Lesson Worksheet: Rewriting Expressions Using the Distributive Property Mathematics • 7th Grade

In this worksheet, we will practice rewriting algebraic expressions using the distributive property.

Q1:

Using the distributive property, rewrite the expression (โˆ’2๐‘ฅโˆ’8)(โˆ’6).

  • A12๐‘ฅโˆ’48
  • B12๐‘ฅโˆ’8
  • Cโˆ’96๐‘ฅ
  • Dโˆ’2๐‘ฅ+48
  • E12๐‘ฅ+48

Q2:

Expand โˆ’2๐‘ฅ(5๐‘ฅโˆ’5๐‘ฅ)๏Šฉ๏Šจ.

  • Aโˆ’10๐‘ฅ+10๐‘ฅ๏Šช๏Šฉ
  • B3๐‘ฅโˆ’7๐‘ฅ๏Šช๏Šฉ
  • Cโˆ’10๐‘ฅ+10๐‘ฅ๏Šฉ๏Šจ
  • Dโˆ’10๐‘ฅโˆ’10๐‘ฅ๏Šช๏Šฉ
  • Eโˆ’10๐‘ฅโˆ’5๐‘ฅ๏Šช๏Šจ

Q3:

Expand and simplify 4(2๐‘ฅ+3)+2(4๐‘ฅ+4).

  • A16๐‘ฅ+7
  • B6๐‘ฅ+20
  • C16๐‘ฅ+20
  • D12๐‘ฅ+7
  • E12๐‘ฅ+14

Q4:

Use the distributive property to rewrite the algebraic expression 4(๐‘ฅโˆ’9).

  • A4๐‘ฅโˆ’36
  • B๐‘ฅโˆ’36
  • C36โˆ’4๐‘ฅ
  • D4๐‘ฅโˆ’9
  • E36โˆ’๐‘ฅ

Q5:

Which of the following demonstrates the distributive property?

  • Aโˆ’4+(๐‘ฅ+3)=3+(๐‘ฅโˆ’4)
  • Bโˆ’4๐‘ฅ+3=3โˆ’4๐‘ฅ
  • Cโˆ’4(๐‘ฅ+3)=โˆ’4๐‘ฅโˆ’12
  • Dโˆ’4๐‘ฅ+3+0=โˆ’4๐‘ฅ+3

Q6:

Identify the expression which is not equivalent to the other three.

  • A9(๐‘ฅโˆ’17)
  • B4๐‘ฅโˆ’17+5๐‘ฅ
  • Cโˆ’8+9๐‘ฅโˆ’9
  • D9๐‘ฅโˆ’17

Q7:

Liam had ๐‘ dollars in his savings account and then he deposited $11; 7 months later, his balance had doubled. Which of the following is equivalent to his new balance of 2(๐‘+11) dollars?

  • A๐‘+22
  • B2๐‘+22
  • C2๐‘+11
  • D๐‘+13
  • E2๐‘+13

Q8:

Write an expression in terms of ๐‘ฅ, for the perimeter of the figure below.

  • A19๐‘ฅ length units
  • B34๐‘ฅ length units
  • C23๐‘ฅ length units
  • D38๐‘ฅ length units
  • E60๐‘ฅ length units

Q9:

Find the perimeter of the following shape.

  • A6๐‘ฅ+14
  • B3๐‘ฅ+7
  • C2๐‘ฅ+10๐‘ฅ+12๏Šจ
  • D2๐‘ฅ+10๐‘ฅโˆ’12๏Šจ
  • E5๐‘ฅ+11

Q10:

A square of side 3 cm has a square of side 6๐‘ฅ cm cut from one corner as shown in the diagram. Write, in its simplest form, an expression for the perimeter of the remaining shape.

Q11:

Factor 30๐‘Ž๐‘+45๐‘Ž๐‘๏Šจ๏Šจ completely.

  • A15๐‘Ž๐‘(2๐‘+3๐‘Ž)
  • B15๐‘Ž๐‘(2๐‘+3๐‘Ž๐‘)
  • C30๐‘Ž๐‘(2๐‘+45๐‘Ž๐‘)
  • D15๐‘Ž๐‘(30๐‘+3๐‘Ž)
  • E15๐‘Ž๐‘(2๐‘+45๐‘Ž๐‘)

Q12:

A student solving the equation 4(๐‘ฅโˆ’3)=24 writes down 4๐‘ฅโˆ’12=24 as their first line of working. What algebraic property did they use?

  • Athe associative property
  • Bthe distributive property
  • Cthe property of opposites
  • Dthe zero property of addition
  • Ethe commutative property

Q13:

Determine the value of ๐‘ฅ that makes the equation 4(7+5)=28+๐‘ฅ true.

Q14:

Use the properties of real numbers to rewrite 6(๐‘ฅ+3) as an equivalent expression that does not contain parentheses.

  • A6๐‘ฅ+3
  • B3๐‘ฅ+18
  • C6๐‘ฅ+6
  • D6๐‘ฅ+18
  • E6๐‘ฅ+9

Q15:

What property is illustrated by the shown step: ๐‘ฅ+4๐‘ฅโˆ’3โˆ’12=0๐‘ฅ(๐‘ฅ+4)โˆ’3(๐‘ฅ+4)=0?๏Šจ

  • AThe distributive property of multiplication over addition
  • BThe commutative property of addition
  • CThe associative property of addition
  • DThe commutative property of multiplication
  • EThe associative property of multiplication

Q16:

Which of the following expressions is equivalent to 7(3โˆ’8๐‘ฅ)?

  • A21โˆ’56๐‘ฅ
  • B21+7๐‘ฅ
  • C21โˆ’7๐‘ฅ
  • D21+56๐‘ฅ
  • E56+21๐‘ฅ

Q17:

Using the diagram, rewrite ๐‘‘โˆ’2(๐‘’+๐‘“) without brackets.

  • A๐‘‘โˆ’2๐‘’+2๐‘“
  • B๐‘‘โˆ’๐‘’โˆ’๐‘“
  • C๐‘‘โˆ’2๐‘’โˆ’2๐‘“
  • D๐‘‘โˆ’2๐‘’โˆ’๐‘“
  • E๐‘‘โˆ’๐‘’+๐‘“

Q18:

What property is illustrated by the step ๐‘ฅ(๐‘ฅ+4)โˆ’3(๐‘ฅ+4)=0(๐‘ฅโˆ’3)(๐‘ฅ+4)=0?

  • AThe associative property of multiplication
  • BThe distributive property of multiplication over addition
  • CThe commutative property of multiplication
  • DThe associative property of addition
  • EThe commutative property of addition

Q19:

Use the distributive property to fully expand (๐‘ฅ+2)(๐‘ฅ+3).

  • A๐‘ฅ+5๏Šจ
  • B๐‘ฅ+5๐‘ฅ+6๏Šจ
  • C๐‘ฅ+5๐‘ฅ+5๏Šจ
  • D๐‘ฅ+6๐‘ฅ+5๏Šจ
  • E๐‘ฅ+6๏Šจ

Q20:

What property is illustrated by the equation (๐‘Ž+๐‘)๐‘ฅ=๐‘Ž๐‘ฅ+๐‘๐‘ฅ?

  • Athe distributive property of multiplication over addition
  • Bthe associative property of addition
  • Cthe commutative property of addition
  • Dthe commutative property of multiplication
  • Ethe associative property of multiplication

Q21:

The diagram shows a rectangle of sides ๐‘Ž and ๐‘+๐‘. Its area is thus ๐‘Žร—(๐‘+๐‘), also written as ๐‘Ž(๐‘+๐‘). Work out the area of the two rectangles that make up the bigger rectangle to find an equivalent expression to ๐‘Ž(๐‘+๐‘).

  • A๐‘+๐‘Ž๐‘
  • B๐‘Ž๐‘+๐‘Ž๐‘
  • C๐‘Ž๐‘ร—๐‘Ž๐‘
  • D๐‘Ž+๐‘+๐‘
  • E๐‘Ž๐‘+๐‘

Q22:

Solve 8ร—99=(๐‘ฅร—88)+(๐‘ฅร—11).

  • A๐‘ฅ=704
  • B๐‘ฅ=176
  • C๐‘ฅ=99
  • D๐‘ฅ=8
  • E๐‘ฅ=4

Q23:

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

  • A7(๐‘ฅ+2), 7๐‘ฅ+9
  • B7(๐‘ฅ+2), 7๐‘ฅ+14
  • C2(๐‘ฅ+7), 2๐‘ฅ+9
  • D2(๐‘ฅ+7), 2๐‘ฅ+14
  • E7(๐‘ฅ+2), ๐‘ฅ+14

Q24:

The diagram shows the number ๐‘Ž+๐‘. By dividing it into four parts, as shown by the dashed lines, one gets (๐‘Ž+๐‘)รท4.

Using the diagram, find another expression for (๐‘Ž+๐‘)รท4.

  • A๐‘Žรท4+๐‘
  • B4รท๐‘Ž+4รท๐‘
  • C๐‘Žรท4+๐‘รท4
  • D๐‘Ž๐‘รท4
  • E๐‘Ž+๐‘รท4

Given that (๐‘Ž+๐‘)ร—๐‘“ is a multiplication equivalent to this division, what is the multiplication factor ๐‘“?

  • A๐‘Ž
  • B4
  • C14
  • D๐‘
  • E๐‘Ž๐‘4

What property of multiplication was used to rewrite (๐‘Ž+๐‘)ร—14 as 14ร—(๐‘Ž+๐‘)?

  • AThe multiplicative identity property
  • BThe commutative property
  • CThe associative property
  • DThe multiplicative inverse property
  • EThe distributive property

What property of multiplication has then been used to rewrite 14(๐‘Ž+๐‘) as ๐‘Ž4+๐‘4?

  • AThe distributive property
  • BThe multiplicative identity property
  • CThe commutative property
  • DThe multiplicative inverse property
  • EThe associative property

Is 4รท(๐‘Ž+๐‘) equal to 4รท๐‘Ž+4รท๐‘?

  • AYes
  • BNo

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