# Worksheet: Simplifying Algebraic Expressions Using the Commutative and Associative Properties

Q1:

Fill in the blanks:

• A7, 9
• B9, 9
• C6, 8
• D7, 7

Q2:

Fill in the blank: .

Q3:

If , what is the value of ?

Q4:

Rewrite the expression using the associative property.

• A
• B
• C
• D
• E

Q5:

Liam knows that, when you multiply, you can change the order of the factors. So,

Does this work when we divide?

• Ano
• Byes

Q6:

.

• A1, 1
• B0, 9
• C1, 9
• D0, 0

Q7:

Use the properties of real numbers to simplify the expression to one without parentheses.

• A
• B
• C
• D
• E

Q8:

A rectangleβs dimensions are length units and length units. Express the perimeter in terms of and calculate the perimeter when .

• A length units, 44 length units
• B length units, 34 length units
• C length units, 26 length units
• D length units, 68 length units

Q9:

If , what is the value of ?

• A50
• B45
• C36
• D35

Q10:

If , what is the value of ?

Q11:

Chloe is skip counting to solve .

How else could she skip count to find ?

• A
• B
• C
• D

Which other equation would this solve?

• A
• B
• C
• D

Q12:

Simplify .

• A
• B
• C
• D
• E

Q13:

Simplify .

• A
• B
• C
• D
• E

Q14:

Jacob knows that, when you multiply, you can change the order of the factors. So,

Elizabeth says that this works when you divide, so

Is she correct?

• A no
• B yes

Q15:

The associative property tells us we can multiply three numbers in any order, and the commutative property tells us we can swap factors.

Write the missing expression: .

• A
• B
• C
• D

Q16:

Does the associative property apply to division?

• Ano
• Byes

Q17:

Compare the expressions. Pick the symbol that is missing.

• A>
• B<
• C=

Q18:

In a class, Victoria calculates and Liam calculates . Which property of addition tells us that their answers will be the same?

• Bcommutative property
• Cidentity property
• Dassociative property

Q19:

Which of the following illustrates the associative property of addition?

• A
• B
• C
• D
• E

Q20:

Which of the following is true concerning the expression ?

• A The simplified form of the expression is .
• B and 3 are like terms.
• C The simplified form of the expression is .
• D and are like terms.
• E The simplified form of the expression is .

Q21:

Which expression will have a different value to the others?

• A
• B
• C
• D
• E

Q22:

Translate the following verbal expression into an algebraic one, and then simplify it: Four sets of the sum of a number and eleven are added to three times the same number.

• A ,
• B ,
• C ,
• D ,
• E ,

Q23:

Find the missing number: .