How to Solve a Proportion

The Steps

Step 1: Set up the proportion as two equal fractions with the unknown.
Step 2: Cross multiply.
Step 3: Solve for the unknown by dividing.

Worked Examples

Solve: 3/5 = x/20

Cross multiply: 3 × 20 = 5 × x

60 = 5x

Divide: x = 60 ÷ 5 = 12

Check: 3/5 = 12/20 → both equal 0.6 ✓

Solve: 7/x = 21/9

Cross multiply: 7 × 9 = x × 21

63 = 21x

Divide: x = 63 ÷ 21 = 3

Check: 7/3 = 21/9 → both equal 2.333… ✓

Setting Up the Proportion

The hardest part is often setting it up correctly. Keep the same type of quantity on the same side. If the left fraction is miles/hours, the right fraction must also be miles/hours.

If 5 apples cost $3, how much do 8 apples cost?

Set up: apples/cost = apples/cost

5/3 = 8/x

Cross multiply: 5x = 24

x = 24 ÷ 5 = $4.80

💡 Always check: Plug your answer back into the original proportion and verify both sides are equal. This catches setup errors.

🎯 Practice Problems

1. Solve: 2/3 = x/12

A) 4

B) 6

C) 8

D) 18

2. Solve: x/5 = 12/15

A) 3

B) 4

C) 9

D) 6

3. Solve: 6/8 = 9/x

A) 10

B) 11

C) 12

D) 15

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🎯 Bonus Practice

1. Solve: 4/7 = x/35

A) 10

B) 15

C) 20

D) 28

2. Solve: x/9 = 10/3

A) 30

B) 27

C) 3

D) 90

3. If 3 pizzas serve 12 people, how many pizzas for 20 people?

A) 4

B) 5

C) 6

D) 7

4. Solve: 15/x = 5/8

A) 3

B) 20

C) 24

D) 40

5. Solve: 7/11 = 28/x

A) 22

B) 33

C) 44

D) 55