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Get the free Proportions Worksheet and other resources for teaching & understanding Proportions

## Here’s how to Solve Proportions

A Proportion is when two ratios are equal to each other. When solving Proportions you must know that their cross products will be equal. This means that when you multiply the numerator of the first ratio times the denominator of the second ratio, and do the same thing in reverse, you will get an equal statement. You can find the missing number in a proportion by determining the common multiplier that is used to go from one Proportion to the other.

Common Core Standard: 6.RP.2

## What are Proportions in Math?

Are you wondering how to do proportions? We have a simple guide to follow. When two ratios are identical to each other they are said to be proportions. In order to solve for proportions, you have to understand that their cross products will be equal. For example, when you multiply the numerator of one ratio by the denominator of the other ratio, and reverse the process, you will create a state that is equal. Determine the common multiplier to go from on proportion to the other in order to fill in any missing quantities.

## 3 Quick Steps for Solving Proportions

1. Determine the common multiplier by using division to go from one proportion to the other proportion.
2. Use the common multiplier to multiply the proportion to find the missing value.
3. Check your answer by multiplying the two proportions together to get a statement that is equal.

## How to Solve Proportions Practice Problems Quiz

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Proportions Quiz

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Find the value of x.

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Find the value of x.

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Find the value of x.

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Find the value of x.

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Find the value of x.

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## Watch the video explanation of our Proportions Worksheet

Watch our free video on how to solve Proportions. This video shows how to solve problems that are on our free Solving Proportions worksheet that you can get by submitting your email above.

Watch the free Proportions Worksheet video on YouTube here: How to Solve Proportions Video

Video Transcript:

This video is about how to solve proportions. You can get the ratios and proportions worksheet used in this video with a ton of ratio and proportion examples for free by clicking on the link in the description below.

The definition of proportions just says that a proportion is a statement of equality between two ratios. For example if you look at our example problem here we have 3 over 15 equals 9 over x. This ratio 3 over 15 is equal to the ratio of 9 over x. This is a proportion because it’s a statement of equality between two ratios with one ratio being 3 over 15 and the other ratio being 9 over x.

In this video we’re going to solve proportions by finding what’s called the common multiplier. The common multiplier is the multiplier that you can use to go from 1 ratio to the other ratio. This multiplier will work for both the numerator which is the top part of the fraction and the denominator. The common multiplier will work for going from the first ratio to the second ratio or from going from the second ratio back to the first ratio so it’s going to work in either direction. We’re going to complete this proportions example using the common multiplier method.

In order to find the common multiplier, we have to take either the numerator or the denominator in one of the ratios and divide it by the numerator or denominator in the other ratio. If your x is in your denominator that means you have to use the numerators to find the common multiplier, we’re going to take the largest number in the numerator in this case which is 9 and we’re going to divide it by the other numerator which is 3. In this case nine divided by three is three which means our common multiplier is going to be three. In order to go from the first ratio to the second ratio we’re going to multiply times three. Three times three is 9. In order to find x in the denominator we’re also going to multiply times 3. If the common multiplier of 3 works in the numerator it’s also going to work in the denominator. We’re going to take 15 and multiply 15 times 3. We’re going to do 15 times 3 15 times 3 is 45 and that means that x here has to be equal to 45. If the common multiplier of times 3 in the numerator works that means it’s also going to work in the denominator. If you can use 3 times 3 in the numerator to get 9 you can also do 15 times 3 in the denominator to get x and in this case, x is going to be equal to 45. That means that our solution to this proportion that means that our solution to x for this proportion is 45. Let’s do a couple practice problems on our proportion’s worksheet.

The first problem on our proportion worksheet gives us a statement of equality between two ratios. The first ratio is one third and it is equal to a ratio that is x divided by 12. Now we know we have to find the common multiplier to go from one ratio to the other. We can’t use the numerator because x is in the numerator so we have to use the denominator to determine the common multiplier. We’re going to take the larger number in the denominator which in this case is 12 and we’re going to divide it by the smaller number and the other denominator which is 3. 12 divided by 3 is 4 so we know that our common multiplier is going to be 4 because 3 times 4 equals 12. In order to determine x, we’re going to use the same common multiplier this time we’re going to say 1 times our common multiplier which is 4 is going to be equal to x. 1 times 4 is 4 which means that x has to be equal to four. I know that the solution to this proportion is x equals four because we can use the common multiplier to find it.

The second problem we’re going to do on our proportion worksheets is number three. This problem gives us the ratio of two over x is equal to ten over twenty-five. Now x this time is in the denominator which means that we’re going to use our numerators to determine what our common multiplier is. I’m going to take 10 which is the larger number and divide it by 2 which is the smaller number 10 divided by 2 is 5. I know that we can use 2 times 5 to get 10. Our common multiplier is 5. Now what’s different about this proportion is we are missing an x in the first ratio in order to find x we can’t do x times 5 to get 25 because we don’t know x you have to do it in the opposite direction. So we’re going to do 25 divided by 5 which is 5 to determine x. If you’re going to go from the first ratio to the second ratio you multiply times five but to go backwards to go from the second ratio back to the first ratio instead of doing times five you’re going to divide by five. 25 divided by 5 is 5. I know the solution to this proportion is going to be x equals 5 because we use our common multiplier to go from the second ratio back to the first ratio.

The last problem we’re going to complete on our solve proportions worksheet is number seven. This problem gives us the ratio of x over nine is equal to the ratio of 27 over 81 and is similar to solving proportions with decimals. Now we’re missing x which is in the numerator. In order to find our common multiplier we have to use the denominator that means we’re going to take 81, which is the larger number and divide it by 9 which is the smaller number 81 divided by 9 is 9. I know the common multiplier is going to be times 9 9 times 9 is 81. In order to find x we can’t do x times 9 to get 27 because we don’t know x. You have to go in the opposite direction. We’re going to do 27 divided by 9 which is our common multiplier so we divide by 9 and then 27 divided by 9 is 3. Now I know that x has to equal 3 because 3 times 9 equals 27 and we have to use 9 for the common multiplier. Hopefully this video was helpful for teaching how to solve proportions in math. You can try all the practice problems by downloading the free solving proportions worksheets above.