Worksheet: Evaluating Numerical Expressions Using the Distributive Property

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In this worksheet, we will practice using the distributive property on numerical expressions.

Q1:

Evaluate 3 ( 2 6 + 1 1 ) using the distributive property.

Q2:

Evaluate 5 ( 4 0 ) + 5 ( 2 6 ) using the distribute property.

Q3:

Rewrite the expression 2 0 ( 1 1 − 3 ) using the distributive property.

  • A ( 2 0 − 1 1 ) − ( 2 0 − 3 )
  • B 2 0 × 1 1 + 2 0 × 3
  • C 3 ( 2 0 − 1 1 )
  • D 1 1 ( 2 0 − 3 )
  • E 2 0 × 1 1 − 2 0 × 3

Q4:

Which of these equations is numerical?

  • A ○ + 2 = 1 1 0
  • B △ − 5 = 1 2
  • C ○ 8 = 2 1 6
  • D 2 0 − 6 = 1 4
  • E ▽ × 1 1 = 1 0

Q5:

Which multiplication property of natural numbers is used in the expression 1 3 × ( 4 5 − 2 3 ) = 1 3 × 4 5 − 1 3 × 2 3 ?

  • Amultiplicative identity
  • Bdistributive
  • Cclosure
  • Dcommutative
  • Eassociative

Q6:

Evaluate 7 ( 1 9 + 1 7 ) using the distributive property.

Q7:

Evaluate 7 ( 4 1 + 1 2 ) using the distributive property.

Q8:

Evaluate 9 ( 4 4 + 2 6 ) using the distributive property.

Q9:

Evaluate 4 ( 4 0 + 2 6 ) using the distributive property.

Q10:

Write the multiplication expression that is missing: 5 × 7 = ( 5 × 3 ) + ( ) = 1 5 + 2 0 = 3 5 .

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

Q11:

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

Q12:

Calculate 8 2 × 2 8 − 8 2 × 6 0 .

Q13:

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

  • A0, 5
  • B1, 1
  • C1, 6
  • D0, 0

Q14:

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 .

Q15:

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

  • A8, 1
  • B4, 1
  • C4, 5
  • D8, 4

Q16:

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

  • A6, 6
  • B0, 7
  • C6, 7
  • D7, 6

Q17:

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

Q18:

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

  • A <
  • B =
  • C >

Q19:

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

Q20:

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

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

Q21:

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

Q22:

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

Q23:

Which of the following equations demonstrates the distributive property?

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

Q24:

Complete: 4 × 8 = 4 × 9 − .

Q25:

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

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