How to Cross Multiply

What Is Cross Multiplication?

Given two fractions set equal: a/b = c/d
Cross multiply means: a × d = b × c
Multiply diagonally — each numerator times the opposite denominator.

Using It to Solve for an Unknown

Solve: x/6 = 5/10

Cross multiply: x × 10 = 6 × 5

10x = 30

Divide both sides by 10: x = 3

Solve: 8/3 = 24/x

Cross multiply: 8 × x = 3 × 24

8x = 72

Divide: x = 72 ÷ 8 = 9

Using It to Compare Fractions

Cross multiplication also tells you which fraction is larger — no common denominator needed.

Which is larger: 3/7 or 5/11?

Left cross product: 3 × 11 = 33

Right cross product: 7 × 5 = 35

33 < 35 → 3/7 < 5/11

The cross product belongs to the numerator it started from. So 3×11=33 belongs to the fraction with 3 on top (3/7), and 7×5=35 belongs to 5/11. Bigger cross product → bigger fraction.

💡 When to use it: Cross multiplication only works with equations (proportions) or comparisons between two fractions. You can't cross multiply when adding or subtracting fractions.

🎯 Practice Problems

1. Solve: x/4 = 6/8

A) 2

B) 3

C) 12

D) 24

2. Solve: 5/9 = 15/x

A) 3

B) 9

C) 27

D) 45

3. Which is larger: 2/5 or 3/8?

A) 2/5

B) 3/8

C) They're equal

D) Can't tell

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🎯 Bonus Practice

1. Solve: 10/x = 2/7

A) 35

B) 14

C) 70

D) 1.4

2. Which is larger: 7/9 or 4/5?

A) 7/9

B) 4/5

C) Equal

D) Can't compare

3. Solve: 3/x = 12/20

A) 5

B) 4

C) 15

D) 9

4. Can you cross multiply when adding fractions like 1/3 + 2/5?

A) Yes — always works

B) No — only for proportions and comparisons

C) Only if denominators match

D) Yes — for subtraction too

5. Solve: x/12 = 3/4

A) 9

B) 6

C) 16

D) 36