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Unit 02 · Fraction Operations and ModelsLesson

Day 029Explaining Fraction Division

LearnClassworkAnswer keyPDF packet ↗
Standards 6.NS.A.1
LEARNING TARGET

I can divide fractions and check using multiplication.

01 · LEARN

Build the idea

If (a/b) ÷ (c/d) = q, then (c/d) × q = a/b. Multiplying by d/c undoes multiplying by c/d, so divide by a nonzero fraction by multiplying by its reciprocal. Simplify the product.

WORKED EXAMPLE 1

Calculate 1/2 ÷ 1/4. Simplify.

2

1/2 ÷ 1/4 = 1/2 × 4 = 2.

WORKED EXAMPLE 2

Calculate 2 ÷ 3/5. Simplify and explain why your answer is reasonable.

10/3

2 ÷ 3/5 = 2 × 5/3 = 10/3.

02 · PRACTICE

Your turn

Work in order. Start with the foundations, then build toward explanation and application.

  1. Calculate 1/2 ÷ 1/4. Simplify.

  2. Calculate 1 ÷ 1/2. Simplify.

  3. Calculate 1/2 ÷ 1/2. Simplify.

  4. Calculate 7/6 ÷ 1. Simplify.

  5. Calculate 2 ÷ 2. Simplify.

  6. Calculate 3/8 ÷ 3/2. Simplify.

  7. Calculate 2/5 ÷ 1/4. Simplify and explain why your answer is reasonable.

  8. Calculate 4/3 ÷ 1/2. Simplify and explain why your answer is reasonable.

  9. Calculate 1/2 ÷ 4/3. Simplify and explain why your answer is reasonable.

  10. Calculate 2 ÷ 1/5. Simplify and explain why your answer is reasonable.

03 · CHECK

Answers and reasoning

Reveal the teacher answer key
  1. 2

    1/2 ÷ 1/4 = 1/2 × 4 = 2.

  2. 2

    1 ÷ 1/2 = 1 × 2 = 2.

  3. 1

    1/2 ÷ 1/2 = 1/2 × 2 = 1.

  4. 7/6

    7/6 ÷ 1 = 7/6 × 1 = 7/6.

  5. 1

    2 ÷ 2 = 2 × 1/2 = 1.

  6. 1/4

    3/8 ÷ 3/2 = 3/8 × 2/3 = 1/4.

  7. 8/5

    2/5 ÷ 1/4 = 2/5 × 4 = 8/5.

  8. 8/3

    4/3 ÷ 1/2 = 4/3 × 2 = 8/3.

  9. 3/8

    1/2 ÷ 4/3 = 1/2 × 3/4 = 3/8.

  10. 10

    2 ÷ 1/5 = 2 × 5 = 10.

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