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Learning Goal: Divide a fraction by a fraction to find how many groups fit, using models and the keep-change-flip rule.

Vocabulary

dividendThe number being split up (it comes first in the division).
divisorThe number you divide by (it comes after the ÷ sign).
reciprocalA fraction flipped upside down; 3/4 becomes 4/3.
quotientThe answer to a division problem.

What You Need to Know

  • Dividing asks 'how many of the divisor fit into the dividend?'
  • Keep the first fraction, Change ÷ to ×, Flip the second fraction (its reciprocal).
  • A whole number like 4 can be written as 4/1 before flipping.
  • Dividing by a fraction smaller than 1 gives an answer larger than the dividend.
  • Always simplify your final answer and write any improper fraction or mixed number clearly.
  • A bar model or number line shows the same answer the rule gives.

Worked Example I Do — watch how it works

A ribbon is 3/4 yard long. Each bow needs 1/8 yard. How many bows can you make?
  1. Step 1. Write the division: 3/4 ÷ 1/8.
  2. Step 2. Keep 3/4, change ÷ to ×, flip 1/8 to 8/1: 3/4 × 8/1.
  3. Step 3. Multiply: (3 × 8)/(4 × 1) = 24/4, then simplify to 6.
Answer: 6 bows

Guided Practice We Do — try it together

  1. 1. 2/3 ÷ 1/6
    💡 Hint: Flip 1/6 to 6/1, then multiply 2/3 × 6/1.
  2. 2. How many 1/3-cup scoops are in 5/6 cup of flour?
    💡 Hint: 5/6 ÷ 1/3, flip the divisor to 3/1.
  3. 3. 3/4 ÷ 2/3
    💡 Hint: Multiply 3/4 × 3/2; do not simplify too early.

Independent Practice You Do — show your work

  1. 1. 7/8 ÷ 1/4
  2. 2. 4/5 ÷ 2/3
  3. 3. 5/8 ÷ 1/2
  4. 4. A board is 2/3 meter long and is cut into 4 equal pieces. How long is each piece?
  5. 5. How many 2/3-liter bottles can be filled from 6 liters of juice?

MCAP-Style Practice

Directions: Answer each item the way you would on the MCAP. For selected-response items, fill in the circle (○) next to the correct answer. For constructed-response items, enter your answer and show your work. Every item below assesses standard 6.NS.A.1.
Item 1Selected Response6.NS.A.1

A baker has 9/10 kg of dough and uses 3/5 kg per loaf. How many loaves can she make?

Select the correct answer.

Item 2Selected Response6.NS.A.1

Which expression has the same value as 5/6 ÷ 1/3?

Select the correct answer.

Item 3Constructed Response6.NS.A.1

Use a model or the rule: 1/2 ÷ 1/8 = ____.

Enter your answer in the space provided. Show your work.

Enter your answer:
Teacher Answer Key (click to show)
Independent 17/2, or 3 1/2
Independent 26/5, or 1 1/5
Independent 35/4, or 1 1/4
Independent 41/6 meter
Independent 59 bottles
Item 1 · 6.NS.A.1C — 9/10 ÷ 3/5 = 9/10 × 5/3 = 45/30 = 3/2, which is 1 1/2 loaves.
Item 2 · 6.NS.A.1B — Dividing by 1/3 means multiplying by its reciprocal, 3/1.
Item 3 · 6.NS.A.14 — Shade 1/2 of a whole, then split it into 1/8 pieces; there are 4 eighths inside the half.
Neft Teacher · Grade 6 MCAP Mathematics Review · Standard 6.NS.A.1