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

Lesson 6.26.2 Small Group · Group 1

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target With my small group, I can divide a fraction by a fraction and divide with mixed numbers by multiplying by the reciprocal — one step at a time, with support.

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 1

Group 1Supported practice

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

Learning target With my small group, I can divide a fraction by a fraction and divide with mixed numbers by multiplying by the reciprocal — one step at a time, with support.

Part 1Practice the skillshow every step
  1. 1Complete each step, then write the final answer.

    Find 4/5 ÷ 1/10.

    Show your work

    Hint Keep 4/5. Change ÷ to ×. Flip 1/10.

    Final answer:
Part 2Apply itreal-world problems
  1. 2Complete each step, then write the final answer.
    23 cupone pancake: 16 cup
    23 cup is the same as some sixths.

    Kai has 2/3 cup of milk. Each pancake uses 1/6 cup. How many pancakes can he make? Find 2/3 ÷ 1/6.

    1. 1Keep, Change, Flip. What is the new problem?
    2. 2Multiply the tops. Multiply the bottoms. What fraction do you get?
    3. 3Simplify. How many pancakes can Kai make?
    Final answer:
  2. 3Complete each step, then write the final answer.
    1 mile34 mile
    Count the fourths in 134 miles.

    A trail is 1 3/4 miles long. There is a sign every 1/4 mile. How many 1/4-mile parts are on the trail? Find 1 3/4 ÷ 1/4.

    1. 1Change 1 3/4 to an improper fraction.
    2. 2Keep, Change, Flip. What is the new problem?
    3. 3Multiply and simplify. How many parts?
    Final answer:
  3. 4Complete each step, then write the final answer.

    Find 5/6 ÷ 2/3. Write your answer as a mixed number.

    Show your work

    Hint Flip 2/3 to get 3/2. Then multiply and simplify.

    Final answer:
  4. 5Complete each step, then write the final answer.

    A ribbon is 4 1/2 feet long. Each bow uses 3/4 foot. How many bows can you make?

    Show your work

    Hint Change 4 1/2 to an improper fraction first. Then divide by 3/4.

    Final answer:
  5. 6Complete 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

    Hint Keep the first fraction. Flip only the fraction you divide by.

    Final answer:

Explain your thinkingWhen you find 2/3 ÷ 1/6, why do you flip 1/6 and not 2/3?

Sentence starter I keep {2/3} because ___. · I flip {1/6} because ___.

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