Solve One-Step Multiplication and Division Equations

Students solve equations of the form px = q and x/p = q using inverse operations (division and multiplication, respectively). They work with rational number coefficients and constants, showing balanced steps and checking solutions.

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Grade 6 · Equations and Inequalities · question 1 of 3

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3x = 15, x =

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A coefficient is multiplied by the variable.

Undo that with the inverse on both sides.

Read it: Equations with × and ÷

3x = 33 is a tape of 33 cut into 3 equal parts, and each part is x. Undo the × 3 by dividing both sides by 3: x = 33 ÷ 3 = 11.

Find what was done to x: here it was multiplied by 3.
Undo it on both sides: × is undone by ÷, and ÷ is undone by ×.
Check by putting x back in: 3 × 11 = 33.

3x means 3 equal parts of x, so one part is the whole shared by 3: 33 ÷ 3.

x ÷ 3 = 11 cuts x into 3 parts of 11, so x is all 3 parts together: 3 × 11 = 33.

Doing the same to both sides keeps them equal, so the x you find makes the equation true.

Undo × by dividing both sides, and undo ÷ by multiplying both sides.

Taking the 3 away: x = 33 − 3 = 30.

3x is 3 equal parts, not 3 more: x = 33 ÷ 3 = 11.

9x = 108, x = ___ — 12. 108 ÷ 9 = 12. Check: 9 × 12 = 108.

3x = 18

Let's solve a one-step equation. We have three x equals eighteen. What number does x stand for?

Three x means three times x. We need to find the value of x that makes both sides equal.

Right now, x is being multiplied by three. To undo multiplication, we use its inverse — division.

To keep the equation balanced, whatever we do to one side, we must do to the other.

So we divide both sides by three.

Grade 6 · Use inverse operations to keep the equation balanced

On the left, three divided by three is one. One x is just x.

On the right, eighteen divided by three is six.

So x equals six.

Let's check. Substitute six back in: three times six is eighteen. It works!

x equals six. To solve a multiplication equation, divide both sides by the coefficient. Great job!

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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