Grade 6 Mathematics · Unit 6: Numerical and Algebraic ExpressionsStandard 6.NOS.1

Lesson 6.9Divide Whole Numbers by Fractions

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can divide a whole number by a fraction by multiplying by the reciprocal.

Start hereWords for this lesson

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

WordWhat it meansExample
Whole NumberSpanish: Número entero A counting number with no fraction or decimal, like 0, 1, 2, 3. 4 is a whole number; as a fraction it is 4/1
FractionSpanish: Fracción A number that shows part of a whole, like 3/4. 1/2 means 1 out of 2 equal parts — like cutting a sandwich in half and taking one piece
ReciprocalSpanish: Recíproco A fraction turned upside down. The reciprocal of 2/3 is 3/2. Flip the fraction to divide: 6 ÷ 2/3 = 6 × 3/2
Keep, Change, FlipSpanish: Mantener, cambiar, invertir A way to divide fractions: keep the first, change ÷ to ×, flip the second. 6 ÷ 1/3 → Keep 6, Change ÷ to ×, Flip 1/3 to 3/1 → 6 × 3 = 18
QuotientSpanish: Cociente The answer when you divide. In 4 ÷ 1/2 = 8, the quotient is 8

How it worksWorked example

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

Agent Park has 4 pounds of powder and each bag holds 1/2 pound. I want 4 ÷ 1/2.

  1. Keep the 4. Change ÷ to ×. Flip 1/2 to make 2/1, which is just 2.
  2. Now I multiply: 4 × 2 = 8.
  3. So 4 ÷ 1/2 = 8. He can fill 8 bags. That makes sense: each pound fills 2 bags, and 4 pounds × 2 = 8.

Now you trySame steps, your turn

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

Let's try 3 ÷ 1/4 together. What do we keep? The 3.

Answer:

Say it and write itSentence starters

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

  • 3 ÷ 1/4 = 12 because it takes jumps of to get from 0 to .

Word bank Whole NumberFractionReciprocalKeep, Change, FlipQuotient12fourthjumps3four timeseach whole

Watch outA common mistake

A common mistake in Divide Whole Numbers by Fractions is doing 'Keep, Change' but skipping the 'Flip' — students multiply by the divisor as it is instead of by its reciprocal. For example, for 6 ÷ 3/4, a student might write 6 × 3/4 = 4 1/2 and stop there, but the divisor 3/4 must be flipped to 4/3 first: 6 × 4/3 = 24/3 = 8. Before you submit, check: did I flip the second fraction (the divisor) upside down before multiplying?

Grade 6 Mathematics · Unit 6: Numerical and Algebraic ExpressionsStandard 6.NOS.1

Lesson 6.9Divide Whole Numbers by Fractions

Version ASupported practice

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

Learning target I can divide a whole number by a fraction by multiplying by the reciprocal.

Part 1Understand the ideamodels and meaning
  1. 1Mark and label each value on the number line.

    How many jumps of 1/4 does it take to get from 0 to 2?

    00.250.50.7511.251.51.752

    Hint Each jump is exactly 1/4, and your goal is to land right on 2.

    Show your thinking
Part 2Practice the skillshow every step
  1. 2Circle the letter of the best answer. Show how you know.

    What is 6 ÷ 1/3?

    1. A2
    2. B3
    3. C6/3
    4. D18

    Hint 6 ÷ 1/3 asks how many 1/3-size pieces fit into 6 wholes. Predict: bigger or smaller than 6?

    Show your work
  2. 3Circle the letter of the best answer. Show how you know.

    What is 3 ÷ 1/5?

    1. A3/5
    2. B5/3
    3. C8
    4. D15

    Hint The total is 3 wholes and each piece is 1/5 — every whole holds several fifths.

    Show your work
  3. 4Circle the letter of the best answer. Show how you know.

    What is 10 ÷ 1/4?

    1. A2.5
    2. B10/4
    3. C14
    4. D40

    Hint You're counting 1/4-size pieces inside 10 wholes — every whole holds more than one.

    Show your work
  4. 5Circle the letter of the best answer. Show how you know.

    What is 5 ÷ 1/2?

    1. A2.5
    2. B5/2
    3. C7
    4. D10

    Hint How many 1/2-size pieces fit into 5 wholes? Each whole holds more than one half.

    Show your work
Part 3Explain and correctreasoning
  1. 6Find the mistake. Explain it, then show the correct work.

    Spot the Common Mistake

    1. 1Problem4 ÷ 1/5
    2. 2Keep, Change, FlipKept the 4 and changed ÷ to ×, but forgot to flip: 4 × 1/5
    3. 3Multiply4 × 1/5 = 4/5

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Hint After 'Change,' you still have to 'Flip' the second fraction.

    Correct work
    Correct answer:

Explain your thinkingWhy does 3 ÷ 1/4 = 12? How does the number line show this?

Sentence starter 3 ÷ 1/4 = 12 because it takes ___ jumps of ___ to get from 0 to ___.

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 6: Numerical and Algebraic ExpressionsStandard 6.NOS.1

Lesson 6.9Divide Whole Numbers by Fractions

Version BCore practice

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

Learning target I can divide a whole number by a fraction by multiplying by the reciprocal.

Part 1Understand the ideamodels and meaning
  1. 1Complete the table. Show how you found each value.

    Complete the table: Whole Number ÷ Fraction. Use Keep, Change, Flip.

    ExpressionRewrite as MultiplicationQuotient
    5 ÷ 1/4
    8 ÷ 1/2
    3 ÷ 1/6
    7 ÷ 1/3
    Show your work
  2. 2Write the letter of the matching item on each line.

    Match each division expression to its quotient.

    1. 4 ÷ 1/3
    2. 7 ÷ 1/2
    3. 5 ÷ 1/6
    4. 2 ÷ 1/8
    5. 9 ÷ 1/4
    6. 6 ÷ 1/5
    • A12
    • B14
    • C30
    • D16
    • E36
    • F30
  3. 3Use the model to solve. Show your work.
    3 wholes = 9 thirds. Groups of 2/3: 9 ÷ 2 = 4 R 1 → 4 1/2 groups1/31/31/31/31/31/31/31/31/3

    How many groups of 2/3 fit into 3?

    Show your work
    Answer:
Part 2Practice the skillshow every step
  1. 4Circle the letter of the best answer. Show how you know.

    What is 6 ÷ 2/3?

    1. A2/18
    2. B4
    3. C9
    4. D12
    Show your work
Part 3Explain and correctreasoning
  1. 5Find the mistake. Explain it, then show the correct work.

    Spot the Common Mistake

    1. 1Problem8 ÷ 3/4
    2. 2Keep, Change, FlipFlipped the wrong number — wrote 1/8 × 3/4 instead of 8 × 4/3
    3. 3Multiply1/8 × 3/4 = 3/32

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Correct work
    Correct answer:

Explain your thinkingWhy does 3 ÷ 1/4 = 12? How does the number line show this?

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 6: Numerical and Algebraic ExpressionsStandard 6.NOS.1

Lesson 6.9Divide Whole Numbers by Fractions

ChallengeExtension

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

Learning target I can divide a whole number by a fraction by multiplying by the reciprocal.

Part 1Understand the ideamodels and meaning
  1. 1Complete the table. Show how you found each value.

    Compare: what happens when you divide the same whole number by different fractions?

    ExpressionQuotientObservation
    12 ÷ 1/2
    12 ÷ 1/3
    12 ÷ 1/4
    12 ÷ 2/3
    12 ÷ 3/4
    Show your work
Part 2Explain and correctreasoning
  1. 2Find the mistake. Explain it, then show the correct work.

    Find the Division Error

    1. 1Problem6 ÷ 2/3
    2. 2Keep, Change, Flip6 × 2/3
    3. 3Multiply12/3
    4. 4Simplify4

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Correct work
    Correct answer:
  2. 3Answer in complete sentences.

    A pizza shop has 8 whole pizzas. Each serving is 2/3 of a pizza. How many servings can they make? Write and solve an equation, then explain why the answer is greater than 8.

    Write your answer

Explain your thinkingWhy does 3 ÷ 1/4 = 12? How does the number line show this?

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