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Worksheet: The Distributive Property of Multiplication over Addition and Subtraction

Q1:

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 .

Q2:

Write the multiplication expression that is missing:

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

Q3:

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

Q4:

Calculate .

Q5:

Fill in the blanks:

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

Q6:

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

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

Q7:

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

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

Q8:

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

Q9:

Use , , or to fill in the blank:

  • A
  • B
  • C

Q10:

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

Q11:

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

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

Q12:

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

Q13:

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

Q14:

Complete:

Q15:

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

Q16:

Complete:

Q17:

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

  • A
  • B
  • C
  • D
  • E

Q18:

Complete:

Q19:

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

Q20:

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