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Worksheet: Distributive Property of Multiplication

In this worksheet, we will practice using the distributive property of multiplication to perform mental calculations.

Q1:

Amelia drew this to help her calculate 3 × 1 7 .

What expression is missing in the following:

  • A 3 × 1 0
  • B 7 × 1 0
  • C 3 × 3
  • D 3 × 7

What is 3 × 1 7 ?

Q2:

Ethan is using this model to find 1 2 × 1 6 .

He split 16 into 1 0 + 6 . What did he split 12 into?

  • A 6 + 6
  • B 5 + 7
  • C 9 + 3
  • D 1 0 + 2

Finish his equation by writing the missing addition expression: 1 2 × 1 6 = 1 0 0 + 6 0 + + .

  • A 3 0 + 1 2
  • B 3 0 + 1 3
  • C 2 0 + 1 1
  • D 2 0 + 1 2

What is 1 2 × 1 6 ?

Q3:

Mason is learning to multiply by breaking apart factors and then adding.

For 6 × 1 2 , he draws a 6-by-12 rectangle and splits it into two parts.

What is the missing expression in 6 × 1 2 = ( ) + ( 6 × 4 ) ?

  • A 6 × 7
  • B 6 × 1 0
  • C 6 × 9
  • D 6 × 8

What is 6 × 1 2 ?

Q4:

Anthony and Olivia want to use area to find 6 × 1 4 .

Olivia splits this rectangle in half, but she can’t finish because she doesn’t know 6 × 7 .

Anthony says it is easier to use the 10 times table. How would he split the rectangle?

  • A
  • B

Pick the next step in Anthony’s calculation.

  • A ( 6 × 8 ) + 6
  • B ( 6 × 8 ) + ( 6 × 6 )
  • C ( 6 × 1 0 ) + 4
  • D ( 6 × 1 0 ) + ( 6 × 4 )

Add the areas of the two parts to figure out 6 × 1 4 .

Q5:

Elizabeth used 9 = 1 0 − 1 to find 9 × 1 5 .

Liam used 1 5 = 1 0 + 5 to find 9 × 1 5 .

Whose method is correct?

  • AOnly Liam’s method is correct.
  • BOnly Elizabeth’s method is correct.
  • CThey are both wrong.
  • DThey are both correct.

What is 9 × 1 5 ?

Q6:

Anthony used 8 = 1 0 − 2 to solve 8 × 7 .

Use his method to answer these questions.

3 9 × 4 = .

Q7:

Evaluate ( 1 0 0 × 8 + 1 0 × 8 0 ) × 3 0 using the distributive property.

Q8:

James split 6 into 3 + 3 to find 6 × 9 .

Scarlett split 6 into 5 + 1 to find 6 × 9 .

Whose method is correct?

  • AOnly Scarlett’s method is correct.
  • BOnly James’s method is correct.
  • CThey are both wrong.
  • DThey are both correct.

What is 6 × 9 ?

Q9:

The number bond shows that 7 = 1 0 − 3 .

What expression is missing?

  • A 1 0 × 1 6
  • B 4 × 8
  • C 4 × 1 6
  • D 1 0 × 8

Fill in the blank: 7 × 8 = − 2 4 .

Hint: Use the number bond and that 3 × 8 = 2 4 .

Q10:

The number bond shows that 1 2 = 8 + 4 .

What expression is missing?

  • A 3 × 5
  • B 1 6 × 5
  • C 8 × 4
  • D 8 × 5

Find the missing number in

Hint: Use the number bond and the fact that 4 × 5 = 2 0 .

Q11:

Fill in the blank: 4 × 1 0 = 4 × 5 + 4 × .

Q12:

Evaluate 1 0 0 0 × ( 5 5 + 9 1 2 − 4 5 ) using the distributive property.

Q13:

Calculate 1 4 × 8 .

Use Amelia’s multiplication fact to help you.

Q14:

Complete:

Q15:

Write the subtraction expression that is missing:

  • A 2 6 − 1 4
  • B 1 6 − 1 4
  • C 1 8 − 4
  • D 1 6 − 4

Q16:

Olivia is learning about different strategies to multiply.

She drew this to help her calculate 9 × 4 .

What expression is missing in 4 × 9 = ( ) − ( 4 × 1 ) ?

  • A 4 × 1 1
  • B 6 × 6
  • C 1 0 × 5
  • D 4 × 1 0

What is 4 × 9 ?

Q17:

Use this multiplication fact to find the missing numbers.

Q18:

The diagram shows a rectangle of sides 𝑎 and 𝑏 + 𝑐 . Its area is thus 𝑎 × ( 𝑏 + 𝑐 ) , also written as 𝑎 ( 𝑏 + 𝑐 ) . Work out the area of the two rectangles that make up the bigger rectangle to find an equivalent expression to 𝑎 ( 𝑏 + 𝑐 ) .

  • A 𝑏 + 𝑎 𝑐
  • B 𝑎 𝑏 + 𝑐
  • C 𝑎 + 𝑏 + 𝑐
  • D 𝑎 𝑏 + 𝑎 𝑐
  • E 𝑎 𝑏 × 𝑎 𝑐

Q19:

Michael has been told that he can solve 7 × 6 using the fact that 7 = 1 0 − 3 .

He drew a model to show how.

What multiplication expression is missing to describe the model?

  • A 3 × 1 0
  • B 3 × 7
  • C 6 × 6
  • D 3 × 6

Pick the subtraction equation that is equal to 7 × 6 .

  • A 6 0 − 3 6 = 2 4
  • B 6 0 − 3 0 = 3 0
  • C 6 0 − 2 1 = 3 9
  • D 6 0 − 1 8 = 4 2

Q20:

Jacob has drawn this to help him multiply 3 and 18.