Writing Proportions

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

Table of Contents:

• Writing Proportions
• Solved Examples
• FAQs

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.

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

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