Product of fractional units

The idea

When two fractional units are multiplied, the whole is divided into b × d equal parts, so the product is 1/(product of denominators): 1/b × 1/d = 1/(b × d).

A piece of a piece

Dina has 1/3 of a chocolate bar. She gives 1/4 of her piece to her brother.

What fraction of the whole bar does her brother get?

• 1/12
• 1/7
• 1/4

Count the cells

The whole is cut into rows and columns. The first row is the multiplicand and the gold cell is a part of it. Change the rows and the columns.

Rows times columns

Dina’s piece is one of 3 rows. Cutting that row into 4 parts makes the whole 3 × 4 = 12 equal parts. Her brother’s piece is one of them: 1/12.

When two fractional units are multiplied, the whole is divided into b × d equal parts. So the product is 1 over the product of the denominators: 1/b × 1/d = 1/(b × d)

• Product | Rows × columns | One cell
• 1/3 × 1/4 | 3 × 4 = 12 | 1/12
• 1/2 × 1/5 | 2 × 5 = 10 | 1/10
• 1/18 × 1/12 | 18 × 12 = 216 | 1/216

Notes

When two fractional units are multiplied, the whole is divided into b × d equal parts. So the product is 1 over the product of the denominators: 1/b × 1/d = 1/(b × d)

Check yourself

Find 1/5 × 1/6. Type a fraction like 1/9.

Answer: 1/30

5 × 6 = 30 equal parts, so 1/5 × 1/6 = 1/30.

In 1/18 × 1/12 = 1/?, what is the missing number?

Answer: 216

18 × 12 = 216, so 1/18 × 1/12 = 1/216.

Which product is equal to 1/20?

A whole is cut into 7 rows and 3 columns. How much of the whole is one cell?

• 1/4 × 1/5 — correct. Yes! 4 × 5 = 20, so the product is 1/20.
• 1/9 × 1/11. The denominators are added here: 9 + 11 = 20. But they must be multiplied: 9 × 11 = 99, so this is 1/99.
• 1/2 × 1/18. Here 2 + 18 = 20, but the product needs 2 × 18 = 36, so this is 1/36.
• 1/21 — correct. Yes! There are 7 × 3 = 21 equal cells.
• 1/10. That counts 7 + 3 = 10. A grid has rows × columns cells.
• 1/3. That is one cell of a single row of 3. The whole has 7 rows too.