Ratios Introduction — Answer Key
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
A car drives 120 miles in 3 hours, so the unit rate are 40 miles per hour.
Corrected: A car drives 120 miles in 3 hours, so the unit rate is 40 miles per hour.
A singular subject takes a singular verb, so 'is' agrees with 'rate'.
2. Fix the sentence:
If 5 apples cost $2, then each apple cost 40 cents.
Corrected: If 5 apples cost $2, then each apple costs 40 cents.
Singular subject 'apple' needs the verb 'costs' with an s ending.
3. Fix the sentence:
She run 6 miles in 1 hour, which gives a unit rate of 6 mph.
Corrected: She runs 6 miles in 1 hour, which gives a unit rate of 6 mph.
Third person singular pronouns require the verb form ending in s.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. If 4 pounds of rice cost $12, the unit rate is $3 per pound.
12 divided by 4 equals 3, giving the cost for one pound.
2. A car travels 180 miles in 3 hours, so its unit rate is 60 miles per hour.
180 divided by 3 equals 60, the speed in miles per hour.
3. Comparing 8 cookies for $4 versus 12 cookies for $9, the better deal is 8 cookies.
8 cookies cost 50 cents each while 12 cost 75 cents each.
4. If a printer prints 90 pages in 6 minutes, the unit rate is 15 pages per minute.
90 divided by 6 equals 15, the printing rate per minute.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Which is the better buy: 6 yogurts for $3 or 10 yogurts for $4? Show your work.
Sample answer: 6 yogurts for $3 is $0.50 each. 10 yogurts for $4 is $0.40 each. The 10-pack is the better buy because each yogurt costs less.
Unit rates let us compare deals fairly even when quantities differ.
2. A train travels 240 miles in 4 hours. What is the unit rate, and how far would it go in 7 hours?
Sample answer: Unit rate is 240 divided by 4, which equals 60 miles per hour. In 7 hours, the train travels 60 times 7, or 420 miles.
Unit rates make it easy to scale up to any number of hours.