Grade 6 · Math

6th grade Equivalent expressions and the distributive property worksheet

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Equivalent expressions and the distributive property

Grade 6 Math Worksheet - Building Confidence

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Circle the best answer, or write your answer on the line.

A clue is taped to Bo's backpack. The x parts of 4(x + 3) make 4x. How would Bo write all of 4(x + 3) without parentheses, with as few terms as possible?
Jun finds a riddle in the lunchbox. Think of 3 bars, each cut into x and 4. How would Jun write 3(x + 4) without parentheses, with as few terms as possible?
Kira puts on glasses to read tiny print. Think of 6 bars, each cut into x and 2. How would Kira write 6(x + 2) without parentheses, with as few terms as possible?
4.
A very serious pencil helps Luz crack a secret code. Which expression is equal to 2(x + 6)?
- x + 8
- 2x + 12
- 2x + 6
- 12x
5.
Milo opens an envelope with a puzzle inside. Which expression is equal to 4(x + 5)?
- 4x + 20
- 20x
- 4x + 5
- x + 9
Pia sets the timer for a speed round. The bars add up: 3 + 5 = 8 bars of x. How would Pia write 3x + 5x as one term?
Tala opens the math book to a puzzle. Think of 3 bars of x end to end. How would Tala write x + x + x as one term?
Zee solves a clue. Join the bars of x and keep the plain number apart. How would Zee combine like terms in 3x + 4 + 2x, using as few terms as possible?
Ari solves a clue. Join the bars of x and keep the plain number apart. How would Ari combine like terms in 5x + 4 + 3x, using as few terms as possible?
10.
Bo opens an envelope with a puzzle inside. Which expression is equal to 6x + 9?
- 15x
- 3(2x + 3)
- 3(2x + 9)
- 2(3x + 3)

6th grade Equivalent expressions and the distributive property worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Equivalent expressions and the distributive property. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can write 3(x + 2) without parentheses as 3x + 6, because all 3 bars have a 2.
I can join terms with the same letter (2x + 3x = 5x) and leave different terms apart (2x + 3 stays 2x + 3).
I can check my answer by putting the same number into the question and into my answer.

Standard: 6.EE.A.3, 6.EE.A.4

Words to know

expression: Numbers, letters and operations put together, with no equal sign, like 3x + 6.

term: One part of an expression that is added or taken away, like 3x or 6.

like terms: Terms with the same letter part, like 2x and 5x. Plain numbers are like terms with each other.

equivalent: Two expressions are equivalent if they give the same number for every x.

distributive property: A number times a sum is that number times each part: 3(x + 2) = 3x + 6.

parentheses: The curved brackets in 3(x + 2). They show that 3 multiplies the whole sum.

Common mistakes

Your child multiplied only the first term inside the parentheses, so 3(x + 2) became 3x + 2. Try asking them to draw 3 bars that each hold x and 2, then count all the 2s.

Your child multiplied the two numbers and put the answer on x, so 3(x + 2) became 6x. Try drawing 3 bars of x + 2 and asking which parts are x and which are plain 2s.

Your child joined terms that are not alike, so 2x + 3 became 5x. Try asking if 2 pencils and 3 erasers make 5 pencils.

Questions parents ask

What is the most common mistake with equivalent expressions and the distributive property?

Your child multiplied only the first term inside the parentheses, so 3(x + 2) became 3x + 2. Try asking them to draw 3 bars that each hold x and 2, then count all the 2s.

Are these 6th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More grade 6 math

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