Fractions · Ages 10–11
Bar models for fraction problems worksheet
Part of: Multiplying and dividing fractions
In the print window, choose “Save as PDF” to download it. The answers print on the last page.
Bar models for fraction problems worksheet
Fractions · Ages 10–11
Numsprite
numsprite.com
Name:Date:Score:／48
Write each answer in the space. For word problems, show your working and write a sentence answer.
Part A: Working out and filling in (2 marks each)
1.Ka-yan spent 35 of the pocket money and has $28 left. How many dollars is each cell of the bar model worth?
Answer:
2.May spent 45 of the pocket money and has $2 left. How many dollars did May have to begin with?
Answer:
3.Ka-lok spent 58 of the pocket money and has $9 left. How many dollars is each cell of the bar model worth?
Answer:
4.Chi-keung spent 110 of the pocket money and has $18 left. How many dollars did Chi-keung have to begin with?
Answer:
5.A has 27 as many stickers as B. B has 15 more than A. How many stickers does A have?
Answer:
6.A and B have 144 marbles altogether, and A has 57 as many as B. A has marbles and B has .
Fill in each blank
Answer:
7.A has 110 as many stickers as B. B has 18 more than A. How many stickers does A have?
Answer:
8.Tsz-ching has some stickers, gives away 23 of them, then 12 of the rest, and has 1 left. How many stickers did Tsz-ching have to begin with?
Answer:
9.Tsz-ching has some stickers, gives away 23 of them, then 13 of the rest, and has 12 left. How many stickers did Tsz-ching have to begin with?
Answer:
Part B: Choose, or true or false (2 marks each)
10.A is 23 of B, and B is 11 more than A. So A is 22.
True or false?
Answer:
11.Which bar model shows “A is 35 of B”?
- A
- B
- C
- D
Choose the right picture
Answer:
12.Which bar model shows “A is 13 of B”?
- A
- B
- C
- D
Choose the right picture
Answer:
Part C: Word problems (4 marks each)
13.In a bakery, there are 710 as many lotus seed mooncakes as double-yolk ones, and 36 more double-yolk ones. How many lotus seed mooncakes are there?
Working:
Answer:
14.Tsz-hin reads a storybook: 25 of it on the first day and 15 of the rest on the second, with 84 pages still to read. How many pages does the book have?
Working:
Answer:
15.After using 45 of the money on May's Octopus card, $3 is left. How many dollars were on the card to begin with?
Working:
Answer:
16.A cha chaan teng sells 90 cups of milk tea in the morning and afternoon together. The morning's is 27 of the afternoon's. How many cups were sold in the afternoon?
Working:
Answer:
17.Tsz-ching has 78 as many stickers as Ka-lok. After Ka-lok gives Tsz-ching 2 stickers, they have the same number. How many stickers did Ka-lok have to begin with?
Working:
Answer:
18.A cha chaan teng sells 180 cups of milk tea in the morning and afternoon together. The morning's is 57 of the afternoon's. How many cups were sold in the afternoon?
Working:
Answer:
Show the answers and working
Bar models for fraction problems worksheet: Answers and working
Part A: Working out and filling in
1. 14 dollars
The bar has 5 cells and 3 are spent. Count the cells left first: together they are worth $28.
5 cells in all, 3 used (dashed), so the 2 left are 28: 28 ÷ 2 = 14.
2. 10 dollars
The 1 cells left are worth $2. Find what 1 cell is worth first.
The 1 cells left are 2, so 1 cell is 2; all 5 cells: 2 × 5 = 10.
3. 3 dollars
The bar has 8 cells and 5 are spent. Count the cells left first: together they are worth $9.
8 cells in all, 5 used (dashed), so the 3 left are 9: 9 ÷ 3 = 3.
4. 20 dollars
The 9 cells left are worth $18. Find what 1 cell is worth first.
The 9 cells left are 18, so 1 cell is 2; all 10 cells: 2 × 10 = 20.
5. 6 stickers
Draw B as 7 cells and A as 2. How many cells do B's 15 extra stickers cover?
B is 7 cells and A 2; the 5 extra cells are 15, so 1 cell is 3; A's 2 cells: 6.
6. 60, 84
Draw A as 5 cells and B as 7. How many cells do the 144 marbles cover in all?
A is 5 cells and B 7, 12 cells in all are 144: 1 cell is 12; A 60, B 84.
7. 2 stickers
Draw B as 10 cells and A as 1. How many cells do B's 18 extra stickers cover?
B is 10 cells and A 1; the 9 extra cells are 18, so 1 cell is 2; A's 1 cells: 2.
8. 6 stickers
Work backwards: what fraction of the stickers left after the first gift are the final 1?
Once you know how many were left after the first gift, ask what fraction of the whole that is.
Work backwards: after the second gift, 2 − 12 of the rest is left, so the rest was 2; 2 is 3 − 23 of the whole, so the whole was 6.
9. 54 stickers
Work backwards: what fraction of the stickers left after the first gift are the final 12?
Once you know how many were left after the first gift, ask what fraction of the whole that is.
Work backwards: after the second gift, 3 − 13 of the rest is left, so the rest was 18; 18 is 3 − 23 of the whole, so the whole was 54.
Part B: Choose, or true or false
10. True
Draw B as 3 cells and A as 2. How many cells is the gap of 11? Find 1 cell, then work out A to check 22.
B is 3 cells and A 2; the 1 between them are 11, so 1 cell is 11: A is 2 × 11 = 22.
11. B
Find B's bar first: “35 of B” means splitting B into how many equal cells?
“A is 35 of B”: B is 5 equal cells, and A is 3 of those cells.
12. B
Find B's bar first: “13 of B” means splitting B into how many equal cells?
“A is 13 of B”: B is 3 equal cells, and A is 1 of those cells.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. 84 mooncakes
Draw the double-yolk mooncakes as 10 cells and the lotus seed ones as 7. How many cells are the 36 extra?
Double-yolk 10 cells, lotus seed 7: the 3 between them are 36, so 1 cell is 12, and lotus seed is 7 × 12 = 84.
14. 175 pages
Work backwards: what fraction of the pages left after day one are the 84 still to read?
Once you have the pages left after day one, ask what fraction of the whole book they are.
The 84 pages left are 5 − 15 of the rest, so the rest was 105; 105 is 5 − 25 of the book, so the book has 175.
15. 15 dollars
5 cells in all, 4 used. How many cells is the $3 left? Find 1 cell first.
5 cells in all, 4 used: the 1 left are 3, so 1 cell is 3 and all of it 3 × 5 = 15.
16. 70 cups
Draw the afternoon as 7 cells and the morning as 2. How many cells do the 90 cups cover in all?
Afternoon 7 cells, morning 2, 9 cells together are 90: 1 cell is 10, and the afternoon 7 × 10 = 70.
17. 32 stickers
Draw Ka-lok as 8 cells and Tsz-ching as 7: 1 cells apart. If giving 2 evens them up, how many times 2 was the gap?
Ka-lok is 8 cells, Tsz-ching 7: 1 cells apart. Giving 2 evens them up, so the gap is 2 × 2: 1 cells, 1 cell is 4; Ka-lok had 8 × 4 = 32.
18. 105 cups
Draw the afternoon as 7 cells and the morning as 5. How many cells do the 180 cups cover in all?
Afternoon 7 cells, morning 5, 12 cells together are 180: 1 cell is 15, and the afternoon 7 × 15 = 105.
Numsprite · numsprite.com/en/worksheets/multiplying-and-dividing-fractions/fraction-bar-models
Practise it in the gameBar models for fraction problems · Unlimited questions, no download