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Lesson: Simplifying Algebraic Expressions Using the Commutative and Associative Properties

Video

10:05

Sample Question Videos

Worksheet • 23 Questions • 2 Videos

Q1:

Fill in the blank: ( 2 8 0 + ) + 3 8 8 = 2 8 0 + ( 2 4 4 + 3 8 8 ) .

Q2:

Fill in the blanks:

  • A7, 7
  • B9, 9
  • C6, 8
  • D7, 9

Q3:

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

Q4:

Does the associative property apply to division?

  • Ayes
  • Bno

Q5:

Simplify 3 4 π‘₯ + 5 7 βˆ’ 1 8 π‘₯ + 1 7 .

  • A 5 8 π‘₯ + 6 7
  • B βˆ’ 7 8 π‘₯ + 4 7
  • C βˆ’ 5 8 π‘₯ βˆ’ 6 7
  • D βˆ’ 7 8 π‘₯ βˆ’ 4 7
  • E 7 8 π‘₯ + 4 7

Q6:

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

Q7:

Simplify 6 ( βˆ’ 3 π‘₯ ) .

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

Q8:

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

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

Q9:

Which expression will have a different value to the others?

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

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

Q11:

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

Does this work when we divide?

  • Ayes
  • Bno

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 yes
  • B no

Q13:

Samar is skip counting to solve 5 Γ— 4 .

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

  • A 5 , 1 0 , 1 5 , 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 , 7 , 1 0 , 1 4 , 2 0

Which other equation would this solve?

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

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: 3 Γ— 7 Γ— 3 = 7 Γ— ( Γ— ) .

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

Find the answer: 3 Γ— 7 Γ— 3 = .

Q15:

Compare the expressions. Pick the symbol that is missing.

  • A<
  • B=
  • C>

Q16:

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

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

Q17:

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‘₯ + 2 0 ) length units, 68 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‘₯ βˆ’ 4 ) length units, 44 length units

Q18:

Which of the following illustrates the associative property of addition?

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

Q19:

9 Γ— = Γ— 9 = 0 .

  • A0, 0
  • B0, 9
  • C1, 9
  • D1, 1

Q20:

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

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

Q21:

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

  • Aassociative property
  • Bcommutative property
  • Cidentity property
  • Ddistributive property

Q22:

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

  • A35
  • B45
  • C36
  • D50

Q23:

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

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