8.4 Ratios and Proportions

Ratios and Proportions

Review 7.3-1 Ratios & Proportions

Topics in this Review:

1. Ratios

2. Proportions

3. Ratio Tables

Ratios

A comparison of 2 or more values.

Can be written in 3 ways:

a/b a to b a:b

Should always be written in simplest form!

Ratio & Proportion Review (notes + practice)

WaTch the videos for extra help

You can skip through if you would like - but use it to help you!!!

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​Work through the problems & rewatch the videos as needed

​- you can repeat this lesson as many times as you would like

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​Important stuff here folks!

Ratio & Proportion Review (notes + practice)

• Writing & Simplifying Ratios

• ​Part-Part / Part Whole relationship

• ​Unit Rate

• Double Number Lines

• ​Tables

• ​Graphs

• ​solve proportions by scaling up (mult) or scaling down (div)

Writing & Simplifying Ratios

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Multiple Choice

SIMPLIFY the ratio of RED to WHITE SQUARES

• 12 : 8

• 6 : 4

• 3 : 2

• 2 : 3

​

​ 6 red : 4 white

​

​simplify by dividing by 2​

​= 3 red to 2 white

​ 3 : 2

Ratio Reminders

• Don't forget to reduce your fractions!

• We will typically use fractions when discussing ratios and proportions.

• Double check to make sure you're in the same unit measure!!!

Multiple Choice

A bag has red & blue marbles inside. 4 marbles are red out of 12 total marbles.

Write & SIMPLIFY the ratio of red marbles to blue marbles

• 1 : 2

• 1 : 3

• 3 : 1

• 2 : 1

​A bag has red & blue marbles inside. 4 marbles are red out of 12 total marbles.

Write & SIMPLIFY the ratio of red marbles to blue marbles

​

4 red

​+ 8 blue

​= 12 total

​

​red : blue

​ 4 : 8

​Simplify by dividing by 4

​= 1 : 2

​​Part-Part / Part Whole relationship

Draw

There are 20 children in class. 11 are boys and 9 are girls.

draw a line to match the ratios correctly

Proportions

• A proportion is an equation with a ratio on each side.

• It is a statement that two ratios are equal. 

  
  

• 3/4 = 6/8 is an example of a proportion.

Proportions

Two ratios that are equal are proportional

To check if two ratios are proportional: cross multiply!

Multiple Choice

Solve for x.

$$\frac{2}{5}=\frac{x}{65}$$  

• x = 16

• x =  $$\frac{1}{26}$$  

• x = 28

• x = 26

Multiple Choice

Solve the proportion:

$$\frac{2}{7}=\frac{c}{28}$$  

• 4

• 14

• 8

• 10

Multiple Choice

Solve for the variable k.

$$\frac{k}{6}=\frac{15}{18}$$  

• k = 5

• k = 60

• k =  $$\frac{10}{3}$$  

• k = 90

Multiple Choice

Solve the proportion:

$$\frac{8}{x}=\frac{12}{30}$$  

• x = 15

• x =  $$\frac{1}{11}$$  

• x = 11

• x = 20

Multiply the cross products to determine if the ratios are equal.

Another example:

For the following slides, use the cross products method and determine if the ratios are equal or not.

Multiple Choice

$$\frac{4}{7}=\frac{2}{4}$$  

• True

• False

Multiple Choice

$$\frac{2}{3}=\frac{4}{6}$$  

• True

• False

Multiple Choice

$$\frac{4}{8}=\frac{3}{6}$$  

• True

• False

Multiple Choice

What number would make this a true statement?

• 1

• 3

• 9

• 8

Multiple Choice

$$\frac{4}{5}=\frac{8}{x}$$  

• x = 8

• x = 10

• x = 4

• x = 5

Multiple Choice

$$\frac{x}{5}=\frac{8}{10}$$  

• x=7

• x=4

• x=2

• x=3

Multiple Choice

$$\frac{25}{1}=\frac{x}{3}$$  

• x=75

• x=50

• x=27

• x=43

Multiple Choice

• x = 16

• x = 28

• x = 1/26

• x = 26

Multiple Choice

• x = 6

• x = 25

• x = 28

• x = 17

Multiple Choice

What is a proportion?

• When two ratios can be simplified

• When two ratios are equivalent and show the same value

• When two ratios have the exact same numbers

• When two ratios can be multiplied by 2

Multiple Choice

Do the ratios form a proportion?

• Yes, they form a proportion.

• No, they do not form a proportion.

Proportions

• When two or more ratios are equivalent

• "Proportional" means that both ratios should reduce to the same fraction

Solving Proportions

• Notice that once you are done, the ratios reduce to the same fraction and the cross-products are equal (18=18)

Multiple Choice

Solve the proportion then check your answer by looking at their cross-products

• c = 4

• c = 8

• c = 14

• c = 10

Multiple Choice

Try another: Solve for x

• x = 16

• x = 28

• x = 135

• x = 26

Proportions

Other problems can be a bit more difficult to think about so we can use proportions to solve them. Review the picture before moving onto the next slide