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### Ratios

• A ratio is a comparison of two quantities by division. It can be written in three ways: a/b, a:b, and a to b.
• Equivalent ratios are ratios that name the same quantity and are the same as equivalent fractions.
• To write a ratio in simplest form, divide the numerator and denominator by their greatest common divisor.

## Write two different ratios equivalent to 3:9.

• [(3 ÷3)/(9 ÷3)] = [1/3] = 1:3
• [(3 ×2)/(9 ×2)] = [6/18]

## Write two different ratios equivalent to 4:8.

• [(4 ÷2)/(8 ÷2)] = [2/4]
• [(4 ÷4)/(8 ÷4)] = [1/2]

## Write two different ratios equivalent to 7:28.

• [(7 ÷7)/(28 ÷7)] = [1/4]
• [(1 ×2)/(4 ×2)] = [2/8]

## There are 5 red balls and 10 blue balls. Write the ratio of blue to red balls in simplest form.

• blue balls : red balls
10:5
• [(10 ÷5)/(5 ÷5)] = [2/1]

## There are 12 poodles and 30 golden retrievers. Write the ratio of poodles to golden retrievers in simplest form.

• poodles : golden retrievers
12:30
• [(12 ÷6)/(30 ÷6)] =
• [2/5]

## There are 15 white flowers, 30 yellow flowers, and 5 purple flowers. Write the ratio of yellow to purple to white flowers in simplest form.

• yellow : purple : white
30 : 5 : 15
• 30 ÷5 = 6
5 ÷5 = 1
15 ÷5 = 3

## You have 3 pencils, 4 pens, and 2 highlighters. Write the ratio of pens to highlighters and the ratio of pencils to pens in simplest form.

• pens : highlighters = 4 : 2 =
• [(4 ÷2)/(2 ÷2)] =
• [2/1] =
• 2 : 1

## A recipe needs 3 cups of flour for 12 cookies. How many cups of flour do you need to make 36 cookies?

• The recipe's ratio of flour to cookies is 3:12. The ratio of flour to cookies must remain the same, regardless of how many cookies you make
• So, flour:cookies for 12 cookies = flour:cookies for 36 cookies.
[(3 cups of flour)/(12 cookies)] = [(f cups of flour)/(36 cookies)]
• [3/12] = [f/36]
• You want to multiply the numerator and denominator of [3/12] by the same number, and you want to choose that number so you get 36 as the new denominator.
[(3 ×?)/(12 ×?)] = [f/36]
• That number is 3, because 12 ×3 = 36.
[(3 ×3)/(12 ×3)] = [f/36]
• [9/36] = [f/36]
• f = 9 cups of flour
• Or, if you have already learned cross multiplication, you may do that instead (both methods give the same answer):
12f = 3(36)
• 12f = 108

## A recipe needs 1 cup of sugar for 6 macaroons. How many cups of sugar do you need to make 24 macaroons?

• sugar : macaroons = sugar : macaroons
[(1 cup of sugar)/(6 macaroons)] = [(s cups of sugar)/(24 macaroons)]
• [1/6] = [s/24]
• [(1 ×4)/(6 ×4)] = [s/24]
• [4/24] = [s/24]
• s = 4 cups of sugar
• Or, use cross multiplication:
6s = 1(24)
• 6s = 24

## A recipe calls for 6 teaspoons of salt for 12 muffins. How many muffins could you make with 2 teaspoons of salt?

• salt : muffins = salt : muffins
[(6 teaspoons of salt)/(12 muffins)] = [(2 teaspoons of salt)/(m muffins)]
• [6/12] = [2/m]
• [(6 ÷3)/(12 ÷3)] = [2/m]
• [2/4] = [2/m]
• m = 4 muffins
• Or, use cross multiplication:
• 6m = 2(12)
• 6m = 24

### m = 4 muffins

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

## Ratios

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