# Worksheet: Properties of Equality

In this worksheet, we will practice defining the properties of equality and using them to write an equivalent expression to a given one.

Q1:

The two diagrams show and using an area model for multiplication. What can be said about the areas of the rectangles?

• AThey are equal.
• BThey are not equal.

What does it say about multiplication?

• AThe multiplication is associative: .
• BThe multiplication is commutative: .

Q2:

Complete the equality stating which property is being used: .

• B52, associative
• C9, commutative
• D34, associative

Q3:

What equivalent expression to does this diagram show? • A
• B
• C
• D
• E

Q4:

The diagram shows a rectangular prism (A) that has been divided into three horizontal slices (B) and into four vertical slices (C). The volume of the rectangular prism as represented in (B) is written as , where is the volume of one slice. Choose an expression for as represented in (C).

• A
• B
• C
• D
• E

What property of multiplication does this diagram show?

• Athe multiplicative identity property
• Bthe associative property
• Cthe distributive property
• Dthe multiplicative inverse property
• Ethe commutative property

How many slices with a volume of 12 volume units are there in the rectangular prism?

• A4
• B
• C
• D3
• E

Q5:

Which of the following demonstrates the symmetric property of equality?

• AIf , then .
• BFor any , .
• CIf and , then .

Q6:

Which of the following demonstrates the reflexive property of equality?

• AFor any , .
• BIf , then .
• CIf and , then .

Q7:

Consider the following equality statements:

1. .
2. .
3. .

Without solving for , , , or , select the true statement.

• A
• B
• C
• D
• E

Without solving for , , , or , select the true statement.

• A
• B
• C
• D
• E

Without solving for , , , or , select the true statement.

• A
• B
• C
• D
• E

Without solving for , , , or , select the true statement.

• A
• B
• C
• D
• E

Q8:

Which of the following demonstrates the transitive property of equality?

• AIf and , then .
• BFor any , .
• CIf , then .

Q9:

Which of the following figures has an area that can be represented by the expression ?

• A • B • C • D • E Q10:

The diagram shows a rectangle of sides and . Its area is thus , which can also be written as . Work out the area of the smaller rectangles that make up the bigger rectangle to find an equivalent expression to . • A
• B
• C
• D
• E

Q11:

Which of the following expressions is equivalent to ?

• A
• B
• C
• D
• E

Q12:

Which of the following expressions is equivalent to ?

• A
• B
• C
• D
• E

Q13:

Which value of will make the following statement true: ?

Q14:

Which of the following expressions is equivalent to ?

• A
• B
• C
• D
• E

Q15:

Determine the value of that makes the equation true for all values of .

Q16:

Determine the value of that makes the equation true for all values of .

Q17:

Determine the value of that makes the equation true for all values of .

Q18:

If , then .

• A
• B
• C0
• D

Q19:

If the equation has the same solution set as the equation , what is the value of ?

Q20:

William believes the equation can have more than one solution for special values of and . Is he right? If so, what are the values?

• Ayes, ,
• Bno
• Cyes, ,
• Dyes, ,

Q21:

Determine the value of that makes the equation true for all values of .

Q22:

Given that , what is the value of ?

Q23:

Given that , by comparing coefficients, find and .

• A, ,
• B, ,
• C, ,
• D, ,
• E, ,