Multiplying, dividing and mixed operations · Ages 7–8

Commutative property: multiplying in either order worksheet

Part of: Multiplication and times tables

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Multiplying, dividing and mixed operations · Ages 7–8

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

1.Across, there are 3 rows of 7: 7 × 3 = . Down, there are 7 columns of 3: 3 × 7 = .
Fill in each blank
Answer:
2.4 × 7 = 7 ×
Answer:
3.10 × 9 = 9 ×
Answer:
4.Across, there are 2 rows of 7: 7 × 2 = . Down, there are 7 columns of 2: 2 × 7 = .
Fill in each blank
Answer:
5.You know 6 × 3 = 18. 3 × 6 =
Answer:
6.You know 7 × 4 = 28. 4 × 7 =
Answer:
7.3 × 7 = 7 × =
Fill in each blank
Answer:
8.3 × 12 = 12 × =
Fill in each blank
Answer:

13.A concert hall's chairs stand in 3 rows of 9. How many chairs are there?
Working:
Answer:
14.Tsz-ching sets out 6 counters in rows of 3, making exactly 2 rows. In rows of 2 instead, there would be rows, still counters in all.
Fill in each blank
Working:
Answer:
15.May buys 5 bags of 10 sweets, 50 in all. Ming buys 10 bags of 5. How many sweets does Ming have?
Working:
Answer:
16.Tsz-ching buys 3 bags of 4 sweets, 12 in all. May buys 4 bags of 3. How many sweets does May have?
Working:
Answer:
17.Ming sets out 21 counters in rows of 7, making exactly 3 rows. In rows of 3 instead, there would be rows, still counters in all.
Fill in each blank
Working:
Answer:
18.A concert hall's chairs stand in 4 rows of 4. How many chairs are there?
Working:
Answer:

Show the answers and working

Commutative property: multiplying in either order worksheet: Answers and working

1. 21, 21
Start with the rows: 3 rows of 7. Looking the other way doesn't change how many there are.
Nothing has changed, so both ways give 21: 7 × 3 = 3 × 7 = 21.
2. 4
Swapping the order keeps the answer. Which two numbers are on the left? The right needs the same two.
Swapping them keeps the answer: 4 × 7 = 7 × 4.
3. 10
Swapping the order keeps the answer. Which two numbers are on the left? The right needs the same two.
Swapping them keeps the answer: 10 × 9 = 9 × 10.
4. 14, 14
Start with the rows: 2 rows of 7. Looking the other way doesn't change how many there are.
Nothing has changed, so both ways give 14: 7 × 2 = 2 × 7 = 14.
5. 18
How are 3 × 6 and 6 × 3 related? There's no need to work it out again.
3 × 6 is 6 × 3 the other way round: 18.
6. 28
How are 4 × 7 and 7 × 4 related? There's no need to work it out again.
4 × 7 is 7 × 4 the other way round: 28.
7. 3, 21
First box: a swap keeps the same two numbers. Second box: counting in 7s, 3 times, is the easier way.
7 × 3 is easier: count in 7s 3 times to get 21.
8. 3, 36
First box: a swap keeps the same two numbers. Second box: counting in 12s, 3 times, is the easier way.
12 × 3 is easier: count in 12s 3 times to get 36.

9. True
After a swap, both sides use the same two numbers. Compare the 6 on the right with the numbers on the left.
Swapped, the two numbers stay the same: 6 × 3 = 3 × 6.
10. D. 3 × 2
Check each option: is it still a multiplication, and does it use the same two numbers, 2 and 3?
Swapping keeps the answer: 3 × 2 = 2 × 3.
11. False
After a swap, both sides use the same two numbers. Compare the 8 on the right with the numbers on the left.
Swapped, the two numbers stay the same: 9 × 10 = 10 × 9.
12. C. 4 × 2
Check each option: is it still a multiplication, and does it use the same two numbers, 2 and 4?
Swapping keeps the answer: 4 × 2 = 2 × 4.

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

13. 27 chairs
3 rows of 9 is 3 lots of 9. Multiply in whichever order you know better.
3 lots of 9: 9 × 3 = 27, or 3 × 9.
14. 3, 6
2 rows of 3: what do you see if you look down the columns instead? The number of counters stays the same.
2 rows of 3 seen the other way is 3 rows of 2: 3 × 2 = 2 × 3 = 6.
15. 50 sweets
Ming has 10 lots of 5, and May has 5 lots of 10. How are those two multiplications related?
Ming has 10 lots of 5 and May has 5 lots of 10: 5 × 10 = 10 × 5, both 50.
16. 12 sweets
May has 4 lots of 3, and Tsz-ching has 3 lots of 4. How are those two multiplications related?
May has 4 lots of 3 and Tsz-ching has 3 lots of 4: 3 × 4 = 4 × 3, both 12.
17. 7, 21
3 rows of 7: what do you see if you look down the columns instead? The number of counters stays the same.
3 rows of 7 seen the other way is 7 rows of 3: 7 × 3 = 3 × 7 = 21.
18. 16 chairs
4 rows of 4 is 4 lots of 4. Multiply in whichever order you know better.
4 lots of 4: 4 × 4 = 16, or 4 × 4.

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