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

Lesson 6.2Division Expressions with Fractions and 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.

Why This Matters Agent Rivera is dividing a 3/4-pound evidence bag into portions that each weigh 1/8 pound. She needs to know exactly how many portions she can make for testing. Can you solve the case?

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 example

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

A pitcher has 2/3 liter of juice. Each cup holds 1/6 liter. How many cups can be filled?

  1. Write the division: 2/3 ÷ 1/6.
  2. Flip the divisor and multiply: 2/3 × 6/1 = 12/3.
  3. Simplify: 12/3 = 4. Check: 4 × 1/6 = 4/6 = 2/3.

Answer: 4 cups

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 1/2 ÷ 1/4. How many 1/4s fit in 1/2? Rename 1/2 as 2/4.

Answer:

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 out!A 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

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

Lesson 6.2Division Expressions with Fractions and Mixed Numbers

Level 0Most support · every hint printed

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.

Why This Matters Agent Rivera is dividing a 3/4-pound evidence bag into portions that each weigh 1/8 pound. She needs to know exactly how many portions she can make for testing. Can you solve the case?

How it worksWorked example

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

A pitcher has 2/3 liter of juice. Each cup holds 1/6 liter. How many cups can be filled?

  1. Write the division: 2/3 ÷ 1/6.
  2. Flip the divisor and multiply: 2/3 × 6/1 = 12/3.
  3. Simplify: 12/3 = 4. Check: 4 × 1/6 = 4/6 = 2/3.

Answer: 4 cups

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

    What is 1/2 ÷ 1/4?

    1. A1/8
    2. B1/2
    3. C2
    4. D4
    Steps to try
    1. This asks how many 1/4-size pieces fit inside 1/2 — the pieces are smaller than the amount.
    2. Multiply by the reciprocal: keep 1/2, change ÷ to ×, and flip the divisor 1/4.
    3. 1/4 flips to 4/1, so multiply 1/2 × 4/1 across the tops and bottoms, then simplify your fraction.
    Show your work
  2. 2Circle the letter of the best answer. Show how you know.

    What is 3/4 ÷ 1/8?

    1. A3/32
    2. B6
    3. C8/3
    4. D24
    Steps to try
    1. How many 1/8-pieces fit into 3/4? Eighths are small, so expect several.
    2. Keep 3/4, change ÷ to ×, and flip 1/8 to its reciprocal.
    3. Set up 3/4 × 8/1, multiply tops and bottoms, then simplify the product.
    Show your work
Part 2Apply itreal-world problems
  1. 3Circle the letter of the best answer. Show how you know.

    What is the reciprocal of 3/5?

    1. A1/3
    2. B3/5
    3. C5/3
    4. D5/5
    Steps to try
    1. Re-read 'reciprocal' — it's about the two numbers of the fraction trading places.
    2. Swap the numerator (top number) with the denominator (bottom number). Nothing else changes.
    3. In 3/5, the 3 is on top and the 5 is on the bottom. Trade their spots and match the result to a choice.
    Rewrite each fraction
    Work it out
    Simplify
    1. 1Same size piecesCommon denominator first.
    2. 2OperateOnly then add or subtract.
    3. 3SimplifyDivide out common factors.
  2. 4Circle the letter of the best answer. Show how you know.

    What is the first step in evaluating 2 1/2 ÷ 1/4?

    1. ARewrite 2 1/2 as the improper fraction 5/2
    2. BFlip 2 1/2 to 1/2 2
    3. CDivide 2 by 1/4 and ignore the half
    4. DAdd 2 + 1/2 + 1/4
    Steps to try
    1. Which number in this problem is a mixed number?
    2. How many halves are in 2 1/2?
    3. Rewrite it as one fraction before multiplying by the reciprocal.
    Show your work

Explain your thinkingWhy does 5/6 ÷ 1/12 = 10? How does the bar model show this?

Sentence starter 5/6 ÷ 1/12 = 10 because 5/6 is the same as ___ twelfths, and ___ twelfths divided by 1 twelfth = ___.

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help