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# Writing Proportions

To write a proportion, you need to identify two equivalent ratios and set them equal to each other.

• Writing Proportions
• Solved Examples
• FAQs

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## Writing Proportions

To write a proportion, you need to identify two equivalent ratios and set them equal to each other.

#### Here are the steps to write a proportion:

Identify two equivalent ratios: Look at the problem and identify two ratios that are equal to each other.

For example, if you are given the problem “John can run 5 miles in 45 minutes. How long will it take him to run 8 miles?”, you can identify the ratio of miles to time as 5/45 and the ratio of miles to time for the 8-mile run as 8/x.

Set the ratios equal to each other: Once you have identified the two equivalent ratios, set them equal to each other. This gives you the proportion:

5/45 = 8/x

Simplify the proportion: To simplify the proportion, you can cross-multiply and then solve for the unknown variable x. In this case, you would multiply 5 by x to get 5x and 45 by 8 to get 360. This gives you:

5x = 360

x = 72

So, it would take John 72 minutes to run 8 miles.

Here’s another example:

Suppose you are given the problem “If 5 gallons of gas cost \$16.25, how much will 7 gallons cost?” To write a proportion, you can identify the ratio of gallons to cost as 5/\$16.25 and the ratio of gallons to cost for the 7-gallon purchase as 7/x. Setting these ratios equal to each other gives you the proportion:

5/\$16.25 = 7/x

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

5x = \$113.75

x = \$22.75

So, 7 gallons of gas would cost \$22.75.

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## Solved Examples

Sure, here are some solved examples of proportions:

Example 1: If it takes 3 hours for 5 people to paint a house, how long will it take 8 people to paint the same house?

Solution: Let’s write a proportion to solve the problem. We know that the number of people painting the house is directly proportional to the time taken to paint it. So, we have:

3 hours / 5 people = x hours / 8 people

Now, let’s cross-multiply and solve for x:

3 hours * 8 people = 5 people * x hours

24 hours = 5x

x = 4.8 hours

Therefore, it would take 8 people 4.8 hours to paint the same house.

Example 2: A recipe calls for 2 cups of flour for every 3 cups of sugar. How many cups of flour are needed if you use 5 cups of sugar?

Solution: We can write a proportion to solve this problem as follows:

2 cups flour / 3 cups sugar = x cups flour / 5 cups sugar

Cross-multiplying and solving for x, we get:

2 cups flour * 5 cups sugar = 3 cups sugar * x cups flour

10 cups flour = 3 cups sugar * x cups flour

x = 10 / 3

So, we need 3 1/3 cups of flour if we use 5 cups of sugar in the recipe.

Example 3: If a recipe calls for 1 tablespoon of salt for every 4 cups of flour, how many tablespoons of salt are needed if you use 8 cups of flour?

Solution: We can write a proportion to solve this problem as follows:

1 tablespoon salt / 4 cups flour = x tablespoons salt / 8 cups flour

Cross-multiplying and solving for x, we get:

1 tablespoon salt * 8 cups flour = 4 cups flour * x tablespoons salt

8 tablespoons salt = 4x

x = 2

So, we need 2 tablespoons of salt if we use 8 cups of flour in the recipe.

## Formula

The general formula for writing a proportion is:

a/b = c/d

where a, b, c, and d are numbers or variables.

To solve a proportion for an unknown variable, you can cross-multiply and simplify to get:

a * d = b * c

and then solve for the unknown variable.

## Writing Proportions FAQS

##### What is a proportion in math?

A proportion is a statement that two ratios are equal. It is used to compare two quantities or values and express their relationship in a fraction form.

##### How do you know if two ratios are in proportion?

Two ratios are in proportion if their cross-products are equal. For example, if a/b = c/d, then a * d = b * c, which means the ratios are in proportion.

##### What are some real-life examples of proportions?

Proportions can be found in many real-life situations, such as cooking recipes, mixing solutions, calculating proportions of ingredients, and determining the scale of maps or models.

##### How do you use proportions to solve problems?

To use proportions to solve problems, you need to set up a proportion with the given values and the unknown value, and then solve for the unknown by cross-multiplying and simplifying the equation.

##### What is the difference between a direct proportion and an inverse proportion?

In a direct proportion, two quantities increase or decrease together at the same rate, while in an inverse proportion, one quantity increases as the other decreases, and vice versa. For example, the distance traveled by a car is directly proportional to the time elapsed, while the speed of the car is inversely proportional to the time elapsed.

Gloria Mathew writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn

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