Dividing unit fractions and whole numbers
Solve real-world problems involving division of unit fractions by whole numbers and whole numbers by unit fractions, using visual models and equations
What a learner can do afterwards
- Solve: '3 people share 1/2 lb of chocolate equally, how much each?' (1/6 lb)
- Solve: 'How many 1/3-cup servings in 2 cups of raisins?' (6 servings)
- Create a story context for a given unit-fraction division expression
1 · Read
You already know how to divide by a unit fraction. Now you will use that skill on real problems. Two kinds of stories show up again and again: sharing a small amount equally among people, and figuring out how many small scoops fit inside a bigger amount.
3 people share 1/2 lb of chocolate equally. That is a sharing story, so divide the unit fraction by the whole number: 1/2 ÷ 3 = 1/6. Each person gets 1/6 lb.
You want to scoop 1/3-cup servings out of 2 cups of raisins. That is a scooping story, so divide the whole number by the unit fraction: 2 ÷ 1/3 = 6. You get 6 servings.
Ask yourself which story you are in. Splitting a small amount among people? Divide the fraction by the whole number. Filling scoops from a bigger amount? Divide the whole number by the fraction.
Same fraction-division skill, two stories: split a small amount among people, or count how many scoops fill a bigger amount.
More to read
Reason about the size of quotients
Before you solve, take a second to guess whether the answer will be bigger or smaller. This trick catches many mistakes.
When you divide a whole number by a unit fraction, the answer gets bigger. Think about 5 divided by 1/5. You are asking how many little fifths fit inside 5 wholes, and there are lots of them, 25 in fact.
When you divide a unit fraction by a whole number, the answer gets smaller. Think about 1/5 divided by 5. You are cutting a small piece into 5 even smaller pieces, so the result is a tiny 1/25.
The two problems use the same numbers but do opposite things. One shares a small piece into smaller pieces. The other counts how many small pieces fill up wholes.
Concepts of division
Division has two big ideas, and fraction division uses both.
The first idea is sharing, also called partitive division. You start with an amount and split it into equal groups. If 3 friends share 1/2 of a cake, you are splitting 1/2 into 3 equal parts. Each friend gets 1/6.
The second idea is measuring, also called quotative division. You start with an amount and ask how many groups of a certain size fit inside it. If you have 2 cups of raisins and each serving is 1/3 cup, you ask how many 1/3 cups fit in 2 cups. The answer is 6 servings.
Notice the answers come out differently. Sharing 1/2 among 3 gives a small answer, 1/6. Measuring how many 1/3s fit in 2 gives a big answer, 6. When you read a word problem, ask first: is this sharing into groups, or counting how many groups fit?
Reason about quotients
There is a friendly way to check any division answer: multiply it back.
Division and multiplication are opposite operations. So if you solve 1/2 divided by 3 and get 1/6, you can check by multiplying 1/6 by 3. That gives 3/6, which simplifies to 1/2. The check works, so the answer is right.
Try it with 2 divided by 1/3. If the answer is 6, then 6 times 1/3 should equal 2. And it does, because 6/3 is 2.
This checking trick is extra helpful with fractions, where it is easy to flip a numerator and denominator by accident. Make multiplying back your last step on every problem, and wrong answers will have nowhere to hide.
Explore more
2 · Watch
En anglaisTake it off screen
Where it sits
Optional connections
This opens up
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
16 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.