Multiplying, dividing and mixed operations · Ages 9–10

Taking out a common factor; square brackets worksheet

Part of: The distributive property and mixed operations

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Multiplying, dividing and mixed operations · Ages 9–10

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

1.[31 − (10 + 9)] × 5 =
Answer:
2.20 + 28 = 4 × ( + )
Fill in each blank
Answer:
3.36 + 40 = 4 × ( + )
Fill in each blank
Answer:
4.120 + 72 = × (10 + 6)
Answer:
5.[(2 + 2) × 5 − 4] ÷ 4 =
Answer:
6.Using the highest common factor, write 63 + 108 as × ( + ).
Fill in each blank
Answer:
7.[(12 + 4) × 6 − 8] ÷ 8 =
Answer:
8.Using the highest common factor, write 6 + 16 as × ( + ).
Fill in each blank
Answer:
9.20 + 35 + 15 = 5 ×
Answer:
10.36 + 63 + 72 = 9 ×
Answer:

13.Tsz-hin has $43, buys a $10 book and a $13 pen, and shares the rest equally among 4 charity boxes. How much goes in each box?
Working:
Answer:
14.A factory makes 71 toys a day, 7 of them damaged. After 6 days, the undamaged toys are packed equally into 2 boxes. How many are in each box?
Working:
Answer:
15.Tsz-hin has 28 red beads and 63 blue beads to make identical bracelets, using them all: every bracelet has the same number of red beads and the same number of blue. At most bracelets can be made, with beads on each.
Fill in each blank
Working:
Answer:
16.Ka-yan has $173, buys a $32 book and a $27 pen, and shares the rest equally among 6 charity boxes. How much goes in each box?
Working:
Answer:
17.A factory makes 30 toys a day, 8 of them damaged. After 6 days, the undamaged toys are packed equally into 12 boxes. How many are in each box?
Working:
Answer:
18.Ka-lok has 45 red beads and 54 blue beads to make identical bracelets, using them all: every bracelet has the same number of red beads and the same number of blue. At most bracelets can be made, with beads on each.
Fill in each blank
Working:
Answer:

Show the answers and working

Taking out a common factor; square brackets worksheet: Answers and working

1. 60
Start with the innermost round brackets: 10 + 9 first.
Round brackets first: 10 + 9 = 19; then the square brackets: 31 − 19 = 12; then 12 × 5 = 60.
2. 5, 7
20 and 28 are both multiples of 4. How many 4s make 20? And 28?
20 = 4 × 5 and 28 = 4 × 7; take out the 4: 4 × (5 + 7).
3. 9, 10
36 and 40 are both multiples of 4. How many 4s make 36? And 40?
36 = 4 × 9 and 40 = 4 × 10; take out the 4: 4 × (9 + 10).
4. 12
Which number times 10 gives 120, and times 6 gives 72?
120 ÷ 10 = 12 and 72 ÷ 6 = 12: the common factor taken out is 12.
5. 4
Work from the inside out: the round brackets, 2 + 2, first, then times 5.
2 + 2 = 4, 4 × 5 = 20, 20 − 4 = 16, 16 ÷ 4 = 4.
6. 9, 7, 12
List the factors of 63 and 108, and find the biggest one they share.
The highest common factor of 63 and 108 is 9: 63 = 9 × 7, 108 = 9 × 12, and 7 and 12 share no factor.
7. 11
Work from the inside out: the round brackets, 12 + 4, first, then times 6.
12 + 4 = 16, 16 × 6 = 96, 96 − 8 = 88, 88 ÷ 8 = 11.
8. 2, 3, 8
List the factors of 6 and 16, and find the biggest one they share.
The highest common factor of 6 and 16 is 2: 6 = 2 × 3, 16 = 2 × 8, and 3 and 8 share no factor.
9. 14
20, 35 and 15 are all multiples of 5. How many 5s is each?
20 = 5 × 4, 35 = 5 × 7, 15 = 5 × 3: 5 × (4 + 7 + 3) = 5 × 14.
10. 19
36, 63 and 72 are all multiples of 9. How many 9s is each?
36 = 9 × 4, 63 = 9 × 7, 72 = 9 × 8: 9 × (4 + 7 + 8) = 9 × 19.

11. B. 2 × (4 + 5)
8 and 10 can both be written as 2 times a number. Times what, each?
8 = 2 × 4 and 10 = 2 × 5, so 8 + 10 = 2 × (4 + 5) = 18.
12. True
Divide 56 and 96 each by 8 and see what belongs in the brackets.
56 ÷ 8 = 7 and 96 ÷ 8 = 12: the bracket should be 7 + 12.

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

13. 5 dollars
First add what the book and pen cost, 10 + 13, then see how much is left.
[43 − (10 + 13)] ÷ 4 = [43 − 23] ÷ 4 = 20 ÷ 4 = 5.
14. 192 toys
First find how many toys a day are undamaged: 71 − 7.
[(71 − 7) × 6] ÷ 2 = [64 × 6] ÷ 2 = 384 ÷ 2 = 192.
15. 7, 13
The number of bracelets must divide both 28 and 63. Find their highest common factor.
The highest common factor of 28 and 63 is 7: 28 + 63 = 7 × (4 + 9), so 7 bracelets of 13 beads.
16. 19 dollars
First add what the book and pen cost, 32 + 27, then see how much is left.
[173 − (32 + 27)] ÷ 6 = [173 − 59] ÷ 6 = 114 ÷ 6 = 19.
17. 11 toys
First find how many toys a day are undamaged: 30 − 8.
[(30 − 8) × 6] ÷ 12 = [22 × 6] ÷ 12 = 132 ÷ 12 = 11.
18. 9, 11
The number of bracelets must divide both 45 and 54. Find their highest common factor.
The highest common factor of 45 and 54 is 9: 45 + 54 = 9 × (5 + 6), so 9 bracelets of 11 beads.

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