Grade 6 Math · Topic 08

Proportions and Cross Multiplication

A proportion is an equation that says two ratios are equal: (a)/(b) = (c)/(d). When one of the four numbers is missing, you can solve it quickly with cross multiplication — multiply diagonally and set the products equal, then divide.

Lesson alignment: 6.RP.A.3 · Take your time. You can return to this lesson whenever you need it.

Explore visually

Compare proportional quantities

Line up each equivalent pair to see the constant relationship before solving.

Think first: Which values should line up at matching ticks when both quantities scale together?

Ready? Reveal the model and try your prediction

Swipe horizontally to see the full diagram.

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Follow the worked examples

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

Worked example 1

Solve for x: (x)/15 = 4/5.

Use cross multiplication to keep the proportion balanced: 5 · x = 15 · 4, so 5x = 60. Divide both sides by 5: x = 12. Check: 12/15 = 4/5 (both simplify to 4/5). ✓

Answer: x = 12

Worked example 2

Solve for n: 6/(n) = 9/12.

Use cross multiplication to keep the proportion balanced: 6 · 12 = 9 · n, so 72 = 9n. Divide by 9: n = 8. Check: 6/8 = 3/4 and 9/12 = 3/4. ✓

Answer: n = 8

Try a few on your own

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

  1. (x)/4 = 6/8
    Check

    x=3

  2. 3/5 = (n)/20
    Check

    n=12

  3. 12/(x) = 4/3
    Check

    x=9

  4. (y)/9 = 10/6
    Check

    y=15

  5. 7/14 = (x)/8
    Check

    x=4

  6. 2/(n) = 5/15
    Check

    n=6

  7. (x)/18 = 2/9
    Check

    x=4

  8. 8/12 = 6/(x)
    Check

    x=9

Try this situation 1

A car uses 5 gallons of gas to travel 140 miles. How many gallons does it need to travel 336 miles at the same rate?

Show a worked solution

Answer: 12 gallons.

Start by writing the calculation clearly: 5/140 = (x)/336. Cross multiply: 5 · 336 = 140x, so 1680 = 140x, giving x = 12.

Try this situation 2

On a map, 2 centimeters represents 35 kilometers. How many kilometers does 8 centimeters represent?

Show a worked solution

Answer: 140 kilometers.

Start by writing the calculation clearly: 2/35 = 8/(x). Cross multiply: 2x = 35 · 8 = 280, so x = 140.

Fresh questions · saved on this device

Practice this skill

14 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.

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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. Solve for x: (x)/6 = 7/8

2. Which pair of ratios forms a proportion?

3. A map uses a scale where 2 inches represents 50 miles. If two cities are 5 inches apart on the map, what is the actual distance between them?

4. In a recipe, the ratio of flour to sugar is 5:2. If you use 10 cups of flour, how many cups of sugar do you need?

5. Solve for x: 3/4 = (x)/12

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

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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 ↗