# 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 .

• 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