Worksheet: Distributive Property of Multiplication

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

Q1:

Find the area of the rectangle using the distributive property.

Q2:

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

Q3:

Write two equivalent expressions for the area of the following rectangle.

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

Q4:

Shady used to solve .

Use his method to answer these questions.

Q5:

Calculate .

Use Nehal’s multiplication fact to help you.

Q6:

This area model can be used to solve 8 5 × 9 .

Find the missing partial product.

Q7:

A teacher has 34 children in her class. They each need 7 pieces of homework a week. By using the diagram, find how many pieces she will have to set altogether.

Q8:

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

What expression is missing?

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

What is 3 × 1 7 ?

Q9:

Nader 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 expression is missing?

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

What is 6 × 1 2 ?

Q10:

Shady and Dalia want to use area to find .

Dalia splits this rectangle in half, but she can’t finish because she doesn’t know .

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

  • A
  • B

Pick the next step in Shady’s calculation.

  • A
  • B
  • C
  • D

Add the areas of the two parts to figure out .

Q11:

Mona used to find .

Amir used to find .

Whose method is correct?

  • AOnly Amir’s method is correct.
  • BOnly Mona’s method is correct.
  • CThey are both wrong.
  • DThey are both correct.

What is ?

Q12:

Sherif is using this model to find .

He split 16 into . What did he split 12 into?

  • A
  • B
  • C
  • D

Finish his equation by writing the missing addition expression.

  • A
  • B
  • C
  • D

What is ?

Q13:

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

Q14:

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

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

Whose method is correct?

  • AOnly Farida’s method is correct.
  • BOnly Ramy’s method is correct.
  • CThey are both wrong.
  • DThey are both correct.

What is 6 × 9 ?

Q15:

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 .

Q16:

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 .

Q17:

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

Q18:

Evaluate 1 0 0 × ( 4 6 + 3 3 4 − 3 6 ) using the distributive property.

Q19:

Complete: 7 × = 7 × 9 + 7 × 7 .

Q20:

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

Q21:

Dalia is learning about different strategies to multiply.

She drew this to help her calculate .

What expression is missing?

  • A
  • B
  • C
  • D

What is ?

Q22:

Use this multiplication fact to find the missing numbers.