6th Grade - Big Ideas - Chapter 5 Review

Algebraic Expressions

100

Evaluate the expression for x = 5: 3x + 2

17

200

Simplify the expression: 4y + 2y - 5y

y

300

If n = 7, what is the value of the expression 2n - 5?

9

400

What is the sum of 3p + 2 and 4p - 1 when p = 2?

15

500

Find the value of 5(x + 3) when x = 4.

35

Writing Expressions

100

Write an expression for "nine less than a number x."

x - 9

200

Translate "the sum of a number y and 8" into an algebraic expression.

y + 8

300

Express "twice a number n increased by 5" as an algebraic expression.

2n + 5

400

Write an expression for "three times the difference between a number m and 4."

3(m - 4)

500

Create an expression for "the product of a number p and 6 decreased by 9."

6p - 9

Properties of Addition and Multiplcation

100

State the commutative property of addition.

The commutative property of addition states that changing the order of addends does not change the sum. For example: a+b=b+a

200

Explain the associative property of multiplication with an example.

The associative property of multiplication states that changing the grouping of factors does not change the product. For example: (a⋅b)⋅c=a⋅(b⋅c)

300

Identify the property demonstrated: 8 + 3 = 3 + 8

This demonstrates the commutative property of addition.

400

Describe the distributive property of multiplication over addition.

The distributive property states that for any numbers a, b and c. 

a⋅(b+c)=a⋅b+a⋅c

500

What is the identity property of multiplication?

The identity property of multiplication states that multiplying a number by 1 gives the number itself: a⋅1=a

Distributive Property

100

Apply the distributive property to simplify: 3(2x + 4).

3(2x+4) = 3⋅2x+3⋅4 = 6x+12

200

Expand the expression using the distributive property: 2(3y - 7).

2(3y−7) = 2⋅3y−2⋅7 = 6y−14

300

Combine like terms in the expression: 5(2a + 3) + 4(a - 1).

5(2a+3)+4(a−1) = 10a+15+4a-4 = 14a+11

400

Using the distributive property, simplify: 4(2x + 3) + 2(3x - 1).

4(2x+3)+2(3x−1) = 8x+12+6x-2 = 14x+10

500

Using the distributive property, simplify: 5(x + 3x) + 4x(x + 2).

5(x+3)+4x(x+2) = 5x+15+4x²+8x = 4x²+13x+15

Factoring Expressions

100

Factorize the expression: 6x + 9.

Factor out the common factor (3): 

6x+9 = 3(2x+3)

200

Factor out the greatest common factor in the expression: 12a + 16.

Factor out 4: 

12a+16 = 4(3a+4)

300

Factor out the common factor: 9x + 36.

Factor out 9: 

9x+36 = 9(x+4)

400

Factor the expression using the GCF:

27x - 18y

Factor out the 9:

9(3x - 2y)

500

Factor the expression using the GCF:

42a - 14b

Factor out the 14:

14(3a - b)