Ratios Introduction — Answer Key
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
The ratio 6:2 are equal to the ratio 9:3 because both simplify to 3:1.
Corrected: The ratios 6:2 and 9:3 are equal because both simplify to 3:1.
Plural verb needs a plural subject, so we change to 'ratios'.
2. Fix the sentence:
10 books for $20 are cheaper per book than 6 books for $18.
Corrected: 10 books for $20 is cheaper per book than 6 books for $18.
When comparing one rate to another, we use a singular verb.
3. Fix the sentence:
Each runner finish the race in different times, so their rates differ.
Corrected: Each runner finishes the race in different times, so their rates differ.
The word 'each' makes the subject singular, requiring 'finishes'.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. Which is faster: 30 miles in 2 hours or 50 miles in 4 hours? Answer: 30 miles in 2 hours.
30 over 2 equals 15 mph; 50 over 4 equals 12.5 mph, so 30 wins.
2. A baker uses 9 cups of flour for 6 loaves. The unit rate is 1.5 cups per loaf.
9 divided by 6 equals 1.5 cups per single loaf.
3. If 3 pencils cost 75 cents, then 1 pencil costs 25 cents.
75 divided by 3 equals 25, the cost per pencil.
4. Comparing 12 oranges for $6 and 20 oranges for $8, the better deal is 20 oranges.
12 oranges cost 50 cents each, but 20 cost only 40 cents each.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. A bike rider goes 24 miles in 3 hours. A jogger covers 12 miles in 2 hours. Who is faster and by how much?
Sample answer: The bike rider's rate is 24 divided by 3, which is 8 mph. The jogger's rate is 12 divided by 2, which is 6 mph. The bike rider is 2 mph faster.
Comparing unit rates shows the difference in speed clearly.
2. Store A sells 4 cans for $5. Store B sells 6 cans for $9. Which store has the better unit price?
Sample answer: Store A: $5 divided by 4 equals $1.25 per can. Store B: $9 divided by 6 equals $1.50 per can. Store A has the better price at $1.25.
The lower unit price means each can costs less, saving money.