Fractions

Divide Fractions

Divide 3/4 ÷ 2/3 using the "flip and multiply" rule. Keep the first fraction, flip the second (2/3 becomes 3/2), then multiply: 3/4 × 3/2 = 9/8 = 1 1/8.

Example

Divide 3/4 by 2/3 by inverting and multiplying.

highlighted = computed this step

Step 1 — Set up

Set up the fraction expression.

34÷23\frac{3}{4} \div \frac{2}{3}
How many 2/3-sized pieces fit in 3/4?3/4 = 9/122/3 = 8/12Common 12ths: dividend has 9 parts; divisor has 8.

Step 2 — Invert the divisor

Invert the divisor: 2/3 becomes 3/2.

34÷23=34×32\frac{3}{4} \div \frac{2}{3} = \frac{3}{4} \times \hlmath{\frac{3}{2}}
Use the reciprocal shortcut: 2/3 becomes 3/23/4 = 9/122/3 = 8/121 divisor-size pieceextra 1/8The bar shows the fit idea; the reciprocal is the calculation shortcut.2/3reciprocal3/2

Step 3 — Multiply

Multiply across to get numerator 9 and denominator 8.

34×32=98\frac{3}{4} \times \frac{3}{2} = \hlmath{\frac{9}{8}}
Multiply: 3/4 x 3/2 = 9/83/4 = 9/122/3 = 8/121 divisor-size pieceextra 1/8Across multiplication gives 9/8; same as 9 parts in groups of 8.2/3reciprocal3/23/4 x 3/2 = 9/8

Step 4 — Write mixed number

Write the improper fraction as 1 1/8.

98=1 18\frac{9}{8} = \hlmath{1\ \frac{1}{8}}
9/8 is 1 1/83/4 = 9/122/3 = 8/121 divisor-size pieceextra 1/89 result parts of size 1/8 make 1 whole and 1 extra part.2/3reciprocal3/23/4 x 3/2 = 9/89/89/8 = 1 1/8

Step 5 — Result

Read the final result.

34÷23=1 18\frac{3}{4} \div \frac{2}{3} = 1\ \frac{1}{8}
3/4 / 2/3 = 1 1/83/4 = 9/122/3 = 8/121 divisor-size pieceextra 1/8The exact result stays 1 1/8.2/3reciprocal3/23/4 x 3/2 = 9/89/89/8 = 1 1/8
reciprocal-and-multiply Dividing by a fraction is the same as multiplying by its reciprocal (the fraction flipped upside-down). Keep the dividend, change ÷ to ×, and flip the divisor. Then multiply and simplify as usual.