Fractions

Multiply Fractions

Multiply 2/3 × 3/4. Multiply the numerators (2 × 3 = 6) and the denominators (3 × 4 = 12) to get 6/12, then simplify to 1/2.

Example

Multiply 2/3 by 3/4, then simplify.

highlighted = computed this step

Step 1 — Set up

Set up the fraction expression.

23×34\frac{2}{3} \times \frac{3}{4}
Shade 2/3 one way and 3/4 the other way2 of 3 columns3 of 4 rowsThe whole is split into 3 columns and 4 rows.

Step 2 — Multiply across

Multiply across to get numerator 6 and denominator 12.

23×34=612\frac{2}{3} \times \frac{3}{4} = \hlmath{\frac{6}{12}}
Overlap: 2 x 3 = 6 parts2 of 3 columns3 of 4 rows6/126 overlap parts out of 12 total parts.

Step 3 — Simplify

Simplify the fraction to 1/2.

612=12\frac{6}{12} = \hlmath{\frac{1}{2}}
6/12 simplifies to 1/22 of 3 columns3 of 4 rows6/12Both 6 and 12 divide down to 1/2.

Step 4 — Result

Read the final result.

23×34=12\frac{2}{3} \times \frac{3}{4} = \frac{1}{2}
2/3 x 3/4 = 1/22 of 3 columns3 of 4 rows6/12The overlap area is 1/2 of the whole.
fraction-multiplication To multiply fractions, multiply straight across: numerator × numerator and denominator × denominator. The result often simplifies, so always check for common factors after multiplying.