Neft Teacher · Learn It

Unit 8 · Standard 6.AT.8

Write and Solve Equations Using Multiplication or Division

Lesson 8-3 · Learn It — how the math works

Why we're learning this

Detective Park discovered that 3 identical locked boxes contain a total of 21 pieces of evidence. She writes the equation 3x = 21 to find how many pieces are in each box. How can she solve for x?

✱ Math Workbench

Learn It

How do I solve a multiplication or division equation?

When a variable is multiplied or divided by a number, I use the inverse operation to get it alone. Division undoes multiplication, and multiplication undoes division.

Picture itSee what the math looks like before you read about it

Detective Park lines up 3 identical locked evidence boxes on a table. Together the 3 boxes hold 21 pieces of evidence, and each box holds the same amount.
Where you see this in real lifeDetective Park lines up 3 identical locked evidence boxes on a table. Together the 3 boxes hold 21 pieces of evidence, and each box holds the same amount.

Watch me solve itI do — read one step at a time

The problem looks like this
A bar model: 3 equal boxes, each labelled x, making a total of 21. total = 21 xxx 3 equal groups of x make 21.
  1. Solve 3x = 21. This means 3 times x equals 21.
  2. The inverse of multiplying by 3 is dividing by 3.
  3. I both sides by 3: 3x ÷ 3 = 21 ÷ 3.
  4. That leaves x = 7. Check: 3 × 7 = 21. True!3 × 7 = 21

Try it with meWe do — you answer first, then check

Same steps, new numbers.

  1. Solve x ÷ 4 = 9. Is x multiplied or divided?x ÷ 4 = 9
  2. It is divided by 4, so the inverse is multiplying both sides by 4.
  3. x = 9 × 4 = 36. Check: 36 ÷ 4 = 9. True?x = 9 × 4 = 36

On your ownYou do — solve this one by yourself

Before you start, remember:

  • Fill in the table to solve 3x = 21 and the other equations, showing your .
  • Then finish the practice problems on your own.

Solve: Complete the table.

EquationWorkSolutionCheck
8m = 56
y / 6 = 11
12k = 96

Stuck? Open one hint at a time.

Hint 1

First decide for each row: is the variable being MULTIPLIED (like 8m) or DIVIDED (like y / 6)?

Hint 2

Use the inverse: divide both sides when the equation multiplies; multiply both sides when it divides. The Check column rebuilds the original.

Hint 3

Row 1: 8m = 56 multiplies by 8, so compute 56 ÷ 8 for m. Check it by multiplying back, then handle y / 6 = 11 with the opposite move.

Check my answer
✅ Answers:
  • 8m = 56 → Work: 56 ÷ 8
  • 8m = 56 → Solution: m = 7
  • 8m = 56 → Check: 8 × 7 = 56 ✓
  • y / 6 = 11 → Work: 11 × 6
  • y / 6 = 11 → Solution: y = 66
  • y / 6 = 11 → Check: 66 / 6 = 11 ✓
  • 12k = 96 → Work: 96 ÷ 12
  • 12k = 96 → Solution: k = 8
  • 12k = 96 → Check: 12 × 8 = 96 ✓
Each row undoes whatever is being done to the variable and then verifies it. 8m = 56 multiplies, so divide: 56 ÷ 8 = 7, checked by 8 × 7 = 56. y / 6 = 11 divides, so multiply: 11 × 6 = 66, checked by 66 / 6 = 11. And 12k = 96 gives 96 ÷ 12 = 8, checked by 12 × 8 = 96.

Turn & TalkSay it out loud with a partner

Detective Park has 3 identical boxes holding 21 pieces of evidence total, written as 3x = 21. What does each part of the equation mean, and how is solving this different from solving x + 3 = 21?

Try starting with:

  • The 3 means ___ and x means ___.El 3 significa ___ y x significa ___.
  • Solving 3x = 21 is different from x + 3 = 21 because ___.Resolver 3x = 21 es diferente de x + 3 = 21 porque ___.
Use these wordsinverse operationmultiplydivideisolate