Dividing fractions (unit fractions)
Interpret and compute division of a unit fraction by a non-zero whole number (e.g. 1/3 ÷ 4 = 1/12); use visual models and the relationship between multiplication and division to explain the result
What a learner can do afterwards
- Compute (1/3) ÷ 4 = 1/12 and explain using a visual model of splitting 1/3 into 4 equal parts
- Create a story context for (1/6) ÷ 3 and solve it
- Verify (1/3) ÷ 4 = 1/12 by showing (1/12) × 4 = 1/3
1 · Read
Dividing a fraction by a whole number splits an already-small piece into even smaller equal pieces. If you have 1/3 of a bag of rice and share it evenly among 4 people, each person gets less than 1/3.
To work out 1/3 ÷ 4, cut the shaded third into 4 equal strips. The whole bar is now cut into 3 × 4 = 12 equal parts, and only 1 of those parts is shaded. So 1/3 ÷ 4 = 1/12.
The shortcut: to divide a unit fraction by a whole number, multiply the denominator by that whole number. The numerator stays 1. Check your answer by multiplying it back: 1/12 × 4 = 1/3.
Dividing a fraction by a whole number greater than 1 splits it into more, smaller equal pieces, so the answer is smaller than what you started with.
More to read
4.2 Multiply and Divide Fractions
Dividing by a fraction is the same as multiplying by its flip. To divide 1/3 by 4, write 4 as 4/1 and multiply 1/3 by 1/4. That gives 1/12. Splitting a third into 4 equal parts leaves pieces that are twelfths of the whole. Multiplying back checks the work: 1/12 times 4 returns 1/3.
4.3 Multiply and Divide Mixed Numbers and Complex Fractions
Stories make division concrete. Sharing 1/6 of a cake among 3 people means computing 1/6 divided by 3. Write 3 as 3/1, flip it to 1/3, and multiply: 1/6 times 1/3 = 1/18. Each person gets 1/18 of the whole cake.
23.1: Dividing by Unit and Non-Unit Fractions
Unit fractions have a 1 on top, which makes their division neat. Dividing a unit fraction by a whole number n multiplies the bottom by n. So 1/3 divided by 4 is 1/12, and 1/6 divided by 3 is 1/18. Drawing the split as a bar cut into equal slices shows each new piece clearly.
Dividing Whole Numbers by Unit Fractions
Dividing whole numbers by unit fractions goes the other way and grows the answer. How many halves fit in 3 wholes? Six, because 3 divided by 1/2 equals 6. Flipping the divisor explains it: 3 times 2/1 = 6. Comparing both directions builds strong number sense.
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2 · Watch
En anglaisTake it off screen
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
18 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.