Dividing by Fractions
Interpret and compute division of a whole number by a unit fraction (e.g. 4 ÷ 1/5 = 20); 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
The lesson
You already know how to split a fraction into equal parts. Now you will divide a whole number by a fraction, like 4 ÷ 1/5. This question means: how many fifths fit inside 4 wholes?
To solve 4 ÷ 1/5, count the fifths in each whole, then multiply by how many wholes you have. Each whole holds 5 fifths, and you have 4 wholes, so 4 × 5 = 20 fifths in total. That means 4 ÷ 1/5 = 20.
Mia has 6 metres of rope for a craft class. Each bracelet uses 1/4 of a metre. To find how many bracelets she can make, solve 6 ÷ 1/4. Each whole metre holds 4 fourths, and she has 6 metres, so 6 × 4 = 24 bracelets.
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 (4 ÷ 1/5 = 4 × 5). Second, multiply your answer back: 20 × 1/5 = 4. If you land back on the number you started with, the division is correct.
Dividing by a fraction smaller than 1 always gives a bigger answer, because you are counting how many tiny pieces fit inside the whole.
Watch it
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 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.