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

Lesson 6.106.10 Small Group · Group 2

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can divide mixed numbers by first changing them to improper fractions, 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
Mixed NumberSpanish: Número mixto A whole number plus a fraction, like 2 1/3. 2 1/3 means 2 wholes and 1/3 more — picture 2 full circles and 1/3 of another
Improper FractionSpanish: Fracción impropia A fraction where the top is bigger than or equal to the bottom, like 7/4. 7/3 is improper because 7 > 3. It equals 2 1/3 as a mixed number.
ConvertSpanish: Convertir To change a number to a new form but keep the same value. 2 1/3 → multiply 2 × 3 = 6, add 1 → 7/3. Same value, different form.
SimplifySpanish: Simplificar To write a fraction with smaller numbers that names the same amount, like 2/4 = 1/2. 8/6: GCF is 2 → 8÷2 / 6÷2 = 4/3 = 1 1/3
ReciprocalSpanish: Recíproco A fraction turned upside down. You use it in keep-change-flip. The reciprocal of 3/4 is 4/3. To divide by 3/4, multiply by 4/3.

How it worksWorked example

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

A trail is 33/4 miles long. It is split into parts that are 11/4 miles long. How many parts are there? Sam divides the wholes and the fractions on their own. He gets 6. Is he right?

  1. Change both mixed numbers to improper fractions: 33/4 = 15/4 → 11/4 = 5/4
  2. Multiply by the reciprocal of 5/4: 15/4 × 4/5 = 60/20 = 3
  3. Check the answer by multiplying back: 3 × 5/4 = 15/4 = 33/4
  4. Look at Sam's way: 3 ÷ 1 = 3 → 3/4 ÷ 1/4 = 3 → 3 + 3 = 6
  5. There are 3 parts. Sam is not right. You cannot divide wholes by wholes and fractions by fractions.

Now you trySame steps, your turn

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

Find 21/2 ÷ 1/2. Then explain why the answer is greater than 21/2.

Answer:

Say it and write itSentence starters

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

  • Before dividing, I convert 2 1/2 to because it is easier to with improper fractions.

Word bank Mixed NumberImproper FractionConvertSimplifyReciprocalimproper5/2convertmultiplyreciprocalkeep-change-flip

Watch outA common mistake

A common mistake in Divide Mixed Numbers is dividing the whole-number parts and fraction parts separately instead of converting first — for example, treating 4 1/2 ÷ 1 1/2 as (4 ÷ 1) + (1/2 ÷ 1/2) = 5. Always convert each mixed number to one improper fraction first, then divide using Keep, Change, Flip: 4 1/2 ÷ 1 1/2 = 9/2 ÷ 3/2 = 9/2 × 2/3 = 3.

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

Lesson 6.106.10 Small Group · Group 2

Group 2Challenge practice

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

Learning target I can divide mixed numbers by first changing them to improper fractions, explain why the method works, and use it on a problem I have not seen before.

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

    Find 4 2/3 ÷ 1 1/6.

    Show your work
    Final answer:
Part 2Apply itreal-world problems
  1. 2Complete each step, then write the final answer.
    0123456134514
    How many jumps of 134 fit in 514?

    A trail is 5 1/4 miles long. It is split into parts that are 1 3/4 miles long. How many parts are there?

    1. 1Change both mixed numbers to improper fractions.
    2. 2Multiply 21/4 by the reciprocal of 7/4. What is the quotient?
    3. 3Check: what is 3 × 1 3/4?
    Final answer:
  2. 3Complete each step, then write the final answer.
    01234567114614
    How many jumps of 114 reach 614?

    Find 6 1/4 ÷ 1 1/4. Then explain why dividing the wholes and the fractions on their own does not work.

    1. 1Change both mixed numbers to improper fractions.
    2. 2Multiply by the reciprocal of 5/4. What is the quotient?
    3. 3Split way: 6 ÷ 1 and 1/4 ÷ 1/4 gives 7. Why is 7 wrong?
    Final answer:
  3. 4Complete each step, then write the final answer.

    A number divided by 1 1/2 is 3 1/3. What is the number?

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

    Lena has 8 3/4 pounds of clay. Each pot uses 1 1/4 pounds. How many pots can she make?

    Show your work
    Final answer:
  5. 6Complete each step, then write the final answer.

    Omar finds 5 1/2 ÷ 2 3/4. He divides 5 by 2 and 1/2 by 3/4 on their own. What is the correct quotient?

    Show your work
    Final answer:

Explain your thinkingSam divides wholes by wholes and fractions by fractions. Use 61/4 ÷ 11/4 to show why that does not work.

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