Ratios and Rate

Vocabulary• A ratio is a comparison of two quantities by

division.

Example 1:For lunch during the summer recreation

program, the Youth Center orders 8 pepperoni pizzas out of every 10 pizzas that they order. What is the ratio of pepperoni pizzas to the total number purchased?

pizzas total

pizzas pepperoni

5

4

10

8

Write a verbal model of what you are comparing.

Substitute in the values given for each quantity, and simplify the fraction.

Example 2:Last year, Andy’s hockey team had a record of 48

wins out of 64 games played. What was the ratio of wins to games played?

played total

wongames

4

3

64

48

Write a verbal model of what you are comparing.

Substitute in the values given for each quantity, and simplify the fraction.

Vocabulary• A rate is a special type of ratio comparing two

quantities with different kinds of units.– Traveling 180 miles on 9 gallons of gas– $8.00 for 2 pounds of roast beef– A verbal model can help us write rates.

• A unit rate is a rate that is simplified so that it has a denominator of 1 unit. – A unit rate compares a quantity to 1 unit of another

quantity.– The speed limit on I-86 is 65 miles per hour.– NYS minimum wage is currently $7.25 per hour

Example 3:On his trip to Pittsburgh, Alex drove 161

miles on 7 gallons of gas. What was his gas mileage on the trip in miles per gallon?

gallons

miles

gallons 7

miles 161

Write a verbal model of what you are comparing.

Substitute in the values given for each quantity.

gallon 1

miles 23

7 7

7 161

Since a unit rate has a

denominator of 1 unit, divide the numerator and denominator by 7.

Alex’s car got 23 miles per gallon on his trip.

Example 4:Lola is painting her room. If ½ gallon of

paint covers ⅙ of her walls, how much paint does she need for her entire room?

room

gallons

room 61

gallon 21

Write a verbal model of what you are comparing.

Substitute in the values given for each quantity.

Divide the numerator and denominator by ⅙ to find the unit rate.

Lola will need 3 gallons of paint for her room.

room 1

gallons 3

116

21

61

61

61

21

Example 5:During the holidays, Emily spends $12.50 for 2

pounds of fudge and $23.85 for 5 pounds of wrapped candy. Which item costs less per pound? By how much?

Sometimes, we are asked to compare unit rates…..

pound

costWrite a verbal model of what you are comparing.

pound 1

$6.25

2 2

2 $12.50

For the fudge,

pound 1

$4.77

5 5

5 $23.85

For the wrapped candy,

To find the difference in price, subtract.$6.25 – $4.77 = $1.48.

The wrapped candy costs less by $1.48 per pound.

Example 6:At Euclid Middle School, of the thirty girls

who tried out for the lacrosse team, 12 were selected and of the forty boys who tried out, 16 were selected. Are the ratios of number of students on the team to number of students trying out the same for both boys and girls? How do you know?

Write a verbal model of what you are comparing.

teamfor theout tried

teamfor the selected

For the girls, For the boys,

5

2

6 30

612

5

2

8 40

816

Yes, the ratios are the same. The value of each ratio is the same.