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# Proportions Worksheet, Examples, and Definition

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

How to Solve Proportions in 3 EASY steps (Avoid these Common Mistakes)

• Proportions are used to compare quantities and are an important concept in mathematics.
• A proportion is a statement that two ratios are equal to each other.
• Proportions can be used in various fields, including science, cooking, and finance.

## 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.

Proportions are an important concept in mathematics that are used to compare quantities. In simple terms, a proportion is a statement that two ratios are equal. Ratios compare two quantities by division, while proportions compare two ratios. They are used in a variety of fields, including science, cooking, and finance, to name a few.

The definition of a proportion is two ratios that are equal to each other. This can be written using the colon symbol, which is read as “is to” or “per.” For example, if a recipe calls for a ratio of 2 cups of flour to 3 cups of sugar, this can be written as 2:3. If another recipe calls for the same ratio, it can be written as 4:6, which is equivalent to 2:3. In other words, these two ratios are proportional to each other.

Common Core Standard: 6.RP.2
Related Topics: Equivalent Ratios, Ratio Tables, Unit Rates, Converting Percents to Decimals, Converting Decimals to Percents

## The Best Proportions Definition

Proportions are a fundamental concept in mathematics that relates to the relative sizes of different parts of a whole. In simple terms, a proportion is a statement that two ratios or rates are equal. A ratio is a comparison of two quantities, while a rate is a comparison of two unlike denominate numbers.

For example, if a recipe calls for 2 cups of flour and 1 cup of sugar, the ratio of flour to sugar is 2:1. This ratio can be expressed as a proportion by comparing it to another ratio, such as the ratio of flour to water in the same recipe. If the ratio of flour to water is 2:1, then the proportion of flour to sugar is also 2:1.

Proportions can be used to solve a wide variety of problems, from simple arithmetic calculations to complex real-world scenarios. They can be used to calculate distances, weights, volumes, and more. Proportions are also used in many areas of science, such as chemistry, physics, and biology.

Proportions are closely related to the concept of fractions, which are also used to express ratios and rates. However, proportions are distinct from fractions in that they compare two ratios or rates, rather than simply expressing a single ratio or rate as a fraction.

In summary, proportions are a mathematical concept that relates to the relative sizes of different parts of a whole. They are used to compare two ratios or rates and can be used to solve a wide variety of problems. You can try Proportion Practice Problems by downloading the free Proportions Worksheet on this page. Proportions are closely related to fractions but are distinct in that they compare two ratios or rates, rather than simply expressing a single ratio or rate as a fraction.

## What are Proportions in Math?

Proportions are an important concept in mathematics that are used to compare two ratios. A proportion is an equation that states that two ratios are equal. This means that if two ratios are in proportion, then they have the same relationship to each other. For example, if one ratio is 2:3, and another ratio is 4:6, then the two ratios are in proportion because they are both equivalent to the ratio 2:3.

### Relationship to Ratios

Proportions are closely related to ratios. A ratio is a comparison of two quantities, and can be expressed in several different forms, including as a fraction, a decimal, or a percent. For example, the ratio of boys to girls in a class might be 2:3, or it might be expressed as a fraction, 2/3, or as a decimal, 0.67.

To solve a proportion, you can use the means-extremes property. This property states that the product of the means of two equivalent ratios is equal to the product of the extremes. For example, if you have the proportion 2/3 = x/12, you can cross-multiply to get 2 * 12 = 3 * x, which simplifies to 24 = 3x. Dividing both sides by 3 gives x = 8, so the equivalent ratio is 8/12.

Another way to solve a proportion is to use equivalent ratios. Equivalent ratios have the same relationship to each other as the original ratio, but with different numbers. For example, if you have the ratio 4:6, you can find an equivalent ratio by multiplying both the numerator and denominator by the same number. Multiplying by 2 gives the equivalent ratio 8:12, which is still in proportion to the original ratio.

In summary, proportions are used to compare two equivalent ratios, and can be solved using equivalent ratios. Understanding proportions is needed to complete our Proportions Worksheet an important concept in mathematics, and is used in many areas of algebra and geometry.

## How to Solve Proportions in 3 Simple Steps

Proportions are mathematical expressions that relate two or more ratios. The process of solving proportions involves finding the unknown value that makes two ratios equal. This section will explain how to solve proportions step-by-step.

To solve a proportion, you need to follow these steps:

1. Identify the two ratios in the proportion: The proportion consists of two ratios that are equal to each other. For example, if the proportion is `a/b = c/d`, then `a/b` and `c/d` are the two ratios.
2. Cross-multiply the ratios: Multiply the numerator of the first ratio (a) by the denominator of the second ratio (d), and multiply the denominator of the first ratio (b) by the numerator of the second ratio (c). This will give you two products: `ad` and `bc`.
3. Solve for the unknown value: If one of the values in the proportion is unknown, you can solve for it by dividing both sides of the equation by the other value. For example, if the proportion is `2/3 = x/9`, you can solve for x by cross-multiplying to get `2*9 = 3*x`, which simplifies to `18 = 3x`. Dividing both sides by 3 gives you the solution: `x = 6`.

It is important to note that proportions can be solved using different methods, such as using equivalent fractions or finding the unit rate. However, the cross-multiplication method is the most commonly used and easiest to understand.

Solving proportions involves identifying the two ratios, cross-multiplying the ratios, and solving for the unknown value. By following these steps, you can easily solve any proportion and find the unknown value of any practice problem on our Proportions Worksheet.

## 5 Exciting Proportions Practice Problems

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Proportions Quiz

Click Start to begin the practice quiz!

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Find the value of x.

2 / 5

Find the value of x.

3 / 5

Find the value of x.

4 / 5

Find the value of x.

5 / 5

Find the value of x.

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## 3 Simple Solving Proportions Examples

Solving proportions is an essential skill in mathematics. It involves finding an unknown value in a ratio or proportion. Here are some examples that illustrate how to solve proportions:

### Example 1: Finding the Unknown Value in a Proportion

Suppose you have a proportion that says 3/5 = x/20. To find the value of x, you can cross-multiply the two fractions as follows:

``````3/5 = x/20
3 * 20 = 5 * x
60 = 5x
x = 12
``````

Therefore, the value of x is 12.

### Example 2: Scaling Up or Down a Proportion

Suppose you have a recipe that calls for 2 cups of flour and 3 cups of sugar to make a cake. If you want to make twice the amount of cake, you need to scale up the proportions accordingly. To do this, you can multiply both the numerator and denominator of each fraction by the same number. In this case, you need to multiply by 2 as follows:

``````2/3 = (2 * 2)/(3 * 2) = 4/6
``````

Therefore, to make twice the amount of cake, you need 4 cups of flour and 6 cups of sugar.

### Example 3: Using Proportions to Solve Word Problems

Suppose you need to find the length of a shadow cast by a 10-foot pole on a sunny day. If you know that a 6-foot person casts a 4-foot shadow, you can set up a proportion as follows:

``````6/4 = 10/x
``````

To solve for x, you can cross-multiply and simplify as follows:

``````6x = 40
x = 6.67
``````

Therefore, the length of the shadow cast by the 10-foot pole is 6.67 feet.

These examples demonstrate how to solve proportions in different contexts. By mastering this skill, you can apply it to a wide range of mathematical problems.

## How to do Proportions and Ratios

To solve a proportion, one can use cross-multiplication. This means multiplying the numerator of one ratio by the denominator of the other ratio and setting them equal to each other. For example, to solve the proportion 2/3 = x/6, one can cross-multiply to get 2*6 = 3x, which simplifies to 12 = 3x. Dividing both sides by 3 gives x = 4. Therefore, 2/3 is proportional to 4/6.

When working with ratios, it’s important to keep the order of the terms consistent. For example, the ratio of apples to oranges is not the same as the ratio of oranges to apples. Similarly, when setting up a proportion, make sure to match the corresponding terms in the same order.

One useful technique for solving ratio problems is to use a table. This can help organize the information and make it easier to see the relationship between the different quantities. For example, if a recipe calls for 2 cups of flour for every 3 cups of sugar, and you want to make half the recipe, you can use a table to find out how much of each ingredient you need:

IngredientRatioAmount
Flour2:31 cup
Sugar3:21.5 cups

To find out how much flour and sugar you need for half the recipe, you can simply divide each amount by 2. Therefore, you need 0.5 cups of flour and 0.75 cups of sugar.

It’s also important to understand the concept of equivalent ratios. Two ratios are equivalent if they have the same value. For example, 2/3 is equivalent to 4/6, since both ratios simplify to 0.6667. To find equivalent ratios, one can multiply or divide both terms of the ratio by the same number. For example, to find a ratio equivalent to 4/5 with a denominator of 20, one can multiply both terms by 4 to get 16/20.

## Solving Proportions FAQ

### What is the difference between a ratio and a proportion?

A ratio is a comparison of two or more quantities of the same type. It can be expressed as a fraction, a decimal, or a percentage. On the other hand, a proportion is a statement that two ratios are equal. In other words, a proportion is an equation that shows that two ratios are equivalent.

### What is the simple definition of proportion?

A proportion is a statement that two ratios are equal. It is a way of comparing two quantities that have different units of measure. For example, if a recipe calls for 2 cups of flour and 1 cup of sugar, the proportion of flour to sugar is 2:1.

### What is an example of a proportion?

An example of a proportion is the recipe for chocolate chip cookies. If the recipe calls for 2 cups of flour, 1 cup of sugar, and 1 cup of chocolate chips, the proportion of flour to sugar to chocolate chips is 2:1:1. This means that for every 2 cups of flour, there is 1 cup of sugar and 1 cup of chocolate chips. See more examples by downloading our Proportions Worksheet.

### How do you solve proportions with fractions?

To solve proportions with fractions, you can use cross-multiplication. This involves multiplying the numerator of one ratio by the denominator of the other ratio, and vice versa. For example, to solve the proportion 2/3 = x/9, you can cross-multiply to get 2 x 9 = 3 x, which simplifies to 18 = 3x. Solving for x, you get x = 6.

### What are some real-world applications of proportions?

Proportions are used in many real-world situations, such as cooking, baking, and mixing chemicals. They are also used in construction to calculate the size and dimensions of buildings, and in finance to calculate interest rates and loan payments. Proportions are also used in medicine to calculate the dosage of medications, and in science to calculate the concentration of solutions.

## Proportions Worksheet Video Explanation

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 proportions 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.