Rates and Ratios. Ratios and Rates ratio – a comparison of two numbers by division written in several different forms.

Rates and Ratios

Ratios and Rates

ratio – a comparison of two numbers by division written in several different forms.

That

This

That

This

Ratios and Rates

rate – a ratio that compares different kinds of units by division to obtain a unit rate or rate per unit.

Ratios and RatesThe order of the numbers in a ratio should match the order of the words in a ratio.

apples to oranges

2 to 3

Ratios and RatesRatios can be written in several different ways.

3 to 1

3 : 1

3/1

red to black

Ratios and RatesRatios can show comparisons between:part to part

red to green

1 to 2

green to red

2 to 1

Ratios and RatesRatios can show comparisons between:part to whole

red to whole

1 to 3

green to whole

2 to 3

Ratios and RatesRatios can show comparisons between:whole to part

whole to red

3 to 1

whole to green

3 to 2

Ratios and RatesCompare octagon to all shapes

1 to 8

1 out of 8 1 : 8

1/8

Ratios and RatesCompare all shapes to trapezoid

8 to 1 8 : 1 8/1

Ratios and RatesCompare pentagons to hexagons

2 to 3 2 : 3 2/3

Ratios and RatesGive each ratio in three forms.

8 roses out of 24 flowers

8 to 24 8 : 24 24

8

3 dogs out of 12 animals

3 to 12 3 : 1212

3

Ratios and RatesA ratio in fraction form can be expressed in simplest form by dividing the numerator and denominator by a common factor.

24

8 ÷ 8

÷ 8=3

1

12

3 ÷ 3

÷ 3=4

1

Ratios and RatesTo express a ratio as a rate per unit, write the ratio as a fraction and then divide the numerator by the denominator.

395 miles in 5 hours

5

395=

79 miles per hour

miles

hours 1

? miles

hours

Ratios and RatesExpress each ratio as a rate.5 inches of rain in 30 days

30

5=6

1inch of rain per day

120 words in 3 minutes

3

120= 40 words

per minute1

? wordsper minute

÷ 5

÷ 5

Rates and Proportions Word Problems

ProportionA proportion is an equation that shows two

equivalent ratios.2:3 = 8:12

=

Fill in the tableThe ratio of boys to girls is 7 to 6:

7 614 ?

21 ?

28 ?

35 ?

42 ?

Fill in the table The ratio of pens to pencils are 12 to 7

12 736

48

72

84

96

What about word problems?

Using Cross Multiplication to Complete ProportionsIn the case that we need to find a missing

value in a proportion we will use cross multiplication.

StepsSet-upCross MultiplyDivide

Examples:1. For every 8 minutes you answer 7 questions.

How many questions could you answer in 32 minutes?

8 = 32 7 n

Solution: Use the cross product method 8n= 224 8n = 224 divide both side by 8

8 n = 28 therefore, 8 = 32

7 28

1You can run a distance of 2 blocks in 3

minutes. How many blocks can you run in 18 minutes?

2You can read 5 pages of a novel in 3 minutes.

How many pages of the novel can you read in60 minutes?

3It takes you 5 minutes to mow 7 square yards

of a lawn. How long would it take to mow 630square yards?

4A running faucet sends 14 gallons of water

down the drain every 3 minutes. How many gallons will go down the drain in 90 minutes?

5A clothes washer uses 170 gallons of water

for 4 loads. How many gallons would be used for 240 loads?

6A volunteer beach clean up crew collected 20

bags of trash in 3 hours. How many hours would it take them to collect 1,000 bags of trash?

7The average American uses about 145

pounds of paper every 3 months. How many pounds of paper are used in 24 months?