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Commutative Property Exploration

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Commutative Property Exploration

A maths club is checking whether swapping the order of two numbers changes an operation’s result. Complete each task and use examples to justify your conclusions.

Test the operations

Compare each expression with the one made by swapping the numbers. Remember: an operation is commutative if a ◇ b always equals b ◇ a.

Operation

First order

Swapped order

Addition

18 + 7 = ____

7 + 18 = ____

Subtraction

18 − 7 = ____

7 − 18 = ____

Multiplication

6 × 9 = ____

9 × 6 = ____

Division

36 ÷ 6 = ____

6 ÷ 36 = ____

1.Which two operations in the swap test gave the same result in both orders? Select all that apply.

Addition and multiplication
Subtraction and division
Addition and subtraction
Multiplication and division

2.Choose the statement that best defines the commutative property.

Swapping the order of the numbers does not change the result.
Changing the numbers always changes the result.
An operation must use exactly two numbers.
The result must be larger than both numbers.

3.A student claims that subtraction is commutative because 18 − 7 and 7 − 18 use the same numbers. Calculate both expressions and explain why the claim is incorrect.

Find the rule

Use variables to describe what happens for any numbers, not just the examples above.

4.Complete both general rules: addition: a + b = ; multiplication: a × b = .

5.True or false? If p and q are whole numbers, p ÷ q always equals q ÷ p. Give a numerical example to support your answer.

TrueFalse

6.Which expression is equal to 14 × 25 by the commutative property?

25 × 14
14 + 25
25 − 14
14 ÷ 25

7.A market stall packs 8 bags with 15 feijoas in each bag. Write a multiplication sentence for the total number of feijoas, then rewrite it with the factors swapped and state the total.

8.Mere says that 24 − 9 = 9 − 24 because she swapped the numbers. Is she right? Calculate both sides and explain.

9.Create one example showing that addition is commutative and one showing that division is not commutative. Include the calculations in both orders.

10.Challenge: A calculator shows 32 × 125 = 4,000. Without multiplying again, use the commutative property to write a different multiplication sentence with the same answer. Explain why it works.

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About This Worksheet

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For Teachers & Parents

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