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

Lesson 6.26.2 Small Group · Group 2

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can divide a fraction by a fraction and divide with mixed numbers by multiplying by the reciprocal, 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
DividendSpanish: Dividendo The total number being divided into equal groups (the number inside the division bracket). In 8/9 ÷ 2/9, 8/9 is the dividend.
DivisorSpanish: Divisor The number of equal groups you are dividing into (the number outside the division bracket). In 8/9 ÷ 2/9, 2/9 is the divisor.
ReciprocalSpanish: Recíproco A fraction turned upside down. 2/9 → 9/2
QuotientSpanish: Cociente The answer when you divide. 8/9 ÷ 2/9 = 4
SimplifySpanish: Simplificar To write a fraction with smaller numbers that names the same amount, like 2/4 = 1/2. 8/12 → GCF is 4 → 8÷4 / 12÷4 = 2/3
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 = 5/2

How it worksWorked exampledividing a fraction by a fraction

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

A pitcher holds 8/9 liter of lemonade. Each glass takes 2/9 liter. How many glasses can be filled?

  1. Write the division. 8/9 ÷ 2/9
  2. Keep, Change, Flip. Keep 8/9, change ÷ to ×, flip the divisor to 9/2
  3. Multiply across. 8/9 × 9/2 = 72/18
  4. Simplify. 72/18 = 4 glasses

Answer: The pitcher fills 4 glasses that each hold 2/9 liter.

Now you trySame steps, your turn

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

A roll holds 6/7 meter of tape. Each label uses 2/7 meter. How many labels can be made?

  1. Write the division. ÷
  2. Keep, Change, Flip. 6/7 × /
  3. Multiply across. /
  4. Simplify. labels
Answer:number of labels

Say it and write itSentence starters

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

  • To divide by , I multiply by its reciprocal .
  • The quotient counts how many groups of fit inside .
  • I did not need a common denominator because .
  • After multiplying across, I simplified to .

Word bank reciprocaldividenddivisorquotientkeepchangeflipmultiply acrosssimplifygroupsfit insidetape diagram

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 6.26.2 Small Group · Group 2

Group 2Challenge practice

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

Learning target I can divide a fraction by a fraction and divide with mixed numbers by multiplying by the reciprocal, 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.
    sugar: 56 cupone batch: 13 cup = 26
    How many 26 parts fit in 56?

    Mo has 5/6 cup of sugar. One batch of cookies needs 1/3 cup. How many batches can he make?

    1. 1Keep, Change, Flip. Then multiply. What fraction do you get?
    2. 2Simplify. Write the answer as a mixed number.
    3. 3What does the 1/2 mean for Mo?
    Final answer:
  2. 2Complete each step, then write the final answer.
    Piece lengthDivisionPieces
    56 foot52 ÷ 56?
    114 feet52 ÷ 54?
    Same board, two piece lengths.

    A board is 2 1/2 feet long. How many 5/6-foot pieces fit? How many 1 1/4-foot pieces fit?

    1. 1Write 2 1/2 as an improper fraction.
    2. 2Find 5/2 ÷ 5/6. How many pieces fit?
    3. 3Find 5/2 ÷ 5/4. How many pieces fit?
    4. 4Why does the longer piece give a smaller quotient?
    Final answer:
  3. 3Complete each step, then write the final answer.

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

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

    2/3 divided by a unit fraction is 8. A unit fraction has 1 on top. What is the unit fraction?

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

    A water jug holds 6 1/4 liters. Each bottle holds 1 1/2 liters. How many bottles can you fill? Give a mixed number.

    Show your work
    Final answer:
  6. 6Complete 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:

Explain your thinkingMo got 21/2 batches. What does the fraction part of a quotient tell you? Use Mo's sugar to explain.

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