Worksheet: Properties of Multiplication

In this worksheet, we will practice using the four properties of multiplication (commutative, associative, identity, and distributive) to solve problems with numbers up to 100.

Q1:

What do you get when you multiply a number by 0?

Q2:

Complete: 1,000×7=×1,000.

Q3:

Complete: 100×6=×100.

Q4:

Identify the property demonstrated in the following equation: 60×1=60.

  • Adistributive property
  • Bcommutative property of multiplication
  • Cidentity property of multiplication
  • Dassociative property of multiplication

Q5:

Complete the following: 9×5=5×.

Q6:

Find the missing numbers.

4×=32.

8×=32.

Q7:

Complete 13×2=2×.

  • A126
  • B113
  • C13
  • D26

Q8:

What is the multiplicative neutral element in ?

Q9:

If 𝑎÷𝑏=𝑎 and 𝑎0 , what is the value of 𝑏?

Q10:

Is 51×7<, = or >50×7?

  • A=
  • B<
  • C>

Q11:

Does the associative property apply to division?

  • Ano
  • Byes

Q12:

Liam knows that, when you multiply, you can change the order of the factors. So,

Does this work when we divide?

  • Ayes
  • Bno

Q13:

Jacob knows that, when you multiply, you can change the order of the factors. So, 6×3=3×6.

Elizabeth says that this works when you divide, so 18÷3=3÷18.

Is she correct?

  • Ayes
  • Bno

Q14:

Chloe is skip counting to solve 5×4.

How else could she skip count to find 5×4?

  • A2,4,6,8,10,12,14,20
  • B2,4,8,12,16,20
  • C5,10,15,20
  • D5,7,10,14,20

Which other equation would this solve?

  • A4×4
  • B4+5
  • C5×5
  • D4×5

Q15:

The associative property tells us we can multiply three numbers in any order, and the commutative property tells us we can swap factors.

Write the missing expression: 3×7×3=7×(×).

  • A7×3
  • B7×7
  • C3×7
  • D3×3

Find the answer: 3×7×3=.

Q16:

Compare the expressions. Pick the symbol that is missing.

  • A>
  • B<
  • C=

Q17:

9×=×9=0.

  • A0, 0
  • B1, 9
  • C0, 9
  • D1, 1

Q18:

Rectangle C is made of 2 copies of Rectangle A. So, its area is 2 times as much as the area of Rectangle A.

Pick another expression that is equal to the area of Rectangle C.

  • A3×(3×5)
  • B2×(2×5)
  • C(2×3)+(3×5)
  • D2×(3×5)

Rectangle D is made from 5 copies of Rectangle B.

Rectangle C has the same area as Rectangle D. Finish the equation by finding the expression in the parentheses.

  • A3×3
  • B5×3
  • C2×3
  • D2×5

Q19:

Complete: 10×4×7=10×.

Q20:

Find the missing numbers.

4×1=.

1×16=.

27×=27

×1=95

Q21:

Find the missing numbers.

7×0=.

0×22=.

36×=0.

×19=0.

Q22:

Complete: 8×1×5=×5.

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