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

Lesson 8.38.3 Small Group · Group 2

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can solve one-step multiplication and division equations using inverse operations, explain why the method works, and use it on a problem I have not seen before.

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. 20 ÷ 4 = 5
IsolateSpanish: Despejar To get the letter by itself on one side. get p by itself
CoefficientSpanish: Coeficiente The number in front of a letter, like the 3 in 3x. the 3 in 3x
SolutionSpanish: Solución A number that makes the equation or inequality true. x = 3 is the solution of 6x = 18 because 6 × 3 = 18.

How it worksWorked examplesolving a multiplication equation

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

A stamp album has 7 pages that each hold p stamps. It holds 91 stamps in all. Solve 7p = 91.

  1. The variable p is multiplied by 7, so the inverse operation is division.
  2. Divide BOTH sides by 7 so the equation stays balanced.
  3. Left side: 7p ÷ 7 leaves p. Right side: 91 ÷ 7 gives 13.
  4. Check: 7 × 13 makes 91, so both sides are equal.

Answer: p = 13, so each page holds 13 stamps.

Now you trySame steps, your turn

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

A choir stands in 9 equal rows and has 108 singers. Solve 9r = 108 for the singers in one row.

  1. The variable r is multiplied by , so the inverse operation is .
  2. Divide both sides by .
  3. Left side leaves . Right side: 108 ÷ 9 = .
  4. Check: 9 × = . Does it balance?
Answer:singers in one row

Say it and write itSentence starters

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

  • The variable is multiplied by , so I both sides by it.
  • My equation is because each group holds .
  • The solution means in this problem.
  • I checked my answer by multiplying and .

Word bank equationcoefficientmultiplydivideinverse operationisolateboth sidesequal groupssolutioncheckundobalance

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 8.38.3 Small Group · Group 2

Group 2Challenge 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, explain why the method works, and use it on a problem I have not seen before.

  1. 1Complete each step, then write the final answer.
    Packpppppppp$3.20
    8 pencils at p dollars each cost $3.20.

    A pack of 8 pencils costs $3.20. Each pencil costs the same. Write and solve an equation for the cost p of one pencil.

    1. 1Write the equation from the story.
    2. 2Divide both sides by 8. What is p?
    3. 3Check: what is 8 × 0.40?
    Final answer:
  2. 2Complete each step, then write the final answer.
    x99x
    Half of x is 9.

    Solve 0.5x = 9. Then explain the size of the answer.

    1. 1What is done to x? What undoes it?
    2. 2Divide both sides by 0.5. What is x?
    3. 3Check: what is 0.5 × 18?
    4. 4Why is x greater than 9, even though we divided?
    Final answer:
  3. 3Complete each step, then write the final answer.

    Solve 12x = 3.

    Show your work
    Final answer:
  4. 4Complete each step, then write the final answer.

    Solve y ÷ 0.4 = 15.

    Show your work
    Final answer:
  5. 5Complete each step, then write the final answer.

    A car goes 210 miles on 7 gallons of gas. It goes the same distance on each gallon. Write and solve an equation for the miles m per gallon.

    Show your work
    Final answer:
  6. 6Complete 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:

Explain your thinkingWhen does dividing give a greater answer, and when does multiplying give a smaller one? Use 0.5x = 9 or y ÷ 0.4 = 15.

ChallengeWrite your own problem

Write a new word problem that uses this lesson's idea. Then solve it and show every step.

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help