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Unit 02 · Fraction Operations and ModelsLesson

Day 028Missing Factors and Quotients

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

I can connect a fraction quotient to a missing factor.

01 · LEARN

Build the idea

Division and multiplication are inverse operations. For T ÷ s = n, the related equation is s × n = T. Label whether the unknown is the total, the group size, or the number of groups.

WORKED EXAMPLE 1

The equation 1/2 × n = 3/4 represents equally sized portions. Find n, write the related division equation, and check.

n = 3/2; 3/4 ÷ 1/2 = 3/2

3/4 ÷ 1/2 = 3/4 × 2 = 3/2. Check: 1/2 × 3/2 = 3/4.

WORKED EXAMPLE 2

The equation 5/2 × n = 7/3 represents equally sized portions. Find n, write the related division equation, and check.

n = 14/15; 7/3 ÷ 5/2 = 14/15

7/3 ÷ 5/2 = 7/3 × 2/5 = 14/15. Check: 5/2 × 14/15 = 7/3.

02 · PRACTICE

Your turn

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

  1. The equation 1/4 × n = 1/4 represents equally sized portions. Find n, write the related division equation, and check.

  2. The equation 1/4 × n = 3/4 represents equally sized portions. Find n, write the related division equation, and check.

  3. The equation 1/4 × n = 1/2 represents equally sized portions. Find n, write the related division equation, and check.

  4. The equation 3/2 × n = 3 represents equally sized portions. Find n, write the related division equation, and check.

  5. The equation 3/4 × n = 7/8 represents equally sized portions. Find n, write the related division equation, and check.

  6. The equation 5/2 × n = 8/3 represents equally sized portions. Find n, write the related division equation, and check.

  7. The equation 1/5 × n = 3/5 represents equally sized portions. Find n, write the related division equation, and check.

  8. The equation 1/4 × n = 3/5 represents equally sized portions. Find n, write the related division equation, and check.

  9. The equation 1 × n = 1/8 represents equally sized portions. Find n, write the related division equation, and check.

  10. The equation 1/2 × n = 1/8 represents equally sized portions. Find n, write the related division equation, and check.

03 · CHECK

Answers and reasoning

Reveal the teacher answer key
  1. n = 1; 1/4 ÷ 1/4 = 1

    1/4 ÷ 1/4 = 1/4 × 4 = 1. Check: 1/4 × 1 = 1/4.

  2. n = 3; 3/4 ÷ 1/4 = 3

    3/4 ÷ 1/4 = 3/4 × 4 = 3. Check: 1/4 × 3 = 3/4.

  3. n = 2; 1/2 ÷ 1/4 = 2

    1/2 ÷ 1/4 = 1/2 × 4 = 2. Check: 1/4 × 2 = 1/2.

  4. n = 2; 3 ÷ 3/2 = 2

    3 ÷ 3/2 = 3 × 2/3 = 2. Check: 3/2 × 2 = 3.

  5. n = 7/6; 7/8 ÷ 3/4 = 7/6

    7/8 ÷ 3/4 = 7/8 × 4/3 = 7/6. Check: 3/4 × 7/6 = 7/8.

  6. n = 16/15; 8/3 ÷ 5/2 = 16/15

    8/3 ÷ 5/2 = 8/3 × 2/5 = 16/15. Check: 5/2 × 16/15 = 8/3.

  7. n = 3; 3/5 ÷ 1/5 = 3

    3/5 ÷ 1/5 = 3/5 × 5 = 3. Check: 1/5 × 3 = 3/5.

  8. n = 12/5; 3/5 ÷ 1/4 = 12/5

    3/5 ÷ 1/4 = 3/5 × 4 = 12/5. Check: 1/4 × 12/5 = 3/5.

  9. n = 1/8; 1/8 ÷ 1 = 1/8

    1/8 ÷ 1 = 1/8 × 1 = 1/8. Check: 1 × 1/8 = 1/8.

  10. n = 1/4; 1/8 ÷ 1/2 = 1/4

    1/8 ÷ 1/2 = 1/8 × 2 = 1/4. Check: 1/2 × 1/4 = 1/8.

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