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Unit 02 · Fraction Operations and ModelsLesson

Day 021Fraction Division and Reciprocals

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 1 ÷ 1. Simplify and explain why your answer is reasonable.

1

1 ÷ 1 = 1 × 1 = 1.

02 · PRACTICE

Your turn

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

  1. Calculate 3/4 ÷ 1/4. Simplify.

  2. Calculate 1/4 ÷ 1/2. Simplify.

  3. Calculate 3/4 ÷ 1/2. Simplify.

  4. Calculate 6/5 ÷ 2. Simplify.

  5. Calculate 2 ÷ 5/4. Simplify.

  6. Calculate 5/3 ÷ 1/2. Simplify.

  7. Calculate 1 ÷ 1. Simplify and explain why your answer is reasonable.

  8. Calculate 1/6 ÷ 1/2. Simplify and explain why your answer is reasonable.

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

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

03 · CHECK

Answers and reasoning

Reveal the teacher answer key
  1. 3

    3/4 ÷ 1/4 = 3/4 × 4 = 3.

  2. 1/2

    1/4 ÷ 1/2 = 1/4 × 2 = 1/2.

  3. 3/2

    3/4 ÷ 1/2 = 3/4 × 2 = 3/2.

  4. 3/5

    6/5 ÷ 2 = 6/5 × 1/2 = 3/5.

  5. 8/5

    2 ÷ 5/4 = 2 × 4/5 = 8/5.

  6. 10/3

    5/3 ÷ 1/2 = 5/3 × 2 = 10/3.

  7. 1

    1 ÷ 1 = 1 × 1 = 1.

  8. 1/3

    1/6 ÷ 1/2 = 1/6 × 2 = 1/3.

  9. 2/5

    1/5 ÷ 1/2 = 1/5 × 2 = 2/5.

  10. 2/25

    1/5 ÷ 5/2 = 1/5 × 2/5 = 2/25.

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