Math · Fractions

How to Multiply Fractions
Numerator × Numerator, Denominator × Denominator — 30 Examples

Learn to multiply fractions in 3 steps: multiply numerators, multiply denominators, simplify. With cross-canceling, mixed numbers and 30 practice problems.

⚡ RESPUESTA RÁPIDA

To multiply fractions: multiply the numerators together, then the denominators. 3/4 × 2/5 = (3×2)/(4×5) = 6/20 = 3/10. No common denominator needed — ever.

Why Multiplying Fractions is Easier Than Adding

Addition needs common denominator. Multiplication: just multiply straight across. 3/4 × 2/5 = (3×2)/(4×5) = 6/20 = 3/10
Multiply numerators together3/4 × 2/5: multiply the top numbers → 3×2=6. Simple.
Multiply denominators togetherNow multiply the bottom numbers → 4×5=20. Result so far: 6/20.
Simplify the result6/20: GCD(6,20)=2. Divide both by 2 → 3/10. Always simplify at the end.
Shortcut — simplify BEFORE multiplyingCross-cancel first: 3/4 × 2/5. The 2 and 4 share factor 2: 3/2 × 1/5=3/10. Same answer, less work.

Multiplying by a Whole Number

Write the whole number as a fraction3/4 × 8 = 3/4 × 8/1. Now multiply: (3×8)/(4×1)=24/4=6.
Shortcut for whole numbers3/4 × 8: the 4 and 8 share factor 4. 3/1 × 2/1=6. Much faster.

Mixed Numbers — Convert First

Convert mixed numbers to improper fractions1½ × 2⅓: convert → 3/2 × 7/3. Now multiply: 21/6=.

30 Practice Problems

2/3×3/4
1/2
3/5×5/6
1/2
4/7×7/8
1/2
1/2×4/5
2/5
3/4×8/9
2/3
5/6×12/25
2/5
2/3×9
6
5×3/5
3
1/4×12
3
8×3/4
6
2/5×10
4
7×2/7
2
1½×2/3
1
2¼×4/9
1
1⅓×3/4
1
2½×⅖
1
3×1/3
1
4/5×5/4
1
2/3×3/2
1
5/8×8/5
1
1½×1½
2⅓×1½
¾×⅘
3/5
⅔×¾
½
5/12×4/5
1/3
3/8×4/3
1/2
7/10×5/7
1/2
9/4×8/3
6
5/6×3/5
1/2
11/4×8/11
2
Why no common denominator needed?

In addition, the denominator represents piece size — pieces must match to add. In multiplication, you're finding a fraction OF a fraction, which works directly without matching sizes.

Real life — recipe scaling

Recipe needs 3/4 cup flour. You want to make 2/3 of the recipe. How much flour? 3/4 × 2/3 = 6/12 = 1/2 cup.

Does order matter in fraction multiplication?

No. 3/4 × 2/5 = 2/5 × 3/4 = 6/20 = 3/10. Multiplication is commutative.

When should I cross-cancel vs simplify at the end?

Cross-cancel when you see common factors between any numerator and any denominator. It keeps numbers small throughout.

What if the result is greater than 1?

It becomes an improper fraction. Convert to mixed number: 9/4 = 2¼. Both forms are correct; mixed is easier to understand.

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