A whole number times a fraction means that many lots of the fraction: 4 × 2/5 is 4 lots of 2 fifths, which is 8 fifths (8/5). The denominator stays the same. To multiply two fractions, multiply the numerators together and the denominators together, then simplify: 2/3 × 3/4 = 6/12 = 1/2. Change mixed numbers to improper fractions first.
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Equal parts, equal wholes
2/4 = 4/8
Both bars are the same length. Find a division of the second bar that lines up exactly with the coloured edge.
Words to know
- product
- the answer to a multiplication
- simplify
- divide the top and bottom by the same number
- improper fraction
- a fraction bigger than 1, like 7/3
Worked examples
4 × 2/5 = ?
- 1.4 lots of 2 fifths: 2 × 4 = 8.
- 2.8 fifths: 8/5.
= 8/5
2/3 × 3/4 = ?
- 1.Numerators: 2 × 3 = 6. Denominators: 3 × 4 = 12.
- 2.6/12 = 1/2.
= 1/2
2 1/3 × 4 = ?
- 1.2 1/3 = 7/3.
- 2.7/3 × 4 = 28/3, which is 9 1/3.
= 28/3
For parents
Method: Multiply across
What to say: Is the answer bigger or smaller than the fraction you started with? Why?
Common mistakes:
- Multiplies both the numerator and the denominator by the whole number, making an equivalent fraction.
- Multiplies the denominator by the whole number instead of the numerator.
- Adds the whole number to the numerator instead of multiplying.
- Multiplies diagonally (a × d over b × c), mixing up the multiplication and division methods.
- Adds the numerators and adds the denominators.
- Uses the addition method: makes a common denominator, multiplies the numerators and keeps that denominator.
- Multiplies only the whole-number part of a mixed number (2 1/3 × 4 → 8 1/3).
- Multiplies only the fraction part of a mixed number and leaves the whole number unchanged.
- Converts the mixed number wrongly by adding the whole to the numerator, then multiplies.