Rates and Ratios

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

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 Rates The 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 Rates Ratios can be written in several different ways. 3 to 1 3 : 1 3/1 red to black

Ratios and Rates Ratios can show comparisons between: part to part red to green 1 to 2 green to red 2 to 1

Ratios and Rates Ratios can show comparisons between: part to whole red to whole 1 to 3 green to whole 2 to 3

Ratios and Rates Ratios can show comparisons between: whole to part whole to red 3 to 1 whole to green 3 to 2

Ratios and Rates Compare octagon to all shapes 1 to 8 1 out of 8 1 : 8 1/8

Ratios and Rates Compare all shapes to trapezoid 8 to 18 : 1 8/18/1

Ratios and Rates Compare pentagons to hexagons 2 to 32 : 32 : 3 2/32/3

Ratios and Rates Give each ratio in three forms. 8 roses out of 24 flowers 8 to 248 : 24 3 dogs out of 12 animals 3 to 123 : 12

Ratios and Rates A ratio in fraction form can be expressed in simplest form by dividing the numerator and denominator by a common factor. ÷ 8 = ÷ 3 =

Ratios and Rates To 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 = 79 miles per hour miles hours miles hours

Ratios and Rates Express each ratio as a rate. 5 inches of rain in 30 days = inch of rain per day 120 words in 3 minutes = 40 words per minute words per minute ÷ 5

Proportion A proportion is an equation that shows two equivalent ratios. 2:3 = 8:12 =

Fill in the table The ratio of boys to girls is 7 to 6: 76 14? 21? 28? 35? 42?

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

What about word problems?

Using Cross Multiplication to Complete Proportions In the case that we need to find a missing value in a proportion we will use cross multiplication. Steps Set-up Cross Multiply Divide

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 =

1 You can run a distance of 2 blocks in 3 minutes. How many blocks can you run in 18 minutes?

2 You can read 5 pages of a novel in 3 minutes. How many pages of the novel can you read in 60 minutes?

3 It takes you 5 minutes to mow 7 square yards of a lawn. How long would it take to mow 630 square yards?

4 A running faucet sends 14 gallons of water down the drain every 3 minutes. How many gallons will go down the drain in 90 minutes?

5 A clothes washer uses 170 gallons of water for 4 loads. How many gallons would be used for 240 loads?

6 A 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?

7 The average American uses about 145 pounds of paper every 3 months. How many pounds of paper are used in 24 months?