Practice Commutative Property in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Worksheet PDF Free Answer-key PDF Family

Quick Recap

A property where swapping the order of two operands does not change the result: a ⋆ b=b ⋆ a.

3+5=5+3 and 3×5=5×3. Swapping the order doesn't change the answer.

Showing a random 20 of 50 problems.

Example 1

medium
Lucy says 7÷1=1÷7 because division is commutative. Is she correct?

Example 2

medium
Does the order in 3×4×5 matter for the product?

Example 3

challenge
Define a⋆b=a+b+ab. Is ⋆ commutative? Justify.

Example 4

easy
Is 10÷2=2÷10?

Example 5

medium
Does commutativity work for subtraction? Check with 10−3 and 3−10.

Example 6

medium
A student writes 12−5=5−12. Explain the error in one property term.

Example 7

easy
Use commutativity to rewrite 15+36 so the smaller addend comes first.

Example 8

easy
Rewrite 6+11 using commutativity.

Example 9

easy
Which property lets you rewrite 3+5 as 5+3?

Example 10

medium
Does forming a fraction commute: is 23=32?

Example 11

easy
A 3×5 array of dots has the same number of dots as a 5×3 array. How many dots?

Example 12

medium
Is the operation a⋆b=ab commutative? Test with 2 and 3.

Example 13

medium
Use commutativity to compute 7+23+3 quickly.

Example 14

medium
Use commutativity to compute 25×17×4 quickly.

Example 15

hard
Is the operation 'subtract then negate', defined as a⋆b=−(a−b), commutative?

Example 16

medium
Rewrite 3×4+4×3 as a single product using commutativity.

Example 17

easy
Does swapping the order in 5+0 to 0+5 change the value?

Example 18

hard
Use commutativity to make 5×13×2 easier, and compute the product.

Example 19

medium
Is matrix-style 'subtract then negate' a⋆b=−(a−b) commutative? Test 5,2.

Example 20

medium
True or false: for all numbers a,b, a+b=b+a.
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