

Select a Worksheet >

Version 1

Version 2

Version 3

Version 4

Version 5

Version 6

Version 7

Version 8

Version 9

Version 10

Grab ’em All

Create New Sheet

Reducing Ratios

6rp3c

Each worksheet has 20 problems reducing a ratio to its lowest form.

One Atta Time

Flash Cards

Distance Learning

Create New Sheet

Select a Worksheet >

Version 1

Version 2

Version 3

Version 4

Version 5

Version 6

Version 7

Version 8

Version 9

Version 10

Grab ’em All

Create New Sheet

Understanding Ratios (Word)

6rp3c

Each worksheet has 10 word problems finding the ratio, other half of a ratio or total number in a ratio.

One Atta Time

Flash Cards

Distance Learning

Create New Sheet

Customize

Select a Worksheet >

Version 1

Version 2

Version 3

Version 4

Version 5

Version 6

Version 7

Version 8

Version 9

Version 10

Grab ’em All

Create New Sheet

Ratios Double Line

6rp3b

Each worksheet has 8 problems using a double line graph to answer ratio questions.

One Atta Time

Flash Cards

Distance Learning

Create New Sheet

Select a Worksheet >

Version 1

Version 2

Version 3

Version 4

Version 5

Version 6

Version 7

Version 8

Version 9

Version 10

Grab ’em All

Create New Sheet

Writing Equations from Ratios

6rp3d

Each worksheet has 15 problems expressing a measurement ratio as an equation.

One Atta Time

Flash Cards

Distance Learning

Create New Sheet

Select a Worksheet >

Version 1

Version 2

Version 3

Version 4

Version 5

Version 6

Version 7

Version 8

Version 9

Version 10

Grab ’em All

Create New Sheet

Using Ratio Equations

6rp3d

Each worksheet has 12 problems using an equation to find an equivalent measurement.

One Atta Time

Flash Cards

Distance Learning

Create New Sheet

Select a Worksheet >

Version 1

Version 2

Version 3

Version 4

Version 5

Version 6

Version 7

Version 8

Version 9

Version 10

Grab ’em All

Create New Sheet

Creating Equivalent Ratios

7rp2a

Each worksheet has 20 problems filling in the blank to generate an equivalent ratio.

One Atta Time

Flash Cards

Distance Learning

Create New Sheet

Select a Worksheet >

Version 1

Version 2

Version 3

Version 4

Version 5

Version 6

Version 7

Version 8

Version 9

Version 10

Grab ’em All

Create New Sheet

Determining Proportionality with Tables

7rp2a

Each worksheet has 12 problems determining if the values in a table are proportional.

One Atta Time

Flash Cards

Distance Learning

Create New Sheet

Select a Worksheet >

Version 1

Version 2

Version 3

Version 4

Version 5

Version 6

Version 7

Version 8

Version 9

Version 10

Grab ’em All

Create New Sheet

Creating Examples for Ratios

6rp1

Each worksheet has 10 problems writing an example of a ratio.

One Atta Time

Flash Cards

Distance Learning

Create New Sheet

Select a Worksheet >

Version 1

Version 2

Version 3

Version 4

Version 5

Version 6

Version 7

Version 8

Version 9

Version 10

Grab ’em All

Create New Sheet

Identifying True and False Ratio Statements

6rp1

Each worksheet has 6 problems

One Atta Time

Flash Cards

Distance Learning

Create New Sheet

Select a Worksheet >

Version 1

Version 2

Version 3

Version 4

Version 5

Version 6

Version 7

Version 8

Version 9

Version 10

Grab ’em All

Create New Sheet

Advertisement


Finding Rate
Link

Using Unit Prices

6rp3b

Each worksheet has 10 problems using unit rate to find the answer.

One Atta Time

Flash Cards

Distance Learning

Create New Sheet

Select a Worksheet >

Version 1

Version 2

Version 3

Version 4

Version 5

Version 6

Version 7

Version 8

Version 9

Version 10

Grab ’em All

Create New Sheet

Ratios and Unit Rates

6rp3b

Each worksheet has 15 problems find the ratio and unit rate of a scenario.

One Atta Time

Flash Cards

Distance Learning

Create New Sheet

Select a Worksheet >

Version 1

Version 2

Version 3

Version 4

Version 5

Version 6

Version 7

Version 8

Version 9

Version 10

Grab ’em All

Create New Sheet

Finding Equivalent Unit Fraction with Fractions

7rp1

Each worksheet has 14 problems finding an equivalent unit fraction using fractions.

One Atta Time

Flash Cards

Distance Learning

Create New Sheet

Select a Worksheet >

Version 1

Version 2

Version 3

Version 4

Version 5

Version 6

Version 7

Version 8

Version 9

Version 10

Grab ’em All

Create New Sheet

Using Unit Rates with Fractions

7rp1

Each worksheet has 10 problems finding the unit rate with fractions.

One Atta Time

Flash Cards

Distance Learning

Create New Sheet

Select a Worksheet >

Version 1

Version 2

Version 3

Version 4

Version 5

Version 6

Version 7

Version 8

Version 9

Version 10

Grab ’em All

Create New Sheet

Understanding Unit Rate

7rp1

Each worksheet has 12 problems determining the solution to a problem with unit rates.

One Atta Time

Flash Cards

Distance Learning

Create New Sheet

Select a Worksheet >

Version 1

Version 2

Version 3

Version 4

Version 5

Version 6

Version 7

Version 8

Version 9

Version 10

Grab ’em All

Create New Sheet

Constant of Proportionality (tables)

7rp2b

Each worksheet has 8 problems using a table to identify the constant of proportionality.

One Atta Time

Flash Cards

Distance Learning

Create New Sheet

Select a Worksheet >

Version 1

Version 2

Version 3

Version 4

Version 5

Version 6

Version 7

Version 8

Version 9

Version 10

Grab ’em All

Create New Sheet

Constant of Proportionality (Graphs)

7rp2b

Each worksheet has 8 problems using a graph to identify the constant of proportionality.

One Atta Time

Flash Cards

Distance Learning

Create New Sheet

Select a Worksheet >

Version 1

Version 2

Version 3

Version 4

Version 5

Version 6

Version 7

Version 8

Version 9

Version 10

Grab ’em All

Create New Sheet

Examining Y=KX

7rp2b

Each worksheet has 10 problems using the formula Y=KX to solve a word problem.

One Atta Time

Flash Cards

Distance Learning

Create New Sheet

Select a Worksheet >

Version 1

Version 2

Version 3

Version 4

Version 5

Version 6

Version 7

Version 8

Version 9

Version 10

Grab ’em All

Create New Sheet

Explaining X and Y with Proportionality

7rp2d

Each worksheet has 6 problems determining the significance of x and y in relation to proportionality.

One Atta Time

Flash Cards

Distance Learning

Create New Sheet

Select a Worksheet >

Version 1

Version 2

Version 3

Version 4

Version 5

Version 6

Version 7

Version 8

Version 9

Version 10

Grab ’em All

Create New Sheet

Creating Tables and Graphs of Ratios

6rp3a

Each worksheet has 4 problems creating a table and graph from a scenario.

One Atta Time

Flash Cards

Distance Learning

Create New Sheet

Select a Worksheet >

Version 1

Version 2

Version 3

Version 4

Version 5

Version 6

Version 7

Version 8

Version 9

Version 10

Grab ’em All

Create New Sheet

Advertisement

Ratio and Proportions Worksheets

Ratios and Proportions Worksheets

These are two concepts that people often confuse for one another, even adults in business workplaces. A ratio is just a fraction that indicates how much of a whole value we have. A proportion is an equation that describes the relationship of two ratios. We will explore this more in this series of worksheets that will give students practical hands-on experience with these aspects. We created two clear and distinct types of worksheets that you will see labelled below.

Ratios Worksheets

• Fruit Stand Ratios — This is a fun one with real world skills. We provide a very well thought out scenario where proportions come into play and are vital for making a living. Not to mention that you get to count fruit.
• Creating Ratios (Ordered) — We work with guided shapes. Create a ratio that clear spreads out each form of data.
• Creating Ratios (Non- Ordered) — Students have to do a bit of organizing here. The items in the ratios are spread out and student must first order them before deciding on a proper ratio.
• Sentence Based Ratios — A step towards the more moderate. All the problems are very straight forward and should make for a solid introduction to this unit or topic.
• Finish Off the Ratios — Make your own equivalent ratios. 4 sheets in all. Complete the series of equivalent proportions three times per question. 4 versions and 8 pages in all.
• Ratio Word Problems — Very simple straight forward problems. We offer up some fair questions for students. It should help build their confidence for the tougher problems that follow.
• Ratio Sentences and Lacrosse — Many teachers rave about this one. The kids started taking up Lacrosse. It is gaining huge popularity in all of North America. So we made a few problems about it. Just wait for our Justin Bieber problems, just kidding!
• Write the Ratio of the Story — Truly reading within the content (math) area on this one. We mix words with numbers in this one to make sure that students read the problems carefully.
• Write the Ratio of the Story 2 — Same format new story from above. This one is much more straight forward than the past version.
• Three Way Ratios — We work on different forms of notation. We have you restate ratios in a various notations and formats.
• Sales, Stars, and Liquid Ratio Word Problems — Students like the scenarios in this one. Each problem is very realistic and can help steer students towards the answer by just following the given data.
• Compare the Ratios — Less than, greater than, or equal. Hopefully students will breeze through this one. Our hint is to reduce them to their lowest form and then go from there.
• Story Based Ratio Problems — A nice set that mimics national learning standards. A very simpole walk into the world of ratios in everyday life. Great for new comers to ratios.
• Writing Ratios Worksheet — Very introductory based. Two sentence ratios that need to be visualized.
• Reducing Ratios — As simple as it gets in this skill set. Find a common denominator and go for it! This should be a quick one for you.

Proportions Worksheets

• Make a Proportion — A deep thinking activity. This is a really neat one. We ask students to find two equivalent proportions from a group of random numbers.
• Shopping with Proportions — This one really hits home with kids for some reason. This introduces students to the concept of unit price which really is just a proportion. WOW! Proportions can save you money, who would have thought!
• Proportion Word Problems (Simple) — Everyday problems all people are faced with regularly. We start thinking about unit price and how it affects us when we buy extra products.
• Proportion Word Problems (Hard) — These can be difficult for anyone. These problems are difficult for even adults at first. They can be tricky. Take your time.
• Are the Ratios Proportional? — Find an equal proportion or create one. We make students apply higher levels of thinking with this one. They may need to create their on proportions.
• Solving for the Missing Proportions — Solve for x over 4 versions here. There are 4 versions of this in the download. That should provide students with a great deal of practice to help improve their skills.
• Horizontal Proportions — We change the typical format to work on the skill more. I just realized that the author on this one must have had crazy eights infiltrate his/her head. See if you get what I mean.
• Using Proportions to Solve Word Problems — These can be a bit wordy like national exams. This is the first time that we add unneeded data to see if students can sift through the data to find the main and critical data.
• Solving Proportions with Decimals — Who would have thought introducing a dot makes it that much harder? Decimals definitely help step up the level of difficulty here.

How Do We Use Ratios and Proportions?

Ratio and proportions are two mathematical principles that are often used interchangeably. However, there is a slight difference between the two terms.

It might be tough to envision how you might use math concepts in everyday life. Ratios, which make up logical relationships between different elements, are excellent illustrations of math in action. Groceries, cooking, and traveling about are typical, real-life circumstances in which ratios and proportions are used frequently and necessary for accurate, cost-effective execution.

Here we’ll mention what ratios and proportions are, all the while highlighting their differences. We’ll also shed some light on the uses of ratios and proportions in real life.

What are Ratios and Proportions?

A ratio expresses the relationship of 2 variables using the mathematical operation: division. Meanwhile, a proportion is the equivalency of two ratios.

Ratios can be expressed in several ways, for instance, a : b or a/b and is usually written as a is to b

A proportion, on the contrary, is a mathematical expression that states that 2 ratios are comparable. A proportion is expressed in this format: a: b : : c : d, and is written as a is to b as c is to d. And it can be expressed like this as well: a/b = c/d where c and d are ≠ 0.

Many people think they are one and the same. The fact is they are very different.

A ratio is just a fraction like 3/4. It can come many forms such as 3 out of 4 equal parts or 3:4, but fundamentally it is a fraction.

A proportion,on the other hand, is an equation that relates 2 ratios. Such as:

3		6
__	=	__
4		8

Real-Life Uses of This Math

Ratios and proportions are used in everyday life in a variety of ways. They help in recognizing patterns and making informed decisions.

1. Cooking Recipes

Ratios are used in cooking. The proportions of various ingredients in recipes are critical to creating the most delectable dishes. For instance, to make the delicious Alfredo sauce, you should mix 1 cup of milk with 1/2 a cup of cream, one teaspoon of chopped garlic, 1/4 a cup of shredded cheese, and salt and pepper to taste. The quantity of these ingredients can be explained through this math as well.

2. Grocery Shopping

The grocery store is a space bursting with the use of ratios in real life. You can easily compare the price of two different products using this type of math. For instance, if a 5-ounce bag of chips costs $4 and a 10-ounce bag of chips costs $5. Each ounce of chips is significantly cheaper, so the 10-ounce bag is the better bargain. You may show the link between quantity and size by dividing the total number of ounces of chips in a bag by the price.

3. Earnings Per Day

They are particularly helpful for those who get paid daily. For instance, if a worker earns $600 a day. It means he’ll earn $1200 in two days and $2400 in four days. The pattern and link seen between the number of days and the sum of cash generated are easily discernible. The amount of money received increases as the duration increases. This validates the use of proportions in everyday life.

4. Road Trips

Another instance where ratios can be used is when traveling to a distant location. For example, in case you are going on a road trip from Los Angeles to San Deigo, you would need to travel up to 120 miles. If you are traveling by car and driving at a speed of 60 miles per hour, keeping in mind the speed and distance ratio, it may take up to 2 hours to reach San Diego.

Business Uses

Businesses employ different ratios to analyze their company’s performance. Some of them include the debt-to-equity ratio, current assets ratio, dividend payout ratio, and more. Here we’ll mention how businesses use them for their benefit.

1. Financial Statements Review

Interpreting financial accounts is critical for firm stakeholders. This form of math aid in comprehending the comparability of this data. Moreover, it aids in forecasting future figures from balance sheets and income statements.

2. Forecasting

As per the perspectives of managers and investors, this type of data can aid in understanding and estimating the firm’s future profitability and operations. Ratios derived from historical financial analysis aid in predicting future finances and budgets.

3. Decision Making

Ratios give critical information about a company’s current performance and resource use. It assists the firm in forecasting and planning ahead, setting new goals, and focusing on other markets.

4. More Effective Communication

This type of data is vital for reporting the firm’s financial results to its stakeholders. Ratios make large and complex numbers easier to grasp. More often than not, figures may be deceiving, causing investors to lose faith, but ratios help investors recognize the firm’s position after comparison, allowing them to continue investing in the business.

5. Trend Line

They can provide the trend line that tells whether or not a firm can perform over time. Businesses obtain data from previous financial periods to create trend lines that may be used to analyze and assess the company’s outcomes and any potential issues that cannot be discovered through a one-year ratio study.

6. Company Performance

Ratios are useful in determining a firm’s ability to create profit. Return on Equity and Return on Asset ratios indicate how much money the business can produce over its investments, whereas net profit and operating profit ratios indicate the firm’s potential to create a revenue through sales and operational efficiency.

To Sum Up

Ratios and proportions are a fundamental part of mathematics. However, understanding how they work is not only beneficial when an individual is solving math equations. They can aid in many other activities and tasks, be it every day or business.

Problems on proportions in mathematics — examples with answers

Let’s help you understand and fall in love with mathematics

Start learning

Proportions 90-60-90 have not been in trend for a long time. But what is always eternal is mathematical proportions in algebra lessons. Let’s practice and solve problems together.

Give your child the best summer

Free children’s online camp with valuable prizes at the end of the shift

The concept of proportion

To solve problems on the topic of proportion, let’s recall the main definition.

A proportion in mathematics is an equality between the ratios of two or more pairs of numbers or quantities.

Main property of proportion: The product of the extreme terms is equal to the product of the middle terms. a : b = c : d, where a, b, c, d are the terms of the proportion, a, d are the extreme terms, b, c are the middle terms.

Derivation from the main property of the proportion:

• The extreme term is equal to the product of the averages, which are divided by the other extreme. That is, for the proportion a/b = c/d:
• The middle term is equal to the product of the extremes, which are divided by another middle one. That is, for the proportion a/b = c/d:

To solve a proportion means to find an unknown term. The proportion property is the main assistant in the solution.

Remember!

The equality of two ratios is called proportion.

Let’s look at easy and difficult problems that can be solved using proportion. 5th, 6th, 7th, 8th grade — it doesn’t matter, it’s useful for all schoolchildren to analyze entertaining puzzles.

Home Lyceum for 5-11 grades

Classes where and when convenient, 10+ circles to choose from, no stress with homework and tedious parent meetings

Problems on proportions with solutions and answers

Proportion properties were invented for a reason! With their help, you can find any of the terms of the proportion, if it is unknown. Let’s solve 10 proportion problems.

Task 1. Find the unknown term of the proportion: x/2 = 3/1

How to solve:

In this example, the extreme term is unknown, so we multiply the middle terms and divide the result by the known extreme term:

x = (2 * 3)/1 = 6

Answer: x = 6.

Task 2. Find the unknown term: 1/3 = 5/y

How to solve:

y = (3 * 5)/ 1 = 15

Answer: y = 15.

Problem 3. Solve the proportion: 30/x = 5/8

How to solve:

x = (30 * 8)/5 = 48

Answer: x = 48.

Task 4. Solve: 7/5 = y/10

9001 4 How do we decide:

y = (7 * 10)/5 = 14

Answer: y = 14.

Task 5. It is known that 21x = 14y. Find the ratio x — to y

How we solve:

• First, we reduce both sides of the equality by a common factor 7: 21x/7 = 14y/7.

  We get: 3x = 2y.

• Now let’s divide both sides by 3y to remove the factor 3 on the left side and get rid of y on the right side: 3x/3y = 2y/3y.
• After reducing the ratio, it turned out: x/y = 2/3.

Answer: 2 to 3.

In the following example, we will learn how to make a proportion for the task 💡

Task 6. Out of 300 Instagram followers, 108 people liked the post. What percentage of all subscribers are those who liked the post and liked it?

How we solve:

• Let’s take all subscribers as 100% and write down the condition of the problem briefly:

  300 — 100%

  108 — ?%

• Let’s make a proportion: 300/108 = 100/x.
• Find x: (108 * 100) : 300 = 36.

Answer: 36% of all subscribers liked the post.

Task 7. Harry Potter’s girlfriend used seaweed and leeches in a ratio of 5 to 2 when brewing the Polyjuice Potion. How much seaweed do you need if there are only 450 grams of leeches?

How we solve:

• Let’s make a proportion: 5/2 = x/450.
• Find x: (5 * 450) : 2 = 1125.

Answer: for 450 grams of leeches, you need to take 1125 grams of algae.

Task 8. It is known that watermelon consists of 98% water. How much water is in 5 kg of watermelon?

How we decide:

The weight of the watermelon (5 kg) is 100%. Water — 98% or x kg.

Let’s make a proportion:

5 : 100 = x : 98

x \u003d (5 * 98): 100

x \u003d 4.9

Answer: 5 kg of watermelon contains 4.9 kg of water.

Let’s move on to more complicated examples. Let’s consider the proportion problem from the 8th grade algebra textbook.

Task 9. Dad’s car travels from one city to another in 13 hours at a speed of 75 km/h. How long will it take him if he travels at a speed of 52 km/h?

As we argue:

Speed ​​and time are inversely related: the greater the speed, the less time is required.

Denote:

• v1 = 75 km/h
• v2 = 52 km/h
• t1 = 13h
• t2 = x

How we solve:

1. Let’s make a proportion: v1/v2 = t2/t1.

   The ratios are equal but inverted relative to each other.

2. Substitute known values: 75/52 = t2/13

   t2 = (75 * 13)/52 = 75/4 = 18 3/4 = 18 h 45 min

Answer: 18 hours 45 minutes.

Task 10. 24 people promoted a Telegram channel in 5 days. In how many days will 30 people do the same job if they work with the same efficiency?

As we argue:

1. In the completed column, put the arrow in the direction from the largest number to the smallest.

2. The more people, the less time it takes to do a certain job (channel promotion). So this is an inverse relationship.

3. So let’s point the second arrow in the opposite direction. The inverse proportion looks like this:

How we solve:

1. Let 30 people can promote the channel in x days. We make a proportion:

   30 : 24 = 5 : x

2. To find the unknown term of the proportion, you need to divide the product of the middle terms by the known extreme term:

   x = 24 * 5: 30

   x = 4

3. So, 30 people will promote the channel in 4 days.

Answer: 4 days.

Online preparation for the OGE in mathematics is a great way to relieve stress and consolidate knowledge before the exam.

Free math cheat sheets

All math formulas at your fingertips in one PDF file. It is convenient to watch from the phone

Lidia Kazantseva

Author Skysmart

To the previous article

Properties of addition and subtraction 9Find the gaps in knowledge and give advice on learning

how are the classes

Let’s choose a course

What is a proportion in mathematics?

We will help you understand and love mathematics

Start learning

Mathematics teaches us the equality of relationships. Proportions are a simple but important topic. Let’s figure out what proportion is and how to deal with it.

Give your child the best summer

Free children’s online camp with valuable prizes at the end of the shift

What is proportion

Definition of proportion:

Proportion is the equality of two ratios.

Proportional is one that is in a certain relation to any value.

Proportion always contains equal factors.

If we express the definition as a formula, it will look like this:

• a : b = c : d

Or like this:

a and d are the extreme terms of the proportion, b and c are the middle terms of the proportion.

This expression is read like this: a is related to b as c is related to d

For example:

15 : 5 = 3

9 : 3 = 3

This is the equality of two ratios: 15 is related to 5 as 9 is related to 3.

15 and 3 are the extreme members of the proportion .

5 and 9 are the middle members of the proportion.

A good example to understand:

We have eight slices of delicious pizza and, let’s say, four hungry friends.

• Let’s write this difficult situation as the ratio of 8 pieces to 4 hungry friends: 8 : 4
• Next, convert this ratio to a fraction: 8/4
• Perform division: 8/4 = 2

This means that 8 delicious pizza slices will treat 4 hungry friends in such a way that each starving person will get 2 slices. Wonderful!

And now let’s imagine a situation in which there is only half of an appetizing pizza, but at the same time there are only two hungry friends.

What we have: 4 pieces and 2 friends claiming them.

• Write as a ratio: 4 : 2
• Convert the resulting ratio to a fraction: 4/2
• Perform division: 4/2 = 2

This means that 4 appetizing pieces will treat 2 hungry friends in such a way that each of them will get 2 pieces.

Having evaluated both situations, we conclude that the ratio 8/4 is proportional to the ratio 4/2. The proportions are equal.

Conclusion: knowledge of mathematical proportions is useful when ordering pizza. We quickly estimate the ratio of the number of people claiming pizza and the number of slices — and immediately order more pizza so that no one is left hungry😉

Home Lyceum for grades 5-11

Classes whenever and wherever convenient, 10+ circles to choose from, no stress with homework and boring parent-teacher meetings

Main property of proportion

Remember the main property of proportion:

The product of the extreme terms of the proportion is equal to the product of the middle terms of this proportion.

As a formula, the property looks like this:

a : b = c : d
a * d = b * c

We know that a and d are the extreme members of the proportion, b and c are the middle ones.

This property should be used to check the aspect ratio. If everything converges according to the wording, the proportion is correct, and the ratios in the proportion are equal to each other.

Let’s check some proportions.

Example 1. Given a proportion: 6/2 = 12/4

• 0048
• Next, we multiply the average terms of the proportion: 2 * 12 = 24
• The product of the extreme terms of the proportion is 24, the product of the middle terms of the proportion is also 24.
• 6 * 4 = 2 * 12
  24 = 24

We conclude that the proportion 6/2 = 12/4 is correct.

Example 2. Given the proportion: 10/2 = 16/4

• Multiply the extreme members of the proportion: 10 * 4 = 40.
• Multiply the middle terms: 16 * 2 = 32.
• The product of the extreme terms of the proportion is 40. The product of the middle terms of the proportion is 32.
• 10 * 4 ≠ 16 * 2
  40 ≠ 32

From this we conclude that ratios in the proportion 10/2 ≠ 16/4 are not equal.

Skysmart math preparation courses for the OGE will give you self-confidence and help you refresh your knowledge before the exam.

Choose your ideal math tutor

15,000+ verified tutors with an average rating of 4.8. We will take into account your schedule and learning goal

Examples of solving problems with proportions

To practice drawing proportions, let’s solve several problems together.

Problem 1. Given a mathematical proportion: 15/3 = x/4

Find x.

How do we decide:

1. According to the main property of the proportion, we multiply the factors:
   15 * 4 = 3x
2. We get the equation: 60 = 3x
3. 60/3 = x
   x = 20.

Answer: in proportion 15/3 = x/4, x = 20

Problem 2. Find the fourth term of the proportion: 18, 9 and 24.

How to solve:

1. Write the numbers as fractions: 18/9 = 24/x
   Where x is the fourth member of the proportion.
2. According to the basic property of proportion, we multiply the middle terms: 9 * 24 = 216
3. Derive the equation 18x = 216
4. Find x:
   x = 216 : 18
   x = 12
5. Checking: 9* 24 = 216, 18 * 12 = 216.
   The proportion is correct.

Answer: the fourth member of the proportion is 12.

Problem 3. 18 people can eat five kilograms of land in 8 hours, how many hours will 9 people need?

How do we decide:

1. We write the numbers as an inverse proportion: 18/9 = x/8
2. Multiplying factors by the basic property of proportion: 18 * 8 = 9x
3. Find x:
   144 = 9x
   144 : 9 = 16

Answer: It will take 9 people 16 hours to eat all the sushi.