Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of a fraction is the fraction turned upside down: the reciprocal of 2/5 is 5/2.
So 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 = 1 7/8. This rule makes sense with a simple case: 1 ÷ 1/2 asks how many halves fit in 1, which is 2, and 1 × 2/1 = 2. With mixed numbers, change them to improper fractions first.
Worked example
2/3 ÷ 4/9 =
- Multiply by the reciprocal of 4/9: 2/3 × 9/4.
- 18/12 = 3/2.
Answer:3/2 = 1 1/2
Key words
- reciprocal
- a fraction turned upside down
- divide
- find how many fit
- improper fraction
- a fraction greater than 1
Practise this
New questions every time.
Common Core-referenced: 6.NS.A.1