Ratios and Proportions

Ratios and Rates

100

Write the ratio as a fraction in the simplest form. 25 to 45

5/9

200

Find the unit rate: 256 miles per 8 gallons

32 miles per gallon

300

Find the unit rate: $4.80 for 6 cans

80 cents for 1 can

400

Over the course of 5 years, the U.S. population changed from 302 million people to 314 million people. How much did it change in 1 year?

2,400,000 people per year or 2.4

500

It costs $68 for 16 square feet of flooring. What is the unit rate?

$4.25 per square foot.

Proportions

100

Tell whether the ratios form a proportion: 

3/4 and 16/24

No, they do not form a proportion.

200

Tell whether the two rates form a proportion: 7 inches in 9 hours; 42 inches in 54 hours.

Yes, the two rates form a proportion.

300

Tell whether the ratios form a proportion: 2 to 4; 11 to 14

No, the ratios do not form a proportion.

400

You can do 90 sit-ups in 2 minutes. Your friend can do 135 sit-ups in 3 minutes. Do these rates form a proportion? Explain.

Yes, the rates form a proportion.

500

A specific shade of red nail polish requires 7 parts red to 2 parts yellow. A mixture contains 35 quarts of red and 8 quarts of yellow. Will the mixture be the correct shade of red?

No.

7/2 != 35/8

Writing Proportions

100

A girl scout troop uses 14 flashlight batteries on a three-night camping trip. If they are planning a seven-night trip, write a proportion to determine how many batteries they should bring? *do not solve*

14/3 = x/7

200

A bag of 8 apples costs $1.50 at Sam’s Orchard. At this same rate,  write a proportion to determine how much 18 apples would cost.  **Do not solve!!

1.50/8 = 18/x

300

You can buy 3 shirts for $24. Write a proportion that gives the cost c of buying 7 shirts. *do not solve*

$24/3 shirts = c/7 shirts

400

Will’s Widget Works can produce 2½ tons of widgets in an 8 hour work day. Write a proportion to determine how many tons of widgets would be produced between 9 am and noon? ** Do not solve!!!

2.5/8 = x/3

500

Denise’s rabbit can eat 70 pounds of food in 80 days. Write a proportion to determine how long it will take the rabbit to eat 87.5 pounds of food?

70/80 = 87.5/x

Solving Proportions

100

Solve the proportion: 

9/5 = x/20

z = 36

200

Solve the proportion: 

10/7 = 8/k

k = 5.6

300

48 pens are packaged in 4 boxes. How many pens are packaged in 9 boxes?

108 pens are packaged in 9 boxes.

400

It costs $10.50 for 3 medium pizzas. How much does it cost to buy 10 medium pizzas?

It will cost $35 for 10 medium pizzas.

500

The ratio of adults to children in an auditorium is 5 to 3.  If there are 54 children, how many adults are there?

90 adults are in the audience.