Multiplying, dividing and mixed operations · Ages 9–10
The distributive property and mixed operations worksheet
Covers: The distributive property, ×9 and ×99, Taking out a common factor; square brackets, Mixed-operation shortcuts, Unitary method: finding one first, Grandmaster mix
In the print window, choose “Save as PDF” to download it. The answers print on the last page.
The distributive property and mixed operations worksheet
Multiplying, dividing and mixed operations · Ages 9–10
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.Work out: 98 × 43 =
Answer:
2.Work out: 73 × 48 + 48 × 27 =
Answer:
3.80 × 99
Answer:
4.16 × 99
Answer:
5.[20 − (4 + 2)] × 2 =
Answer:
6.(3 + 12) × 9
Answer:
7.21 × 5 + 14
Answer:
8.7 kites cost $119. How much do 11 cost?
Answer:
9.22 × 9 − 16
Answer:
10.35 × 5 − 57
Answer:
Part B: Choose, or true or false (2 marks each)
11.Which of these is equal to 35 + 20?
- A. 5 × (7 + 20)
- B. 5 × (7 + 4)
- C. 5 + (7 + 4)
- D. 5 × 7 + 4
Choose the right answer
Answer:
12.2 notebooks cost $48, so 4 cost $50.
True or false?
Answer:
Part C: Word problems (4 marks each)
13.Ka-yan runs 675 m every morning and 625 m every evening. How far does Ka-yan run in 23 days?
Working:
Answer:
14.Sports shirts cost $99 each. A sports club buys 97 for its basketball team. How many dollars must it pay?
Working:
Answer:
15.A factory makes 42 toys a day, 4 of them damaged. After 5 days, the undamaged toys are packed equally into 5 boxes. How many are in each box?
Working:
Answer:
16.Tsz-hin saves $25 a week. After 9 weeks, he buys a pair of trainers for $132. How many dollars does he have left?
Working:
Answer:
17.A car goes 36 km on 3 litres of petrol. At that rate, how far does it go on 11 litres?
Working:
Answer:
18.Ka-yee has three boxes of 67 sweets each and a bag of 67 sweets. She shares all the sweets equally among 4 children. How many sweets does each child get?
Working:
Answer:
Show the answers and working
The distributive property and mixed operations worksheet: Answers and working
Part A: Working out and filling in
1. 4214
98 is close to 100. Work out 100 × 43 first, then think how to adjust.
98 = 100 − 2, so 98 × 43 = 100 × 43 − 2 × 43 = 4300 − 86 = 4214.
2. 4800
73 × 48 is the same as 48 × 73, so both parts are times 48. Now look at 73 and 27.
73 × 48 = 48 × 73, so both parts are times 48: 48 × (73 + 27) = 48 × 100 = 4800.
3. 80 × 99 = 7920
80 × 99: ×99 is ×100 minus one lot, 80 × 100 = 8000, 8000 − 80 = 7920
4. 16 × 99 = 1584
16 × 99: ×99 is ×100 minus one lot, 16 × 100 = 1600, 1600 − 16 = 1584
5. 28
Start with the innermost round brackets: 4 + 2 first.
Round brackets first: 4 + 2 = 6; then the square brackets: 20 − 6 = 14; then 14 × 2 = 28.
6. (3 + 12) × 9 = 135
(3 + 12) × 9: brackets first, 3 + 12 = 15, 15 × 9 = 135
7. 21 × 5 + 14 = 119
21 × 5 + 14: × and ÷ before + and −, 21 × 5 = 105, 105 + 14 = 119
8. 187 dollars
Find the price of one first: share $119 equally into 7.
One: 119 ÷ 7 = $17; 11: 17 × 11 = $187.
9. 22 × 9 − 16 = 182
22 × 9 − 16: × and ÷ before + and −, 22 × 9 = 198, 198 − 16 = 182
10. 35 × 5 − 57 = 118
35 × 5 − 57: × and ÷ before + and −, 35 × 5 = 175, 175 − 57 = 118
Part B: Choose, or true or false
11. B. 5 × (7 + 4)
35 and 20 can both be written as 5 times a number. Times what, each?
35 = 5 × 7 and 20 = 5 × 4, so 35 + 20 = 5 × (7 + 4) = 55.
12. False
Find the price of one, work out what 4 of them cost, and compare with $50.
One costs 48 ÷ 2 = $24, so 4 cost 24 × 4 = $96. 2 more items is 2 more items' worth, not $2 more.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. 29900 m
Find one day's distance first: 675 m in the morning plus 625 m in the evening.
675 + 625 m a day, so 23 × (675 + 625) = 29900 m.
14. Sports shirts cost $99 each. A sports club buys 97 for its basketball team. How many dollars must it pay? (Answer: 9603 dollars)
100 × 97 − 97 = 9603
15. 38 toys
First find how many toys a day are undamaged: 42 − 4.
[(42 − 4) × 5] ÷ 5 = [38 × 5] ÷ 5 = 190 ÷ 5 = 38.
16. Tsz-hin saves $25 a week. After 9 weeks, he buys a pair of trainers for $132. How many dollars does he have left? (Answer: 93 dollars)
25 × 9 − 132 = 93
17. 132 km
Find how far 1 litre goes first: 36 ÷ 3.
1 litre: 36 ÷ 3 = 12 km; 11 litres: 12 × 11 = 132 km.
18. Ka-yee has three boxes of 67 sweets each and a bag of 67 sweets. She shares all the sweets equally among 4 children. How many sweets does each child get? (Answer: 67 sweets)
3 × 67 = 201; (3 × 67 + 67) ÷ 4 = 67
Numsprite · numsprite.com/en/worksheets/distributive-property-and-mixed-operations
Practise it in the gameThe distributive property and mixed operations · Unlimited questions, no download