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Algebraic Properties Introduction

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Algebraic Properties Introduction

The commutative property describes whether changing the order of numbers leaves the result unchanged. Consider how this applies to different operations. Choose or write answers for each question.

Spot the Property

Decide which expressions keep the same value when their terms change order.

1.Which pair has equal values?

12 + 5 and 5 + 12
12 − 5 and 5 − 12
12 ÷ 3 and 3 ÷ 12
12 − 3 and 3 − 12

2.Which pair lists both operations for which swapping the order of two numbers always keeps the result unchanged?

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

3.Complete the sentence: The commutative property means that changing the of the numbers does not change the answer.

4.Match each expression to the expression with its terms in reverse order.

14 + 6
9 × 7
m + n
p × q

7 × 9
q × p
n + m
6 + 14

Complete and Check

Use numbers and variables to show how the property works.

5.Fill each blank to make the equation show the commutative property: 11 + 8 = + 11.

6.Fill each blank to make the equation show the commutative property: 6 × 13 = 13 × .

7.Rewrite r + s with the terms swapped, then state whether the new expression is equal to the original.

8.Rewrite u × v with the factors swapped, then state whether the new expression is equal to the original.

9.True or false: 18 − 4 = 4 − 18 demonstrates the commutative property. Give a calculation to support your choice.

10.Anahera has 9 red counters and 16 blue counters. Write two addition expressions in opposite orders to represent the total, and calculate the total.

11.If a = 7 and b = 12, substitute the values into both sides of a + b = b + a. Show that the two sides are equal.

12.Explain why 8 ÷ 2 and 2 ÷ 8 are not equal, and name the property that does not apply.