Grade 6 Math · Topic 06

Comparing Unit Rates

Better buy? Faster runner? Stronger gas mileage? When two situations have different totals, you cannot compare them directly. Convert each to a unit rate first, then compare the per-unit values. The one with the better per-unit value wins.

Lesson alignment: 6.RP.A.2 · Take your time. You can return to this lesson whenever you need it.

Explore visually

Compare two unit rates

Find the rate for one unit first, then compare the two amounts fairly.

Think first: Which option do you think gives more for each one unit? Estimate before comparing the bars.

Ready? Reveal the model and try your prediction

Swipe horizontally to see the full diagram.

Turn on JavaScript to adjust this model. The examples and practice below work without it.

Follow the worked examples

Read each step, then cover the explanation and see if you can explain why it works.

Worked example 1

Store A: 12 apples for $6. Store B: 8 apples for $3.60. Which store has the better deal?

To compare fairly, find each unit price. Store A: 6 ÷ 12 = $0.50 per apple. Store B: 3.60 ÷ 8 = $0.45 per apple. Since $0.45 < $0.50, Store B is cheaper per apple.

Answer: Store B

Worked example 2

Aiden types 180 words in 4 minutes. Brianna types 250 words in 5 minutes. Who is faster?

Aiden: 180 ÷ 4 = 45 words per minute. Brianna: 250 ÷ 5 = 50 words per minute. Since 50 > 45, Brianna types faster.

Answer: Brianna

Try a few on your own

Work these on paper first. Open “Check” when you are ready to compare your answer.

  1. A: $10/4 lb vs. B: $12/6 lb
    Check

    B: $2/lb

  2. A: 120 mi/3 hr vs. B: 220 mi/5 hr
    Check

    B: 44 mi/hr

  3. A: 8 for $5 vs. B: 12 for $6
    Check

    B: $0.50 each

  4. A: 180/6 min vs. B: 240/10 min
    Check

    A: 30/min

  5. A: $18/3 kg vs. B: $25/5 kg
    Check

    B: $5/kg

  6. A: 150/5 pg vs. B: 210/6 pg
    Check

    B: 35 pages/day

  7. A: $4.50/3 vs. B: $6.00/5
    Check

    B: $1.20 each

  8. A: 96/8 s vs. B: 144/12 s
    Check

    Tie: 12/s

Try this situation 1

A 16-oz juice costs $2.40 and a 24-oz juice costs $3.36. Which size is the better buy per ounce?

Show a worked solution

Answer: The 24-oz size ($0.14/oz vs. $0.15/oz).

Start by writing the calculation clearly: 16-oz: 2.40 ÷ 16 = $0.15/oz. 24-oz: 3.36 ÷ 24 = $0.14/oz. The lower price per ounce wins.

Try this situation 2

Car A drives 240 miles on 8 gallons. Car B drives 300 miles on 12 gallons. Which car gets better gas mileage?

Show a worked solution

Answer: Car A (30 mpg vs. 25 mpg).

Car A: 240 ÷ 8 = 30 mpg. Car B: 300 ÷ 12 = 25 mpg. More miles per gallon is better, so Car A wins.

Fresh questions · saved on this device

Practice this skill

30 question pool

Try a fresh set each time. Answer one question, check your thinking, and read the explanation. If you miss one, return to the visual model and try another round.

Choose a session length

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Check what you learned

Answer these five questions on your own. You can review the explanations after you submit and try again whenever you like. This short check is for practice, not a grade.

1. Brand X sells a 12-ounce bottle of shampoo for 9 dollars. Brand Y sells a 16-ounce bottle for 11 dollars. Which brand costs less per ounce?

2. Train A travels 360 miles in 8 hours. Train B travels 330 miles in 6 hours. Which train travels faster?

3. Bakery P bakes 18 cookies in 3 hours. Bakery Q bakes 28 cookies in 4 hours. Which bakery bakes faster?

4. Athlete A swims 300 meters in 6 minutes. Athlete B swims 250 meters in 5 minutes. Who swims faster?

5. Store A sells 8 apples for 4 dollars. Store B sells 6 apples for 3 dollars. Which store has the cheaper price per apple?

Practice and finish

Try the linked topic quiz for more practice. If something is tricky, return to the example and look for the step that changes the numbers or representation.

Open the practice quiz

Your checkmark, skill-practice sessions, and best exit-check score are saved on this browser and device. The course page can download a progress report to share with a tutor or teacher.

More Grade 6 resources

Use these free materials if you want another explanation, extra paper practice, or a broader review.

Browse free Grade 6 topic lessons ↗Print Grade 6 worksheets ↗Review Grade 6 flashcards ↗Open the formula review ↗Try the Ratios, Rates & Proportions quiz ↗Try a full practice test ↗