🧱 See It
Multiplying two fractions means taking "a fraction of a fraction." To find 1/2 × 1/3, start with a whole cut into thirds and shade just one third:
One third of the whole, shaded.
Now cut that same shaded third in half, and keep only one of those two new pieces:
Half of the shaded third — not half of the whole. This doubly-shaded sliver is the answer.
✏️ Draw It
Cut the whole thing into a grid instead: 2 columns (halves) crossed with 3 rows (thirds) makes 6 equal pieces. Shade the one piece where "one half" and "one third" overlap:
One piece out of 6 equal pieces — half of a third is one sixth.
🔢 Write It
Multiplying: numerator × numerator, denominator × denominator. No common denominator needed — ever.
1/2 × 1/3 = (1×1)/(2×3) = 1/6
Dividing: flip the second fraction upside down (its reciprocal), then multiply instead.
1/2 ÷ 1/3 = 1/2 × 3/1 = 3/2
💡 Worked Examples
Example 1: 2/3 × 3/4
- Multiply the numerators:
2 × 3 = 6 - Multiply the denominators:
3 × 4 = 12 - Combine:
6/12 - Simplify using the GCF:
GCF(6, 12) = 6, so6/12 = 1/2 - Answer:
1/2
Example 2: 3/4 ÷ 1/2
- Flip the second fraction:
1/2 → 2/1 - Multiply instead of dividing:
3/4 × 2/1 - Multiply straight across:
(3×2)/(4×1) = 6/4 - Simplify using the GCF:
GCF(6, 4) = 2, so6/4 = 3/2 - Answer:
3/2
🧠 Quick Reference
| Multiply | Divide | |
|---|---|---|
| Denominators | Numerators together, denominators together | Flip the second fraction (reciprocal) |
| Common denominator? | Not needed | Not needed |
| Final step | Multiply straight across | Multiply straight across |