Ratio, Rate, and Unit Rates

Mary runs 7 miles in 2.25 hours. Ariel runs 2 miles in 36 minutes, or 0.6 hour.

Who runs faster?

• Ariel

• Mary

• Neither, they are equivalent

A group of 15 students is deciding whether to go to the science center or the zoo. Science center tickets are 5 for $35.75 and zoo tickets are 6 for $69.

How much will a group of 15 students save by choosing the science center?

• $4.35

• $7.15

• $65.25

• $107.25

Cindy and Tom are telemarketers.

Yesterday, Cindy reached 7 people in 15 phone calls, while Tom reached 4 people in 9 phone calls.

If they continue at those rates, who will reach more people in 45 phone calls?

• Cindy

• Tom

• They reach the same number of people.

Which of the following are true about unit rates?

• A unit rate relates a quantity to 1.

• Any rate is equivalent to its unit rate.

• A unit rate always relates quantities with the same units.

• Unit rates can be used to compare two rates.

Machine A makes 6.5 ounces of shaved ice in 2 minutes. Machine B makes 15 ounces of shaved ice in 4 minutes.

If each machine makes shaved ice for 8 minutes, will there be enough shaved ice for nine 5-ounce snow-cone cups? Explain.

• No; Machine A and Machine B make 7 ounces in 8 minutes.

  7 < 45, so there will not be enough shaved ice.

• No; Machine A and Machine B make 21.5 ounces in 8 minutes. 21.5 < 45, so there will not be enough shaved ice.

• Yes; Machine A and Machine B make 65 ounces in 8 minutes. 65 > 45, so there will be enough shaved ice.

• Yes; Machine A and Machine B make 56 ounces in 8 minutes. 56 > 45, so there will be enough shaved ice.

At a​ supermarket, a​ 6-ounce bottle of brand A salad dressing costs​ $1.56. A​ 14-ounce bottle costs​ $3.36. A​ 20-ounce bottle costs​ $5.60. What unit prices do you need to know to find the best​ buy?

• The unit prices per bottle

• The unit prices per bottle and per ounce

• The unit prices per ounce

• The unit prices per dollar

At a​ supermarket, a​ 6-ounce bottle of brand A salad dressing costs​ $1.56. A​ 14-ounce bottle costs​ $3.36. A​ 20-ounce bottle costs​ $5.60. What is the best​ buy?

• The 6​-ounce bottle is the best buy.

• The 14​-ounce bottle is the best buy.

• The 20​-ounce bottle is the best buy.

• They are all equivalent

Population density is the number of people per unit of area. The population density of a certain region is 60 people per square kilometer. If the region covers 23 square​ kilometers, what is the population of the​ region?

• The population of the region is

  138 people.

• The population of the region is

  1,380 people.

• The population of the region is

  13,800 people.

• The population of the region is

  6,000 people.

In​ basketball, some baskets are worth two points. Others are worth three points. In one​ game, the ratio of​ three-point baskets to​ three-point tries for one team was 3 : 4. If the team scored 27 points from​ three-point baskets, how many​ three-point tries did the team​ have?

• The team had

  12 three-point tries.

• The team had

  16 ​three-point tries.

• The team had

  24 three-point tries.

• The team had

  36 ​three-point tries.

In a toy​ store, the ratio of the number of dolls to the number of teddy bears is 6 : 5. If the store has 240​ dolls, how many teddy bears are in the​ store? Use pencil and paper. Describe the mental math steps you use to solve this problem.

• There are 200 teddy bears in the store.

• There are 240 teddy bears in the store.

• There are 1,200 teddy bears in the store.

• There are 1,440 teddy bears in the store.