Grade 6 Mathematics · Unit 8: Equations & InequalitiesStandard 6.AT.8

Lesson 8.3Division Equations

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can solve one-step multiplication and division equations using inverse operations.

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
Inverse operationSpanish: Operación inversa Two math actions that undo each other, like × and ÷. ÷ and ×
MultiplySpanish: Multiplicar To add equal groups again and again. 3 × 7 = 21 means 3 groups of 7 equals 21
DivideSpanish: Dividir To split into equal groups. 36 ÷ 4 = 9 means 36 split into 4 equal groups gives 9 per group
IsolateSpanish: Despejar To get the letter by itself on one side. 3x = 21 → divide both sides by 3 → x = 7 (x is alone)
CoefficientSpanish: Coeficiente The number in front of a letter, like the 3 in 3x. In 6x = 18, the coefficient is 6; divide both sides by 6 to get x = 3.
SolutionSpanish: Solución A number that makes the equation or inequality true. n = 32 checks out

How it worksWorked examplesolving a division equation

These numbers are not on your problems. The steps are. Follow them with your own numbers.

A club splits a box of n pens evenly among 6 members. Each member gets 13 pens. Solve n ÷ 6 = 13.

  1. The variable n is divided by 6, so the inverse operation is multiplication.
  2. Multiply BOTH sides by 6 so the equation stays balanced.
  3. Left side: n ÷ 6 × 6 leaves n. Right side: 13 × 6 gives 78.
  4. Check: 78 ÷ 6 gives 13, so the value makes both sides equal.

Answer: n = 78, so the box held 78 pens.

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

A baker splits k cookies evenly onto 8 trays, with 11 cookies per tray. Solve k ÷ 8 = 11.

  1. The variable k is divided by , so the inverse operation is .
  2. Multiply both sides by .
  3. Left side leaves . Right side: 11 × 8 = .
  4. Check: ÷ 8 = . Does it balance?
Answer:cookies the baker started with

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

  • The variable is divided by , so I both sides by it.
  • My equation is because the total was split into .
  • The solution means in this problem.
  • I checked my answer by dividing by .

Word bank equationdivisordividemultiplyinverse operationisolateboth sidesequal groupstotalsolutioncheckbalance

Watch outA common mistake

A common mistake in Solve Multiplication and Division Equations is applying the SAME operation again instead of the inverse — for example, seeing 6x = 42 and multiplying both sides by 6 to get x = 252, instead of dividing by 6 to get x = 7. Before you submit, ask: did I use the OPPOSITE operation shown in the equation, and did I apply it to both sides?

Grade 6 Mathematics · Unit 8: Equations & InequalitiesStandard 6.AT.8

Lesson 8.3Division Equations

Apply Day · Version ASupported practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can solve one-step multiplication and division equations using inverse operations.

  1. 1Complete each step, then write the final answer.

    Solve 2x = 18.

    Show your work

    Hint 2x means 2 times x. Divide both sides by 2.

    Final answer:
  2. 2Complete each step, then write the final answer.

    Solve x ÷ 3 = 5.

    Show your work

    Hint x is divided by 3. Multiply both sides by 3.

    Final answer:
  3. 3Complete each step, then write the final answer.

    Solve 6x = 24.

    Show your work

    Hint 6x means 6 times x. Divide both sides by 6.

    Final answer:
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 8: Equations & InequalitiesStandard 6.AT.8

Lesson 8.3Division Equations

Apply Day · Version BCore practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can solve one-step multiplication and division equations using inverse operations.

  1. 1Complete each step, then write the final answer.

    Lia solved 3x = 45 and got x = 135. Is she right? What is x?

    Show your work
    Final answer:
  2. 2Complete each step, then write the final answer.

    Solve 12x = 3.

    Show your work
    Final answer:
  3. 3Complete each step, then write the final answer.

    Solve 7x = 56.

    Show your work
    Final answer:
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 8: Equations & InequalitiesStandard 6.AT.8

Lesson 8.3Division Equations

Apply Day · ChallengeExtension

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can solve one-step multiplication and division equations using inverse operations.

  1. 1Circle the letter of the best answer. Show how you know.

    What is the solution of 6m = 54?

    1. Am = 9
    2. Bm = 48
    3. Cm = 60
    4. Dm = 324
    Show your work
  2. 2Complete each step, then write the final answer.

    A ribbon is cut into 6 equal pieces. Each piece is 2.5 feet long. Dev writes 6r = 2.5 for the ribbon's length r. Write the right equation. How long is the ribbon?

    Show your work
    Final answer:
  3. 3Complete each step, then write the final answer.

    Solve 0.25x = 7.

    Show your work
    Final answer:
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help