Year 6: Dividing fractions by whole numbers
Part of the Year 6 fractions chapter. Chapter overview · whole chapter on one page
Dividing fractions by whole numbers
Sharing a fraction between people is a division. Look at the picture. 13 of the bar is shaded. If we share it equally between 2 people, each person gets half of that shaded part. The bottom bar is cut into 6 parts, and one part is each share: 16.
So when you divide a fraction by a whole number, multiply the bottom number by that whole number. The top number stays the same. Then simplify if you can.
Key ideas
- Dividing by a whole number makes the fraction smaller.
- To divide a fraction by a whole number, multiply the bottom number by it: 13 ÷ 2 = 16.
- If the top number divides exactly by the whole number, you can divide the top instead: 68 ÷ 2 = 38.
- Check your answer by multiplying it back by the whole number.
Key words. Dividing by a whole number shares a fraction into equal parts. Each part is smaller, so the answer is a smaller fraction.
Method. Dividing by a whole number makes the bottom number bigger. Multiply the bottom, keep the top, then simplify.
- Write the division. We are sharing the fraction into 2 equal parts.13 ÷ 2
- Multiply the bottom number by the whole number. Each piece is cut into smaller parts, so the bottom gets bigger. The top stays the same.13 ÷ 2 = 16
- Check that it cannot be simplified. The top and the bottom have no common factor except 1.16 is in its simplest form
Check. 16 × 2 = 13. ✓
Watch out. When the top divides exactly by the whole number, you can divide the top instead.
Key words. Dividing by a whole number shares a fraction into equal parts. Each part is smaller, so the answer is a smaller fraction.
Method. Dividing by a whole number makes the bottom number bigger. Multiply the bottom, keep the top, then simplify.
- Write the division. We are sharing the fraction into 3 equal parts.34 ÷ 3
- Multiply the bottom number by the whole number. Each piece is cut into smaller parts, so the bottom gets bigger. The top stays the same.34 ÷ 3 = 312
- Simplify. Divide the top and the bottom by their HCF, 3.312 = 14
Check. 14 × 3 = 34. ✓
Watch out. When the top divides exactly by the whole number, you can divide the top instead.
Key words. Dividing by a whole number shares a fraction into equal parts. Each part is smaller, so the answer is a smaller fraction.
Method. Dividing by a whole number makes the bottom number bigger. Multiply the bottom, keep the top, then simplify.
- Write the division. We are sharing the fraction into 4 equal parts.25 ÷ 4
- Multiply the bottom number by the whole number. Each piece is cut into smaller parts, so the bottom gets bigger. The top stays the same.25 ÷ 4 = 220
- Simplify. Divide the top and the bottom by their HCF, 2.220 = 110
Check. 110 × 4 = 25. ✓
Watch out. When the top divides exactly by the whole number, you can divide the top instead.
Watch out
Do not multiply the top number when you divide. 13 ÷ 2 is 16, not 23. Dividing makes the answer smaller, so it must be less than the fraction you started with.Exercise 4F Dividing fractions by whole numbers
Non-calculatorKey words. Dividing by a whole number shares a fraction into equal parts. Each part is smaller, so the answer is a smaller fraction.
Method. Dividing by a whole number makes the bottom number bigger. Multiply the bottom, keep the top, then simplify.
- Write the division. We are sharing the fraction into 2 equal parts.13 ÷ 2
- Multiply the bottom number by the whole number. Each piece is cut into smaller parts, so the bottom gets bigger. The top stays the same.13 ÷ 2 = 16
- Check that it cannot be simplified. The top and the bottom have no common factor except 1.16 is in its simplest form
Check. 16 × 2 = 13. ✓
Watch out. When the top divides exactly by the whole number, you can divide the top instead.
Key words. Dividing by a whole number shares a fraction into equal parts. Each part is smaller, so the answer is a smaller fraction.
Method. Dividing by a whole number makes the bottom number bigger. Multiply the bottom, keep the top, then simplify.
- Write the division. We are sharing the fraction into 3 equal parts.34 ÷ 3
- Multiply the bottom number by the whole number. Each piece is cut into smaller parts, so the bottom gets bigger. The top stays the same.34 ÷ 3 = 312
- Simplify. Divide the top and the bottom by their HCF, 3.312 = 14
Check. 14 × 3 = 34. ✓
Watch out. When the top divides exactly by the whole number, you can divide the top instead.
Key words. Dividing by a whole number shares a fraction into equal parts. Each part is smaller, so the answer is a smaller fraction.
Method. Dividing by a whole number makes the bottom number bigger. Multiply the bottom, keep the top, then simplify.
- Write the division. We are sharing the fraction into 4 equal parts.25 ÷ 4
- Multiply the bottom number by the whole number. Each piece is cut into smaller parts, so the bottom gets bigger. The top stays the same.25 ÷ 4 = 220
- Simplify. Divide the top and the bottom by their HCF, 2.220 = 110
Check. 110 × 4 = 25. ✓
Watch out. When the top divides exactly by the whole number, you can divide the top instead.
Key words. Dividing by a whole number shares a fraction into equal parts. Each part is smaller, so the answer is a smaller fraction.
Method. Dividing by a whole number makes the bottom number bigger. Multiply the bottom, keep the top, then simplify.
- Write the division. We are sharing the fraction into 5 equal parts.56 ÷ 5
- Multiply the bottom number by the whole number. Each piece is cut into smaller parts, so the bottom gets bigger. The top stays the same.56 ÷ 5 = 530
- Simplify. Divide the top and the bottom by their HCF, 5.530 = 16
Check. 16 × 5 = 56. ✓
Watch out. When the top divides exactly by the whole number, you can divide the top instead.
Key words. Dividing by a whole number shares a fraction into equal parts. Each part is smaller, so the answer is a smaller fraction.
Method. Dividing by a whole number makes the bottom number bigger. Multiply the bottom, keep the top, then simplify.
- Write the division. We are sharing the fraction into 3 equal parts.38 ÷ 3
- Multiply the bottom number by the whole number. Each piece is cut into smaller parts, so the bottom gets bigger. The top stays the same.38 ÷ 3 = 324
- Simplify. Divide the top and the bottom by their HCF, 3.324 = 18
Check. 18 × 3 = 38. ✓
Watch out. When the top divides exactly by the whole number, you can divide the top instead.
Key words. Dividing by a whole number shares a fraction into equal parts. Each part is smaller, so the answer is a smaller fraction.
Method. Dividing by a whole number makes the bottom number bigger. Multiply the bottom, keep the top, then simplify.
- Write the division. We are sharing the fraction into 2 equal parts.49 ÷ 2
- Multiply the bottom number by the whole number. Each piece is cut into smaller parts, so the bottom gets bigger. The top stays the same.49 ÷ 2 = 418
- Simplify. Divide the top and the bottom by their HCF, 2.418 = 29
Check. 29 × 2 = 49. ✓
Watch out. When the top divides exactly by the whole number, you can divide the top instead.
Key words. Dividing by a whole number shares a fraction into equal parts. Each part is smaller, so the answer is a smaller fraction.
Method. Dividing by a whole number makes the bottom number bigger. Multiply the bottom, keep the top, then simplify.
- Write the division. We are sharing the fraction into 4 equal parts.23 ÷ 4
- Multiply the bottom number by the whole number. Each piece is cut into smaller parts, so the bottom gets bigger. The top stays the same.23 ÷ 4 = 212
- Simplify. Divide the top and the bottom by their HCF, 2.212 = 16
Check. 16 × 4 = 23. ✓
Watch out. When the top divides exactly by the whole number, you can divide the top instead.
Key words. Dividing by a whole number shares a fraction into equal parts. Each part is smaller, so the answer is a smaller fraction.
Method. Dividing by a whole number makes the bottom number bigger. Multiply the bottom, keep the top, then simplify.
- Write the division. We are sharing the fraction into 5 equal parts.58 ÷ 5
- Multiply the bottom number by the whole number. Each piece is cut into smaller parts, so the bottom gets bigger. The top stays the same.58 ÷ 5 = 540
- Simplify. Divide the top and the bottom by their HCF, 5.540 = 18
Check. 18 × 5 = 58. ✓
Watch out. When the top divides exactly by the whole number, you can divide the top instead.
Key words. Dividing by a whole number shares a fraction into equal parts. Each part is smaller, so the answer is a smaller fraction.
Method. Dividing by a whole number makes the bottom number bigger. Multiply the bottom, keep the top, then simplify.
- Write the division. We are sharing the fraction into 2 equal parts.67 ÷ 2
- Multiply the bottom number by the whole number. Each piece is cut into smaller parts, so the bottom gets bigger. The top stays the same.67 ÷ 2 = 614
- Simplify. Divide the top and the bottom by their HCF, 2.614 = 37
Check. 37 × 2 = 67. ✓
Watch out. When the top divides exactly by the whole number, you can divide the top instead.
Key words. Dividing by a whole number shares a fraction into equal parts. Each part is smaller, so the answer is a smaller fraction.
Method. Dividing by a whole number makes the bottom number bigger. Multiply the bottom, keep the top, then simplify.
- Write the division. We are sharing the fraction into 6 equal parts.310 ÷ 6
- Multiply the bottom number by the whole number. Each piece is cut into smaller parts, so the bottom gets bigger. The top stays the same.310 ÷ 6 = 360
- Simplify. Divide the top and the bottom by their HCF, 3.360 = 120
Check. 120 × 6 = 310. ✓
Watch out. When the top divides exactly by the whole number, you can divide the top instead.
Key words. Dividing by a whole number shares a fraction into equal parts. Each part is smaller, so the answer is a smaller fraction.
Method. Dividing by a whole number makes the bottom number bigger. Multiply the bottom, keep the top, then simplify.
- Write the division. We are sharing the fraction into 3 equal parts.12 ÷ 3
- Multiply the bottom number by the whole number. Each piece is cut into smaller parts, so the bottom gets bigger. The top stays the same.12 ÷ 3 = 16
- Check that it cannot be simplified. The top and the bottom have no common factor except 1.16 is in its simplest form
Check. 16 × 3 = 12. ✓
Watch out. When the top divides exactly by the whole number, you can divide the top instead.
Key words. Dividing by a whole number shares a fraction into equal parts. Each part is smaller, so the answer is a smaller fraction.
Method. Dividing by a whole number makes the bottom number bigger. Multiply the bottom, keep the top, then simplify.
- Write the division. We are sharing the fraction into 2 equal parts.35 ÷ 2
- Multiply the bottom number by the whole number. Each piece is cut into smaller parts, so the bottom gets bigger. The top stays the same.35 ÷ 2 = 310
- Check that it cannot be simplified. The top and the bottom have no common factor except 1.310 is in its simplest form
Check. 310 × 2 = 35. ✓
Watch out. When the top divides exactly by the whole number, you can divide the top instead.
Key words. Dividing by a whole number shares a fraction into equal parts. Each part is smaller, so the answer is a smaller fraction.
Method. Dividing by a whole number makes the bottom number bigger. Multiply the bottom, keep the top, then simplify.
- Write the division. We are sharing the fraction into 4 equal parts.47 ÷ 4
- Multiply the bottom number by the whole number. Each piece is cut into smaller parts, so the bottom gets bigger. The top stays the same.47 ÷ 4 = 428
- Simplify. Divide the top and the bottom by their HCF, 4.428 = 17
Check. 17 × 4 = 47. ✓
Watch out. When the top divides exactly by the whole number, you can divide the top instead.
Key words. Dividing by a whole number shares a fraction into equal parts. Each part is smaller, so the answer is a smaller fraction.
Method. Dividing by a whole number makes the bottom number bigger. Multiply the bottom, keep the top, then simplify.
- Write the division. We are sharing the fraction into 3 equal parts.34 ÷ 3
- Multiply the bottom number by the whole number. Each piece is cut into smaller parts, so the bottom gets bigger. The top stays the same.34 ÷ 3 = 312
- Simplify. Divide the top and the bottom by their HCF, 3.312 = 14
Check. 14 × 3 = 34. ✓
Watch out. When the top divides exactly by the whole number, you can divide the top instead.
Key words. Dividing by a whole number shares a fraction into equal parts. Each part is smaller, so the answer is a smaller fraction.
Method. Dividing by a whole number makes the bottom number bigger. Multiply the bottom, keep the top, then simplify.
- Write the division. We are sharing the fraction into 4 equal parts.23 ÷ 4
- Multiply the bottom number by the whole number. Each piece is cut into smaller parts, so the bottom gets bigger. The top stays the same.23 ÷ 4 = 212
- Simplify. Divide the top and the bottom by their HCF, 2.212 = 16
Check. 16 × 4 = 23. ✓
Watch out. When the top divides exactly by the whole number, you can divide the top instead.
Key words. Dividing by a whole number shares a fraction into equal parts. Each part is smaller, so the answer is a smaller fraction.
Method. Dividing by a whole number makes the bottom number bigger. Multiply the bottom, keep the top, then simplify.
- Write the division. We are sharing the fraction into 3 equal parts.25 ÷ 3
- Multiply the bottom number by the whole number. Each piece is cut into smaller parts, so the bottom gets bigger. The top stays the same.25 ÷ 3 = 215
- Check that it cannot be simplified. The top and the bottom have no common factor except 1.215 is in its simplest form
Check. 215 × 3 = 25. ✓
Watch out. When the top divides exactly by the whole number, you can divide the top instead.
Key words. Dividing by a whole number shares a fraction into equal parts. Each part is smaller, so the answer is a smaller fraction.
Method. Dividing by a whole number makes the bottom number bigger. Multiply the bottom, keep the top, then simplify.
- Write the division. We are sharing the fraction into 2 equal parts.68 ÷ 2
- Multiply the bottom number by the whole number. Each piece is cut into smaller parts, so the bottom gets bigger. The top stays the same.68 ÷ 2 = 616
- Simplify. Divide the top and the bottom by their HCF, 2.616 = 38
Check. 38 × 2 = 68. ✓
Watch out. When the top divides exactly by the whole number, you can divide the top instead.
Key words. Dividing by a whole number shares a fraction into equal parts. Each part is smaller, so the answer is a smaller fraction.
Method. Work out each side separately. Dividing by 2 and multiplying by a half are the same thing.
- Work out Ben’s answer. Divide the fraction by 2.12 ÷ 2 = 14
- Work out Lily’s answer. Multiply the fraction by one half.12 × 12 = 14
- Compare them. Both answers are the same.Both are right: 14
Check. Dividing by 2 and multiplying by 1/2 always give the same answer. ✓
Watch out. Dividing by a whole number is the same as multiplying by its unit fraction.
Key words. Dividing by a whole number shares a fraction into equal parts. Each part is smaller, so the answer is a smaller fraction.
Method. Test some examples, then explain why the answer is always smaller.
- Try some examples. Divide each proper fraction by a whole number and compare.34 ÷ 2 = 38, which is smaller than 34
25 ÷ 3 = 215, which is smaller than 25 - Explain why. Each piece is cut into smaller parts, so each part is smaller than the whole fraction.A proper fraction is less than 1, so a part of it is smaller still
- Decide. The rule works for every proper fraction and every whole number, so it is always true.Always
Check. 34 ÷ 2 = 38, which is smaller than 34. ✓
Watch out. Each share is a part of the fraction, so it is always smaller than the fraction you started with.
Key words. Dividing by a whole number shares a fraction into equal parts. Each part is smaller, so the answer is a smaller fraction.
Method. Undo the division. Multiplying by 4 is the opposite of dividing by 4.
- Multiply the answer by 4 to find the original. This undoes the division.316 × 4 = 1216
- Simplify. Divide the top and bottom by their HCF, 4.1216 = 34
Check. 34 ÷ 4 = 316. ✓
Watch out. Check your answer by doing the division you were given.