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
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=3½.
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
2¼
2⅓×1½
3½
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.