Solving Proportions

Ratios & Proportions

Comparing Ratios and Solving Proportions

A ratio is simply a comparison between two numbers. We often write this as a fraction, but there are other ways.​

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​The image shows the three main ways to express a ratio.

​Ratios

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A proportion is a comparison between two ratios. Usually we put an equal sign between them.

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​Proportions

Multiple Choice

$$\frac{5}{8}$$  is an example of

• A Ratio

• A Proportion

• Neither

• Both

Uses For Proportions

In order to solve proportions, we will use cross multiplication which is something you have already seen.

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​Solving Proportions

​By cross multiplying, we get the question:

Does 1 * 10 = 2 * 5? If they are equal, than the fractions are equal.

In this ​case, 1 * 10 = 10, and 2 * 5 = 10. Therefore, the fractions are equal.

Multiple Choice

Is this proportion true:

$$\frac{6}{10}=\frac{2}{5}$$  

• Yes, they are equal

• No, they are not equal

• I cannot answer that question from the information given

Multiple Choice

Is this proportion true?

$$\frac{1}{6}=\frac{5}{30}$$  

• Yes, this is true

• No, this is not true

• I cannot answer the equation from the information given

We can still cross multiply to give us 8 * x = 4 * 6​ which gives us a nice, one step equation to solve

8x = 24 or x = 3.​

We can use a similar process to solve for one of the four numbers if they are missing.​

Solve For A Variable

Multiple Choice

Solve for X $$\frac{x}{8}=\frac{25}{40}$$  

• 5

• 12.8

• 200

• 480

Multiple Choice

Solve for X $$\frac{4}{7}=\frac{20}{x}$$  

• 35

• 11.43

• 140

• 80

Multiple Choice

Solve for X $$\frac{x+4}{10}=\frac{3}{5}$$  

Don't forget to distribute 5(x+4)

You will need to solve a two step equation this time

• 2

• 5.2

• 6

• 10

Multiple Choice

Solve for X $$\frac{x-2}{14}=\frac{4}{7}$$  

• 10

• 14

• 8.29

• 26.5

Multiple Choice

Word Problem

In the past two years, Chipotle has opened 232 stores. If the rate of growth remains constant, how many stores will the retailer open in the next 3 years?

Which proportion does not represent this situation?

Jot it down in your notebook

• $$\frac{2}{3}=\frac{232}{x}$$  

• $$\frac{3}{2}=\frac{x}{232}$$  

• $$\frac{2}{232}=\frac{3}{x}$$  

• $$\frac{2}{3}=\frac{x}{232}$$  

​See if you can figure out why that one didn't work.

Multiple Choice

Solve the proportion to see how many stores will be opening in the next 3 years.

$$\frac{2}{232}=\frac{3}{x}$$  

• 348

• 154.67

• 38.67

• 464

Begin working on your homework