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).

  • A𝑏+π‘Žπ‘
  • Bπ‘Žπ‘+π‘Žπ‘
  • Cπ‘Žπ‘Γ—π‘Žπ‘
  • Dπ‘Ž+𝑏+𝑐
  • Eπ‘Žπ‘+𝑐

Q2:

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

  • A7(π‘₯+2), 7π‘₯+9
  • B7(π‘₯+2), 7π‘₯+14
  • C2(π‘₯+7), 2π‘₯+9
  • D2(π‘₯+7), 2π‘₯+14
  • E7(π‘₯+2), π‘₯+14

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?

  • A4Γ—8
  • B10Γ—8
  • C4Γ—16
  • D10Γ—16

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.??

  • A16βˆ’14
  • B18βˆ’4
  • C26βˆ’14
  • D16βˆ’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)?

  • A4Γ—11
  • B4Γ—10
  • C6Γ—6
  • D10Γ—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?

  • A3Γ—7
  • B6Γ—6
  • C3Γ—10
  • D3Γ—6

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

  • A60βˆ’30=30
  • B60βˆ’18=42
  • C60βˆ’36=24
  • D60βˆ’21=39

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+?

  • A5Γ—2
  • B4Γ—4
  • C5Γ—4
  • D3Γ—4

What number is missing?

Q12:

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

  • A6+4
  • B8+4
  • C10+2
  • D8+2

Q13:

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

  • A10+8
  • B16+2
  • C12+6
  • D12+16

Q14:

Solve 8Γ—99=(π‘₯Γ—88)+(π‘₯Γ—11).

  • Aπ‘₯=704
  • Bπ‘₯=176
  • Cπ‘₯=99
  • Dπ‘₯=8
  • Eπ‘₯=4

Q15:

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

  • A16βˆ’4
  • B26βˆ’14
  • C18βˆ’4
  • D16βˆ’14

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.

Orangesquares=(10Γ—6)βˆ’()

Pick the equation that shows what he did.

  • A9Γ—6=(10+1)Γ—6
  • B9Γ—6=(10βˆ’1)Γ—6
  • C9Γ—6=(6βˆ’1)Γ—10
  • D10Γ—6=(9βˆ’1)Γ—6

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

  • A1Γ—6
  • B1Γ—1
  • C1Γ—5
  • D6Γ—6

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

  • A60βˆ’10
  • B54+6
  • C60βˆ’6
  • D60+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.

16Γ—6=84+

16Γ—6=

Q22:

Complete: (9Γ—10)+(Γ—10)=120.

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