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In this lesson, we will learn how to simplify algebraic expressions using the commutative and associative properties for addition and multiplication.

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:

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?

Q5:

Simplify 3 4 π₯ + 5 7 β 1 8 π₯ + 1 7 .

Q6:

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

Q7:

Simplify 6 ( β 3 π₯ ) .

Q8:

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

Q9:

Which expression will have a different value to the others?

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.

Q11:

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

Does this work when we divide?

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?

Q13:

Samar is skip counting to solve 5 Γ 4 .

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

Which other equation would this solve?

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 ) .

Find the answer: 3 Γ 7 Γ 3 = .

Q15:

Compare the expressions. Pick the symbol that is missing.

Q16:

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

Q17:

A rectangleβs 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 .

Q18:

Which of the following illustrates the associative property of addition?

Q19:

9 Γ = Γ 9 = 0 .

Q20:

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

Q21:

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

Q22:

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

Q23:

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

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