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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: ( 2 8 0 + ) + 3 8 8 = 2 8 0 + ( 2 4 4 + 3 8 8 ) .

Q3:

If ( π‘₯ + 5 5 ) + 3 2 = 2 4 + ( 5 5 + 3 2 ) , what is the value of π‘₯ ?

Q4:

Rewrite the expression ( π‘₯ + 7 ) + 2 using the associative property.

  • A ( π‘₯ + 2 ) + ( 2 + 7 )
  • B ( π‘₯ + 2 ) + ( π‘₯ + 7 )
  • C π‘₯ β‹… ( 7 + 2 )
  • D π‘₯ + ( 7 + 2 )
  • E ( π‘₯ + 2 ) β‹… ( 2 + 7 )

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:

9 Γ— = Γ— 9 = 0 .

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

Q7:

Use the properties of real numbers to simplify the expression 5 2 + ( 𝑦 + 9 5 ) to one without parentheses.

  • A 1 4 7 βˆ’ 𝑦
  • B 𝑦 βˆ’ 1 4 7
  • C 5 2 𝑦 + 9 5
  • D 𝑦 + 1 4 7
  • E 9 5 𝑦 + 5 2

Q8:

A rectangle’s dimensions are ( 8 π‘₯ + 4 ) length units and ( 1 6 π‘₯ + 6 ) length units. Express the perimeter in terms of π‘₯ and calculate the perimeter when π‘₯ = 1 .

  • A ( 4 8 π‘₯ βˆ’ 4 ) length units, 44 length units
  • B ( 2 4 π‘₯ + 1 0 ) length units, 34 length units
  • C ( 2 4 π‘₯ + 2 ) length units, 26 length units
  • D ( 4 8 π‘₯ + 2 0 ) length units, 68 length units

Q9:

If ( 4 5 Γ— π‘₯ ) Γ— 5 0 = 4 5 Γ— ( 3 5 Γ— 5 0 ) , what is the value of π‘₯ ?

  • A50
  • B45
  • C36
  • D35

Q10:

If 𝑦 5 + 4 5 = 4 5 + 3 5 , what is the value of 𝑦 ?

Q11:

Chloe is skip counting to solve 5 Γ— 4 .

How else could she skip count to find 5 Γ— 4 ?

  • A 5 , 7 , 1 0 , 1 4 , 2 0
  • B 2 , 4 , 8 , 1 2 , 1 6 , 2 0
  • C 2 , 4 , 6 , 8 , 1 0 , 1 2 , 1 4 , 2 0
  • D 5 , 1 0 , 1 5 , 2 0

Which other equation would this solve?

  • A 4 + 5
  • B 4 Γ— 4
  • C 5 Γ— 5
  • D 4 Γ— 5

Q12:

Simplify 6 ( βˆ’ 3 π‘₯ ) .

  • A 3 π‘₯
  • B 1 8 π‘₯
  • C βˆ’ 3 π‘₯
  • D βˆ’ 1 8 π‘₯
  • E βˆ’ 3 6 π‘₯

Q13:

Simplify 4 ( 2 π‘₯ ) .

  • A 6 π‘₯
  • B βˆ’ 8 π‘₯
  • C βˆ’ 6 π‘₯
  • D 8 π‘₯
  • E 1 6 π‘₯

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: 3 Γ— 7 Γ— 3 = 7 Γ— ( Γ— ) .

  • A 7 Γ— 7
  • B 7 Γ— 3
  • C 3 Γ— 7
  • D 3 Γ— 3

Find the answer: 3 Γ— 7 Γ— 3 = .

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 ( π‘Ž + 𝑏 ) βˆ’ 𝑐 and Liam calculates π‘Ž + ( 𝑏 βˆ’ 𝑐 ) . Which property of addition tells us that their answers will be the same?

  • Adistributive property
  • Bcommutative property
  • Cidentity property
  • Dassociative property

Q19:

Which of the following illustrates the associative property of addition?

  • A ( 4 1 + 𝑧 ) + 4 = ( 4 1 + 4 ) + ( 𝑧 + 4 )
  • B ( 4 1 Γ— 𝑧 ) Γ— 4 = 4 1 Γ— ( 𝑧 Γ— 4 )
  • C ( 4 1 + 𝑧 ) Γ— 4 = ( 4 1 Γ— 4 ) + ( 𝑧 Γ— 4 )
  • D ( 4 1 + 𝑧 ) + 4 = 4 1 + ( 𝑧 + 4 )
  • E 𝑧 + 4 1 = 4 1 + 𝑧

Q20:

Which of the following is true concerning the expression 8 π‘₯ + 3 + π‘₯ ?

  • A The simplified form of the expression is 8 π‘₯ + 3 .
  • B 8 π‘₯ and 3 are like terms.
  • C The simplified form of the expression is 1 2 π‘₯ .
  • D 8 π‘₯ and π‘₯ are like terms.
  • E The simplified form of the expression is 9 π‘₯ + 4 .

Q21:

Which expression will have a different value to the others?

  • A βˆ’ 2 ο€Ό βˆ’ 1 2 π‘₯ 
  • B 2 9 ο€Ό 9 2 π‘₯ 
  • C 2 ο€Ό 1 2 π‘₯ 
  • D βˆ’ 2 3 ο€Ό 2 3 π‘₯ 
  • E βˆ’ 8 9 ο€Ό βˆ’ 9 8 π‘₯ 

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 4 ( π‘₯ + 1 1 ) + 3 π‘₯ , 7 π‘₯ + 1 5
  • B ( 4 π‘₯ + 1 1 ) + 3 π‘₯ , 7 π‘₯ + 1 1
  • C 4 ( π‘₯ + 1 1 ) + 3 , 4 π‘₯ + 4 7
  • D 4 ( π‘₯ + 1 1 ) + 3 π‘₯ , 7 π‘₯ + 4 4
  • E 4 ( π‘₯ + 1 1 ) + 3 , 4 π‘₯ + 1 8

Q23:

Find the missing number: ( 8 3 0 4 + 5 6 0 5 ) + 4 7 2 5 = 8 3 0 4 + ( 5 6 0 5 + ) .