Ratio

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4 : 6 (multiply original ratio by by 2)

6 : 9 (multiply original ratio by by 3)

8 : 12 (multiply original ratio by by 4)

The ratio 2 : 3 can be expressed as

2x to 3x (multiply the original ratio by any number x)

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Compound Ratios

A ratio that compares more than 2 quantities is called a compound ratio.

Example:

A cake recipe says the ratio of cups of milk, sugar, and batter are 1:2:4.

This means that there is one cup of milk for every two cups of sugar and four cups of batter.

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A bag contains 18 yellow, blue, and red marbles. The ratio of yellow to blue to red marbles is 4 : 2 : 3.

Write the ratio of yellow to blue marbles in simplest form.

What is the ratio of yellow to red marbles?

How many yellow marbles are there?

4 : 2 can be simplified to 2 : 1

4 : 3

Yellow : Blue : Red is 4 : 2 : 3

Since any multiple of this is an equivalent ratio, this can also be written as 4x : 2x: 3x

Let 4x = yellow, 2x = blue , 3x = red

4x + 2x+ 3x = 18

9x = 18

X= 2

Since the question asks for yellow marbles,

there are 4x or 4 (2) = 8 yellow marbles.

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Practice problem

# 1

(1) You have 100 different shirts. The ratio of blue to black shirts is 20 .

30

a) Write the ratio of blue to black shirts 3 different ways.

b) Write the ratio in simplest form.

c) Explain what this ratio tells us.

d) How many black shirts do you have?

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Solution - # 1 

You have 100 different shirts. The ratio of blue to black shirts is 20 / 30

a) Write the ratio of blue to black shirts 3 different ways.

20 to 30 , 20 : 30, 20

30

b) Write the ratio in simplest form. 2

3

c) Explain what this ratio tells us. For every two blue shirts, there are 3 black shirts.

d) How many black shirts do you have?

2x + 3x = 100

5x = 100

x = 20

There are 2x black shirts so 2 (20) = 40 black shirts

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Practice Word Problems

You go to a party where the ratio of boys to girls is 28 to 56. Express the ratio of boys to girls in simplest form.

Explain what this ratio tells us.

28 / 56 = 1 / 2

The ratio of boys to girls is 1 to 2

(2) For every 1 boy there are 2 girls at the party.

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Practice Word Problems

Mindy has 72 candy bars. If the ratio of Mars to Snickers is 8:4, Find the number of each type of candy.