Worksheet: Distributive Property of Multiplication

In this worksheet, we will practice using the distributive property of multiplication to multiply numbers up to 10×10 by breaking the numbers apart.

Q1:

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

  • A 𝑏 + π‘Ž 𝑐
  • B π‘Ž 𝑏 + π‘Ž 𝑐
  • C π‘Ž 𝑏 Γ— π‘Ž 𝑐
  • D π‘Ž + 𝑏 + 𝑐
  • E π‘Ž 𝑏 + 𝑐

Q2:

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

  • A 7 ( π‘₯ + 2 ) , 7 π‘₯ + 9
  • B 7 ( π‘₯ + 2 ) , 7 π‘₯ + 1 4
  • C 2 ( π‘₯ + 7 ) , 2 π‘₯ + 9
  • D 2 ( π‘₯ + 7 ) , 2 π‘₯ + 1 4
  • E 7 ( π‘₯ + 2 ) , π‘₯ + 1 4

Q3:

James split 6 into 3+3 to find 6Γ—9.

Scarlett split 6 into 5+1 to find 6Γ—9.

Whose method is correct?

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

What is 6Γ—9?

Q4:

The number bond shows that 7=10βˆ’3.

What expression is missing?

  • A 4 Γ— 8
  • B 1 0 Γ— 8
  • C 4 Γ— 1 6
  • D 1 0 Γ— 1 6

Fill in the blank: 7Γ—8=βˆ’24.

Hint: Use the number bond and that 3Γ—8=24.

Q5:

Fill in the blank: 4Γ—10=4Γ—5+4Γ—.

Q6:

Write the subtraction expression that is missing: 3Γ—4=(4Γ—4)βˆ’(4Γ—1)=βˆ’=12.??

  • A 1 6 βˆ’ 1 4
  • B 1 8 βˆ’ 4
  • C 2 6 βˆ’ 1 4
  • D 1 6 βˆ’ 4

Q7:

Olivia is learning about different strategies to multiply.

She drew this to help her calculate 9Γ—4.

What expression is missing in 4Γ—9=()βˆ’(4Γ—1)?

  • A 4 Γ— 1 1
  • B 4 Γ— 1 0
  • C 6 Γ— 6
  • D 1 0 Γ— 5

What is 4Γ—9?

Q8:

Use this multiplication fact to find the missing numbers.

Q9:

Michael has been told that he can solve 7Γ—6 using the fact that 7=10βˆ’3.

He drew a model to show how.

What multiplication expression is missing to describe the model?

  • A 3 Γ— 7
  • B 6 Γ— 6
  • C 3 Γ— 1 0
  • D 3 Γ— 6

Pick the subtraction equation that is equal to 7Γ—6.

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

Q10:

Use this multiplication fact to find the missing numbers.

Q11:

Here are 5 groups of 4 stars.

Write the missing expression.

Hint: 5=2+?

  • A 5 Γ— 2
  • B 4 Γ— 4
  • C 5 Γ— 4
  • D 3 Γ— 4

What number is missing?

Q12:

Write the addition expression that is missing: 6Γ—2=(4Γ—2)+(2Γ—2)=+=12.

  • A 6 + 4
  • B 8 + 4
  • C 1 0 + 2
  • D 8 + 2

Q13:

Write the addition expression that is missing in 3Γ—6=(2Γ—6)+(1Γ—6)=+=18.

  • A 1 0 + 8
  • B 1 6 + 2
  • C 1 2 + 6
  • D 1 2 + 1 6

Q14:

Solve 8Γ—99=(π‘₯Γ—88)+(π‘₯Γ—11).

Q15:

Fill in the blanks with the missing subtraction expression: 3Γ—4=(4Γ—4)βˆ’(1Γ—4)=βˆ’=12.

  • A 1 6 βˆ’ 4
  • B 2 6 βˆ’ 1 4
  • C 1 8 βˆ’ 4
  • D 1 6 βˆ’ 1 4

Q16:

Given that 15Γ—5=75 and 15Γ—30=450, find 15Γ—53.

Hint: Try finding 15Γ—50 and 15Γ—3 first.

Q17:

Mason drew this array to help him multiply 9 by 6.

O r a n g e s q u a r e s = ( 1 0 Γ— 6 ) βˆ’ ( )

Pick the equation that shows what he did.

  • A 9 Γ— 6 = ( 1 0 + 1 ) Γ— 6
  • B 9 Γ— 6 = ( 1 0 βˆ’ 1 ) Γ— 6
  • C 9 Γ— 6 = ( 6 βˆ’ 1 ) Γ— 1 0
  • D 1 0 Γ— 6 = ( 9 βˆ’ 1 ) Γ— 6

Which expression should he write for the number of green squares?

  • A 1 Γ— 6
  • B 1 Γ— 1
  • C 1 Γ— 5
  • D 6 Γ— 6

Which calculation can he do to find 9Γ—6?

  • A 6 0 βˆ’ 1 0
  • B 5 4 + 6
  • C 6 0 βˆ’ 6
  • D 6 0 + 6

Q18:

Given that 73Γ—20=1,460, find 73Γ—22.

Q19:

Michael wants to know the answer to 12Γ—14.

His friends tell him other multiples of 14.

Explain how he can use his friends’ answers to figure out 12Γ—14.

  • AHe can divide 112 by 56.
  • BHe can add 56 and 112.
  • CHe can subtract 56 from 112.
  • DHe can multiply 56 by 112.

What is 12Γ—14?

Q20:

Victoria wants to know the answer to 12Γ—13.

Her friends tell her other multiples of 13.

Explain how she can use her friends’ answers to figure out 12Γ—13.

  • AShe can multiply 91 by 65 because 12=7+5.
  • BShe can add 91 to 65 because 12=7Γ—5.
  • CShe can add 91 to 65 because 12=7+5.
  • DShe can multiply 91 by 65 because 12=7Γ—5.

What is 12Γ—13?

Q21:

Use Anthony’s fact to find the missing numbers.