Worksheet: The Distributive Property of Multiplication over Addition and Subtraction

In this worksheet, we will practice using the distributive property of multiplication over addition and subtraction to rewrite equivalent expressions and evaluate them.

Q1:

Complete the equation: 1 9 × 6 4 = 1 9 × ( 4 + ) .

Q2:

Fill in the blanks: 1 × 6 = ( × 5 ) + .

  • A0, 0
  • B1, 6
  • C0, 5
  • D1, 1

Q3:

You are told that 3 9 × 7 = 2 7 3 and 3 9 × 3 0 = 1 , 1 7 0 . Use this to find 3 9 × 3 7 .

Q4:

Given that 2 1 × 3 = 6 3 , find 2 1 × 3 3 .

Q5:

Notice that 7 × 9 = ( 7 × 1 ) + ( 7 × 8 ) .

Fill in the blank: 3 × 6 = ( 3 × 3 ) + ( 3 × ) .

Q6:

Notice that 9 × 5 = ( 9 × 3 ) + ( 9 × 2 ) . Complete the following in the same way: 6 × 7 = ( 6 × 1 ) + ( × ) .

  • A0, 7
  • B6, 7
  • C7, 6
  • D6, 6

Q7:

Notice that 2 × 7 = ( 2 × 5 ) + ( 2 × 2 ) . Complete the following in the same way: 8 × 4 = ( 8 × 5 ) ( × ) .

  • A4, 1
  • B8, 4
  • C4, 5
  • D8, 1

Q8:

Fill in the blank: 4 × 5 = 4 × 7 4 × .

Q9:

Fill in the blank: 4 × 8 = ( 4 × 7 ) + .

Q10:

Complete: 3 × = 3 × 4 + 3 × 2 .

Q11:

Which of the following equations demonstrates the distributive property?

  • A 7 𝑥 + 1 4 = 7 ( 𝑥 + 7 )
  • B 7 𝑥 + 2 = 7 ( 𝑥 + 2 )
  • C 7 ( 𝑥 + 2 ) = 𝑥 + 1 4
  • D 7 ( 𝑥 + 2 ) = 7 𝑥 + 1 4
  • E 7 ( 𝑥 + 2 ) = 7 𝑥 + 9

Q12:

Evaluate 6 4 4 × 2 and 6 4 4 × 3 0 and then deduce the product of 6 4 4 × 3 2 .

  • A 1,288, 19,320, 18,032
  • B 1,288, 1,932, 3,220
  • C 1,268, 19,620, 20,888
  • D 1,288, 19,320, 20,608

Q13:

Calculate 8 2 × 2 8 8 2 × 6 0 .

Q14:

Calculate 7 × 7 . 3 mentally, using the distributive property.

Q15:

Use < , = , or > to fill in the blank: 1 5 ( 3 × 1 + 3 × 3 ) .

  • A =
  • B <
  • C >

Q16:

Write the multiplication expression that is missing:

  • A 4 × 4
  • B 5 × 5
  • C 3 × 4
  • D 5 × 4

Q17:

Evaluate 9 7 × 1 0 1 using the distributive property.

Q18:

Complete: 4 × 8 = 4 × 9 .

Q19:

Complete: 2 × 6 = 2 × 5 + .

Q20:

Fill in the blank: 1 4 × = 1 4 × 4 4 + 1 4 × 5 6 .

Q21:

Select the rectangle that matches the expression 9 × 4 = ( 5 × 4 ) + ( 4 × 4 ) .

  • A
  • B
  • C
  • D
  • E

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