Equivalent Expressions Lesson

Equivalent Expressions

How do we know if two or more expressions are equivalent?
*Equivalent expressions have the same value and simplify to like terms.

• Apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x

• Apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y)

• Apply properties of operations to y + y + y to produce the equivalent expression 3y.

Examples:

• Apply the properties of operations (including, but not limited to, commutative, associative, and distributive properties) to generate equivalent expressions.

• Identify when expressions are equivalent

Standard 6.EE.A.3 and 6.EE.A.4

IXL - Smith County Schools

You can open this webpage in a new tab.

Copy link

Open in new tab

Distributive Property

a (b+c) = a(b) + a(c) 2 (3+1) = 2 (3) + 2 (1) 6 + 2 = 6 + 2



a (b-c) = a(b) - a(c) 2 (3-1) = 2 (3) - 2 (1) 6 - 2 = 6 - 2

Redistributing Factors

• using a common factor (preferably the greatest common factor), to re-distribute factors

  • 30t + 60t t(30 + 60) 30(t + 2t)

  • Note ALL of these expressions are equivalent to 90t

Multiple Choice

Which expression is equivalent to:

$$2\left(x+2\right)$$  

• 2x + 2

• 2x + 4

Multiple Choice

Which expression is equivalent to:

$$2x+6$$  

• $$2\left(x+3\right)$$

• $$x+1+x+2$$  

Multiple Choice

Use the Distributive Property to write an equivalent expression:

$$2\left(4x+3\right)$$  

• 8x + 3

• 6x + 3

• 8x + 6

• 6x + 6

Multiple Select

Choose all expressions that are equal to:

$$5\left(2x+3\right)$$  

• $$10x+15$$  

• $$5x+15+5x$$  

• $$10x+8$$  

Multiple Select

Choose all expressions that are equal to:

$$4x-8$$  

• $$2\left(2x-6\right)$$  

• $$2\left(2x-4\right)$$  

• $$x-8+3x$$  

Multiple Select

Choose all expressions that are equal to:

$$12x-16$$  

• $$9x-16+3x$$  

• $$3\left(3x-5\right)$$  

• $$4\left(3x-4\right)$$