Dividing by Fractions
Interpret and compute division of a positive whole number by a positive unit fraction below 1; use visual models and the relationship between multiplication and division to explain why the quotient is larger than the dividend.
What a learner can do afterwards
- Compute 4 ÷ (1/5) = 20 and explain: 'How many fifths fit in 4 wholes?'
- Create a story context for 6 ÷ (1/4) and solve it
- Verify 4 ÷ (1/5) = 20 by showing 20 × (1/5) = 4
1 · Read
You already know how to multiply fractions. Now you will divide a whole number by a fraction, like 4 ÷ 1/5. This question means: how many fifths fit inside 4 wholes?
Work a question like that the same way: count the pieces in one whole, then multiply by how many wholes you have. Take 6 ÷ 1/5. Each whole holds 5 fifths, and you have 6 wholes, so 6 × 5 = 30 fifths. That means 6 ÷ 1/5 = 30. The answer is bigger than 6, because dividing a number above 0 by a positive fraction smaller than 1 makes more pieces. Check by multiplying back: 30 × 1/5 = 6.
Ali has 3 litres of soup. Each bowl holds 1/6 of a litre. To find how many bowls he can fill, solve 3 ÷ 1/6. Each whole litre holds 6 sixths, and he has 3 litres, so 3 × 6 = 18 bowls.
There are two ways to check your work. First, dividing by a fraction is the same as multiplying by how many of those pieces fit in one whole (6 ÷ 1/5 = 6 × 5). Second, multiply your answer back: 30 × 1/5 = 6. If you land back on the number you started with, the division is correct.
Dividing a number bigger than 0 by a positive fraction smaller than 1 always gives a bigger answer, because you are counting how many tiny pieces fit inside the whole.
2 · Watch
Take it off screen
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
19 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.