Lesson Worksheet: Rewriting Expressions Using the Distributive Property

Q1:

Using the distributive property, rewrite the expression .

A
B
C
D
E

Q2:

Expand .

A
B
C
D
E

Q3:

Expand and simplify .

A
B
C
D
E

Q4:

Use the distributive property to rewrite the algebraic expression .

A
B
C
D
E

Q5:

Which of the following demonstrates the distributive property?

A
B
C
D

Q6:

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

A
B
C
D

Q7:

Liam had 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 dollars?

A
B
C
D
E

Q8:

Write an expression in terms of , for the perimeter of the figure below.

A length units
B length units
C length units
D length units
E length units

Q9:

Find the perimeter of the following shape.

A
B
C
D
E

Q10:

A square of side 3 cm has a square of side 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 completely.

A
B
C
D
E

Q12:

A student solving the equation writes down 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 that makes the equation true.

Q14:

Use the properties of real numbers to rewrite as an equivalent expression that does not contain parentheses.

A
B
C
D
E

Q15:

What property is illustrated by the shown step:

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 ?

A
B
C
D
E

Q17:

Using the diagram, rewrite without brackets.

A
B
C
D
E

Q18:

What property is illustrated by the step

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 .

A
B
C
D
E

Q20:

What property is illustrated by the equation ?

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 and . Its area is thus , also written as . Work out the area of the two rectangles that make up the bigger rectangle to find an equivalent expression to .

A
B
C
D
E

Q22:

Solve .

A
B
C
D
E

Q23:

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

A,
B,
C,
D,
E,

Q24:

The diagram shows the number . By dividing it into four parts, as shown by the dashed lines, one gets .

Using the diagram, find another expression for .

A
B
C
D
E

Given that is a multiplication equivalent to this division, what is the multiplication factor ?

A
B4
C
D
E

What property of multiplication was used to rewrite as ?

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 as ?

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

Is equal to ?

AYes
BNo

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