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

Lesson 6.2Dividing with Mixed Numbers

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can explain what dividing a fraction by a fraction means, find the quotient with common denominators or by multiplying by the reciprocal, and check it by multiplying.

Start hereWords for this lesson

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

WordWhat it meansExample
DividendSpanish: Dividendo The total number being divided into equal groups (the number inside the division bracket). In 3/4 ÷ 1/2, the dividend is 3/4 — the total amount being split
DivisorSpanish: Divisor The number of equal groups you are dividing into (the number outside the division bracket). In 3/4 ÷ 1/2, the divisor is 1/2 — the size of each group
ReciprocalSpanish: Recíproco A fraction turned upside down. 9/4 → 4/9
QuotientSpanish: Cociente The answer when you divide. 27/4 ÷ 9/4 = 3
SimplifySpanish: Simplificar To write a fraction with smaller numbers that names the same amount, like 2/4 = 1/2. 2/4 = 1/2
Mixed numberSpanish: Número mixto A whole number and a fraction written together, like 2 1/2. It must be rewritten as an improper fraction before dividing. 2 1/2

How it worksWorked exampledividing two mixed numbers

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

A ribbon is 6 3/4 meters long. Each bow uses 2 1/4 meters. How many bows can be made?

  1. Change both to improper fractions. 6 3/4 = 27/4 2 1/4 = 9/4
  2. Keep, Change, Flip. 27/4 × 4/9
  3. Multiply across. 108/36
  4. Simplify. 108/36 = 3 bows

Answer: The ribbon makes 3 bows that each use 2 1/4 meters.

Now you trySame steps, your turn

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

A pipe is 10 1/2 feet long. It is cut into pieces that are each 3 1/2 feet. How many pieces?

  1. Change both to improper fractions. 10 1/2 = / 2 3 1/2 = / 2
  2. Keep, Change, Flip. / 2 × /
  3. Multiply across. /
  4. Simplify. pieces
Answer:number of pipe pieces

Say it and write itSentence starters

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

  • I changed to the improper fraction .
  • To convert, I multiplied by the whole number and added the top.
  • Then I multiplied by the reciprocal .
  • The quotient means that many groups fit inside.

Word bank mixed numberimproper fractionreciprocalquotientconvertnumeratordenominatorflipmultiply acrosssimplifyleft overgroups

Watch outA common mistake

A common mistake in Divide Fractions is flipping the wrong fraction: students flip the dividend (the first fraction) instead of the divisor (the second fraction). For example, solving 3/4 ÷ 5/8 by flipping 3/4 to 4/3 and keeping 5/8 gives 4/3 × 5/8 = 20/24 = 5/6 — but only the divisor gets flipped. Keep 3/4, change ÷ to ×, and flip only the divisor 5/8 to its reciprocal 8/5: 3/4 × 8/5 = 24/20 = 6/5. Before you submit, check that the fraction you kept (the dividend) is still facing the same way it started.

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

Lesson 6.2Dividing with Mixed Numbers

Apply Day · Version ASupported practice

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

Learning target I can explain what dividing a fraction by a fraction means, find the quotient with common denominators or by multiplying by the reciprocal, and check it by multiplying.

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

    Find 2/5 ÷ 1/10.

    Show your work

    Hint Keep 2/5. Change ÷ to ×. Flip 1/10.

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

    Find 1 1/2 ÷ 1/4.

    Show your work

    Hint Change 1 1/2 to an improper fraction first.

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

    Find 3/8 ÷ 3/4.

    Show your work

    Hint Keep 3/8. Flip 3/4. Multiply and simplify.

    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 6: Numerical and Algebraic ExpressionsStandard 6.NOS.1

Lesson 6.2Dividing with Mixed Numbers

Apply Day · Version BCore practice

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

Learning target I can explain what dividing a fraction by a fraction means, find the quotient with common denominators or by multiplying by the reciprocal, and check it by multiplying.

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

    Ben finds 2/3 ÷ 4/9. He flips the 2/3 instead of the 4/9. Find the correct answer.

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

    Find 9/10 ÷ 3/5. Write your answer as a mixed number.

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

    Find 7/8 ÷ 1/4. Write your answer as a mixed number.

    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 6: Numerical and Algebraic ExpressionsStandard 6.NOS.1

Lesson 6.2Dividing with Mixed Numbers

Apply Day · ChallengeExtension

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

Learning target I can explain what dividing a fraction by a fraction means, find the quotient with common denominators or by multiplying by the reciprocal, and check it by multiplying.

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

    What is the value of 2 1/4 ÷ 3/8?

    1. A1/6
    2. B2 2/3
    3. C6
    4. D27/32
    Show your work
  2. 2Complete each step, then write the final answer.

    Lee says 4/5 ÷ 2/5 is less than 4/5, because division makes numbers smaller. Find the quotient.

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

    Find 7/9 ÷ 2/3. Write your answer as a mixed number.

    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