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

NameDate

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

Jun sets the timer for a speed round. How would Jun write 7(x + 4) without parentheses, with as few terms as possible?
Kira studies a puzzle under the lamp, which hums happily. How would Kira write 8(x + 3) without parentheses, with as few terms as possible?
Milo follows a clue on the map. How would Milo write 6(x − 5) without parentheses, with as few terms as possible?
4.
A clue is taped to Pia's backpack. Which expression is equal to 3(x − 4)?
- 3x − 4
- 3x − 12
- 12x
- x − 7
5.
Ren plays a number game on the phone. Which expression is equal to 9(x − 2)?
- 9x − 2
- x − 11
- 18x
- 9x − 18
Ari opens the math book to a puzzle. How would Ari write x + 6x as one term?
Bo follows a clue on the map. How would Bo write 5x + x as one term?
Esme copies a clue onto paper. How would Esme write x + x + x + x as one term?
A clue is taped to Jun's backpack. How would Jun write x + x + x + x + x as one term?
Luz finds a riddle in the lunchbox. How would Luz combine like terms in 8x + 9 + 5x, using as few terms as possible?

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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