Generate Equivalent Expressions Using Properties

Students apply the distributive property, commutative property, and associative property to write equivalent expressions. They use the distributive property to expand products and factor sums, and use combining like terms to simplify expressions.

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Grade 6 · Expressions and Properties · question 1 of 3

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3(a + 6) = 3a +

How it is taught

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Equivalent expressions name the same quantity in different forms.

Distribute, then combine like terms.

Read it: Multiply both parts

3(a + 8) is a rectangle 3 tall and a + 8 wide. Cut it at the +: one part is 3 × a = 3a, the other 3 × 8 = 24. So 3(a + 8) = 3a + 24.

Draw the rectangle: the number outside is its height, the parts inside are its widths.
Multiply the height by each part: 3 × a = 3a and 3 × 8 = 24.
Add the two areas: 3(a + 8) = 3a + 24.

The 3 multiplies everything inside the parentheses, so it multiplies both parts.

Read backwards, the same picture factors 3a + 24 into 3(a + 8).

The rectangle reads both ways, so 3(a + 8) and 3a + 24 are one area; and terms with the same letter, like 2a and 5a, join into 7a.

The number outside the parentheses multiplies every part inside.

Writing 3(a + 8) = 3a + 8.

The 3 multiplies the 8 too: 3 × 8 = 24, so 3(a + 8) = 3a + 24.

13(x + 14) = 13x + ___ — 182. The 13 multiplies both parts: 13 × 14 = 182.

2(x + 5) + 3x

Today we'll simplify an expression by using two properties: the distributive property and combining like terms.

Here's our expression: two times the quantity x plus five, plus three x.

First, let's use the distributive property. The two outside the parentheses needs to multiply BOTH things inside.

Two times x is two x. Write that down.

Two times five is ten. Now the parentheses are gone.

Grade 6 · Distribute, then combine like terms

Our expression is now two x plus ten plus three x.

Look for like terms — terms with the same variable. Two x and three x are both x-terms.

Combine them: two x plus three x is five x.

The ten has no like term, so it stays. We're left with five x plus ten.

Two times the quantity x plus five, plus three x simplifies to five x plus ten. Equivalent expressions, made simpler!

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics

Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal: 1 star — one skill mastered, every rung of its ladder climbed
Climbing now: Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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