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

Lesson 6.1Dividing a Fraction by a Whole Number

Apply Day · Set BSecond form · new problems, same idea

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

Learning target I can explain what dividing with a whole number and a unit fraction means — how many groups fit, or how much is in one group — find the quotient with a model, and check it by multiplying.

Remember6.1 · Part II

Dividing Whole Numbers & Fractions

  1. Name the question: 3 ÷ 1/4 asks how many 1/4s fit in 3, and 1/2 ÷ 4 asks how much is in each of 4 equal shares
  2. Use the model: each whole holds 4 fourths, so 3 wholes hold 3 × 4 = 12 fourths, and 3 ÷ 1/4 = 12
  3. Check by multiplying: 12 × 1/4 = 3. Shortcut: dividing by 1/4 gives the same answer as multiplying by its reciprocal, 4

Words: Reciprocal (Recíproco)Quotient (Cociente)Dividend (Dividendo)Divisor (Divisor)Unit fraction (Fracción unitaria)

Part 1Understand the ideamodels and meaning
  1. 1Circle the letter of the best answer. Show how you know.

    What does 3 ÷ 1/4 mean?

    1. AHow many 1/4-size pieces fit into 3
    2. B1/4 of 3
    3. C3 groups of 1/4
    4. D3 minus 1/4
    Show your work
  2. 2Circle the letter of the best answer. Show how you know.

    Which expression means 'how many 1/3-size pieces are in 2'?

    1. A1/3 ÷ 2
    2. B2 ÷ 1/3
    3. C2 × 1/3
    4. D2 + 1/3
    Show your work
  3. 3Circle the letter of the best answer. Show how you know.

    The model shows a 3-foot ribbon cut into 1/4-foot pieces. Which expression does the model represent, and how many pieces are there?

    1. A3 × 1/4 = 3/4 of a piece
    2. B3 ÷ 1/4 = 12 pieces
    3. C1/4 ÷ 3 = 1/12 of a piece
    4. D3 ÷ 4 = 3/4 of a piece
    Show your work
Part 2Practice the skillshow every step
  1. 4Complete each step, then write the final answer.

    Find 3 ÷ 1/2.

    Show your work
    Final answer:
  2. 5Complete each step, then write the final answer.

    Find 3/5 ÷ 2.

    Show your work
    Final answer:
Part 3Apply itreal-world problems
  1. 6Complete each step, then write the final answer.

    A fraction divided by 5 is 1/10. What is the fraction?

    Show your work
    Final answer:
  2. 7Complete each step, then write the final answer.

    A farmer has 5/6 acre of land. She splits it into 5 equal gardens. How big is each garden?

    Show your work
    Final answer:
  3. 8Complete each step, then write the final answer.

    One lap of a track is 1/4 mile. Mo runs 9 miles. How many laps does he run?

    Show your work
    Final answer:
  4. 9Complete each step, then write the final answer.

    A ribbon is 6 feet long. You cut it into 1/4-foot pieces. Then you cut each piece into 3 equal parts. How many small parts do you get?

    Show your work
    Final answer:
  5. 10Circle the letter of the best answer. Show how you know.

    A rope is 4 feet long. How many 1/2-foot pieces can be cut from it?

    1. A1/2 piece
    2. B2 pieces
    3. C4 pieces
    4. D8 pieces
    Write any whole number over 1
    Keep · Change · Flip
    Multiply across
    Simplify · label the units
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help