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 - Challenge Me

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

Pia opens an envelope with a puzzle inside. How would Pia write 3(2x + 5) without parentheses, with as few terms as possible?
Ren checks the clock before a quiz. How would Ren write 5(3x + 2) without parentheses, with as few terms as possible?
Tala sets the timer for a speed round. How would Tala write 6(2x + 3) without parentheses, with as few terms as possible?
Ari finds a riddle in the lunchbox. How would Ari write 8(x + 0.25) without parentheses, with as few terms as possible?
Bo puts on glasses to read tiny print. How would Bo write 5(x − 0.4) without parentheses, with as few terms as possible?
Jun opens an envelope with a puzzle inside. How would Jun write 2x + 3x + 4x as one term?
Luz sets the timer for a speed round. How would Luz combine like terms in 3x + 4 + 2x + 5, using as few terms as possible?
Milo studies a puzzle under the lamp, which hums happily. How would Milo combine like terms in 6x + 2 + 3x + 8, using as few terms as possible?
Noah opens the math book to a puzzle. How would Noah combine like terms in 7x + 1 + 4x + 3, using as few terms as possible?
10.
Pia follows a clue on the map. Which expression writes 18x + 24 using the greatest common factor?
- 3(6x + 8)
- 6(3x + 24)
- 2(9x + 12)
- 6(3x + 4)

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

See all grade 6 math

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