Dividing fractions · Grade 6
In Grade 6 you learn: dividing by a fraction and dividing mixed numbers.
Dividing by a fraction asks “how many of these fit?”. Dividing a fraction by a whole number shares it into equal parts. To divide by a fraction, multiply by its reciprocal: keep, change, flip.
Key facts
- Dividing a fraction by a whole number shares it: 1/2 ÷ 3 = 1/6, the same as 1/2 × 1/3.
- The reciprocal of a/b is b/a; the reciprocal of 5 is 1/5.
- To divide by a fraction, multiply by its reciprocal: a/b ÷ c/d = a/b × d/c (keep, change, flip).
- Change mixed numbers into improper fractions before multiplying or dividing.
- Multiplying by a fraction less than 1 makes a number smaller; dividing by it makes it bigger.
Worked examples
Example 1
Work out 1/2 ÷ 3.
Answer: 1/6
Example 2
Work out 2/3 ÷ 4.
Answer: 1/6
Example 3
Half a pizza is shared equally between 4 friends. What fraction of the whole pizza does each friend get?
Answer: 1/8
Example 4
How many 1/3s are there in 4?
Answer: 12
Example 5
Work out 3/4 ÷ 2/5.
Answer: 1 7/8
Example 6
How many 3/8-liter cups can be filled from a 4 1/2-liter jug?
Answer: 12 cups
Example 7
Work out 3 3/4 ÷ 1 1/2.
Answer: 2 1/2