7.1 - Ratios and Proportions

7.1 - Ratios and Proportions

By Steve Dull

Objective

To write ratios and solve proportions

​What would Barbie look like if she were life-sized?

How'd they get those numbers?

The producers calculated a ratio

They wanted to find out the comparison of the height of the doll with the height of the average woman in the US.

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A ratio is a comparison of two quantities by division.​

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Ratios can be written three ways

You can express the ratio of the numbers a and b (b ≠​ 0) as:

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Ratios can be simplified.​

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Let's practice:

Write each ratio in simplest form:

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Open Ended

What is the ratio of "people wearing Jordans" to "students" in class right now?

Extended Ratios

Compare three (or more numbers)

In the extended ratio a:b:c, the ratio of the first two numbers is a:b, the ratio of the second two numbers is b:c, and the ratio of the first and third numbers is a:c.

Multiple Choice

• $$40\degree,\ 70\degree,\ 90\degree$$  

• $$36\degree,\ 63\degree,\ 81\degree$$  

• $$30\degree,\ 60\degree,\ 90\degree$$  

• $$45\degree,\ 25\degree,\ 20\degree$$  

Proportions

A proportion is an equation that states two fractions are equal.

A proportion is written as:

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​In any proportion, the product of the means is equal to the product of the extremes. Often, people say "cross products are equal".

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Multiple Choice

Solve the proportion $$\frac{4}{x}=\frac{2}{7}$$  

• $$x=28$$  

• $$x=\frac{1}{2}$$  

• $$x=14$$  

• $$x=2$$  

Open Ended

Solve the proportion $$\frac{5}{17}=\frac{19}{x+4}$$  

The next slide will be your summary

Open Ended

Based on the results of your ratio earlier ("people wearing Jordans in class" to "students in class") write and solve a proportion to estimate how many Morton students are wearing Jordans today. (Morton enrollment is approximately 1800 students).