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

In this worksheet, we will practice simplifying algebraic expressions using the commutative and associative properties for addition and multiplication.

**Q3: **

Find the missing number: .

**Q4: **

Does the associative property apply to division?

- Ano
- Byes

**Q5: **

Simplify .

- A
- B
- C
- D
- E

**Q6: **

If , what is the value of ?

**Q7: **

Simplify .

- A
- B
- C
- D
- E

**Q8: **

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 .

**Q9: **

Which expression will have a different value to the others?

- A
- B
- C
- D
- E

**Q10: **

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 ,

**Q11: **

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

Does this work when we divide?

- Ano
- Byes

**Q12: **

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

Mona says that this works when you divide, so

Is she correct?

- A no
- B yes

**Q13: **

Samar 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

**Q14: **

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

Find the answer: .

**Q15: **

Compare the expressions. Pick the symbol that is missing.

- A>
- B<
- C=

**Q16: **

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

- A
- B
- C
- D
- E

**Q17: **

A rectangleβs 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

**Q18: **

Which of the following illustrates the associative property of addition?

- A
- B
- C
- D
- E

**Q19: **

.

- A1, 1
- B0, 9
- C1, 9
- D0, 0

**Q20: **

Rewrite the expression using the associative property.

- A
- B
- C
- D
- E

**Q21: **

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

- Adistributive property
- Bcommutative property
- Cidentity property
- Dassociative property

**Q22: **

If , what is the value of ?

- A50
- B45
- C36
- D35

**Q23: **

If , what is the value of ?