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Apply the Properties of Operations to Generate Equivalent Expressions

Show all steps. When distributing, write each multiplication before simplifying. When factoring, identify the GCF first.

Grade 6·19 problems·~30 min·Common Core Math - Grade 6·standard·6-ee-a-3
Work through problems with immediate feedback
A

Recall / Warm-Up

1.

What is the GCF of 12 and 8?

2.

Which number property does this show? 3 × 27 = 3 × 20 + 3 × 7

3.

Which is a correct simplification of 5a+3a5a + 3a?

B

Fluency Practice

1.

Which expression is equivalent to 3(2+x)3(2 + x)?

2.

Expand 5(x+2y+3)5(x + 2y + 3).

3.

Simplify 4x+7x+34x + 7x + 3.

4.

Which is the fully factored form of 24x+18y24x + 18y?

5.

Factor 15a+1015a + 10 completely.

C

Varied Practice

Area model showing 4 multiplied by each of the three terms inside the parentheses, without showing the simplified results.
1.

Use the distributive property to complete: 4(3x+2y+5)=‾+‾+‾4(3x + 2y + 5) = \underline{\hspace{5em}} + \underline{\hspace{5em}} + \underline{\hspace{5em}}

first term:
second term:
third term:
2.

Which expression is equivalent to 7(2y+4)7(2y + 4)?

3.

Which is the completely factored form of 20x+1220x + 12?

4.

Which expression cannot be simplified further by combining like terms?

5.

Simplify 3(2x+4)+5x3(2x + 4) + 5x.

D

Word Problems / Application

1.

A school is ordering boxes of pencils. Each box holds (p+4)(p + 4) pencils, and they order 6 boxes.

The simplified expression for the total number of pencils is   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   .

If p=8p = 8, the total number of pencils is   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   .

simplified expression:
total pencils:
2.

A store sells two types of notebooks. A student buys 4 packs of lined notebooks and 4 packs of graph notebooks. Each lined pack costs xx dollars and each graph pack costs yy dollars.

Write a factored expression for the total cost:   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   .

factored expression:
E

Error Analysis

1.

Tomas expanded 3(2+x)3(2 + x) and got 6+x6 + x.

What error did Tomas make, and what is the correct answer?

2.

Aisha factored 24x+18y24x + 18y as 2(22x+16y)2(22x + 16y).

What error did Aisha make, and what is the correct factored form?

F

Challenge

1.

Simplify 4(2x+3)−2(x+5)4(2x + 3) - 2(x + 5).

2.

Are the expressions 3(2x+4)3(2x + 4) and 6x+46x + 4 equivalent? Explain your reasoning using the distributive property.

0 of 19 answered