Fractions · Ages 10–11

From a part to the whole (unitary method) worksheet

Part of: Multiplying and dividing fractions

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Fractions · Ages 10–11

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Write each answer in the space. For word problems, show your working and write a sentence answer.

1.19 of a number is 19. What is 29 of the number?
Answer:
2.15 of a number is 7. What is the number?
Answer:
3.35 of a number is 21. What is the number?
Answer:
4.13 of a number is 23. What is 23 of the number?
Answer:
5.13 kg of sugar costs $10. How much does 25 kg cost?
Answer:
6.23 kg of apples costs $26. How much is 1 kg?
Answer:
7.29 of a number is 38. 19 of the number is , and the number is .
Fill in each blank
Answer:
8.12 kg of sugar costs $25. How much does 35 kg cost?
Answer:
9.12 kg of apples costs $9. How much is 1 kg?
Answer:
10.512 of a number is 85. 112 of the number is , and the number is .
Fill in each blank
Answer:

13.12 of a barrel of water is 3 litres. How many litres is 13 of the barrel?
Working:
Answer:
14.Ka-yee builds 2 models in 12 hour. At that rate, how many can Ka-yee build in 4 hours?
Working:
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15.Ka-lok spends 15 of Ka-lok's pocket money on books: $6. How many dollars are left?
Working:
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16.Tsz-ching has read 18 of a storybook, 17 pages. How many pages does the book have?
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Answer:
17.47 of a sports club's members are women, and there are 8 women. How many men are there?
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Answer:
18.Tsz-hin builds 18 models in 34 hour. At that rate, how many can Tsz-hin build in 5 hours?
Working:
Answer:

Show the answers and working

From a part to the whole (unitary method) worksheet: Answers and working

1. 38
19 is one part, and 29 is 2 of those parts.
1 part is 19, so 2 parts are 19 × 2 = 38.
2. 35
1 parts are 7. Find what 1 part is first.
1 parts are 7, so 1 part is 7 ÷ 1 = 7, and 5 parts are 7 × 5 = 35.
3. 35
3 parts are 21. Find what 1 part is first.
3 parts are 21, so 1 part is 21 ÷ 3 = 7, and 5 parts are 7 × 5 = 35.
4. 46
13 is one part, and 23 is 2 of those parts.
1 part is 23, so 2 parts are 23 × 2 = 46.
5. 12 dollars
Find the price of 1 kg first: 10 ÷ 13.
Find 1 kg first: 10 ÷ 13; then × 25: $12.
6. 39 dollars
23 kg is 2 lots of 13 kg. Find the price of 13 kg first.
26 ÷ 23 = 26 × 32 = 39; or 13 kg costs 13, so 1 kg costs 13 × 3.
7. 19, 171
2 parts are 38, and 19 of the number is one part. Into how many equal parts should 38 be split?
2 parts are 38: 1 part is 38 ÷ 2 = 19; 9 parts are 171.
8. 30 dollars
Find the price of 1 kg first: 25 ÷ 12.
Find 1 kg first: 25 ÷ 12; then × 35: $30.
9. 18 dollars
12 kg is 1 lots of 12 kg. Find the price of 12 kg first.
9 ÷ 12 = 9 × 21 = 18; or 12 kg costs 9, so 1 kg costs 9 × 2.
10. 17, 204
5 parts are 85, and 112 of the number is one part. Into how many equal parts should 85 be split?
5 parts are 85: 1 part is 85 ÷ 5 = 17; 12 parts are 204.

11. A. 28 ÷ 23
Call the number □: □ × 23 = 28. Knowing a product and one factor, which operation finds the other?
The number × 23 = 28, so the number = 28 ÷ 23 (that is, 28 ÷ 2 × 3).
12. C. 112 ÷ 89
Call the number □: □ × 89 = 112. Knowing a product and one factor, which operation finds the other?
The number × 89 = 112, so the number = 112 ÷ 89 (that is, 112 ÷ 8 × 9).

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 2 litres
3 litres is 12 of the barrel. Find the whole barrel first.
The whole barrel first: 3 ÷ 12 = 6; then 13 of it: 6 × 13 = 2 litres.
14. 16 models
Find how many Ka-yee builds in 1 hour first: 2 ÷ 12.
In 1 hour: 2 ÷ 12 = 2 × 21; in 4 hours, × 4: 16.
15. 24 dollars
1 parts are $6. Find 1 part first, then think how many parts are left.
1 part is 6 ÷ 1 = 6, the whole 30; left: 30 − 6 = 24.
16. 136 pages
1 parts are 17 pages. Find what 1 part is first.
1 parts are 17 pages, 1 part is 17, and the book is 8 parts: 136 pages.
17. 6 men
4 parts are 8 women. Find 1 part first: how many parts are men?
4 parts are 8, so 1 part is 2; men are 7 − 4 parts: 6.
18. 120 models
Find how many Tsz-hin builds in 1 hour first: 18 ÷ 34.
In 1 hour: 18 ÷ 34 = 18 × 43; in 5 hours, × 5: 120.

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