Lesson 6.9Divide Whole Numbers by Fractions
Start hereWords, worked example, and sentence starters
Learning target I can explain what dividing a whole number by a fraction means — how many pieces fit, or how much is in one whole — find the quotient with a model or by multiplying by the reciprocal, and check it by multiplying.
Why This Matters Agent Park has 4 pounds of evidence powder. Each testing bag holds exactly 1/2 pound. He needs to prepare as many testing bags as possible before the lab deadline. How many bags can he fill?
Start hereWords for this lesson
Read each word before you begin. Say it out loud.
| Word | What it means | Example |
|---|---|---|
| Whole NumberSpanish: Número entero | A counting number with no fraction or decimal, like 0, 1, 2, 3. | 4 is a whole number; as a fraction it is 4/1 |
| FractionSpanish: Fracción | A number that shows part of a whole, like 3/4. | 1/2 means 1 out of 2 equal parts — like cutting a sandwich in half and taking one piece |
| ReciprocalSpanish: Recíproco | A fraction turned upside down. | The reciprocal of 2/3 is 3/2. Flip the fraction to divide: 6 ÷ 2/3 = 6 × 3/2 |
| Keep, Change, FlipSpanish: Mantener, cambiar, invertir | A shortcut for dividing fractions: keep the first number, change ÷ to ×, flip the second. It works because dividing by a fraction gives the same answer as multiplying by its reciprocal. | 6 ÷ 1/3 → Keep 6, Change ÷ to ×, Flip 1/3 to 3/1 → 6 × 3 = 18 |
| QuotientSpanish: Cociente | The answer when you divide. | In 4 ÷ 1/2 = 8, the quotient is 8 |
How it worksWorked example
These numbers are not on your problems. The steps are. Follow them with your own numbers.
Agent Park has 4 pounds of powder and each bag holds 1/2 pound. I want 4 ÷ 1/2.
- Each pound fills 2 half-pound bags, so 4 pounds fill 4 × 2 = 8 bags.
- That is the same as multiplying by the reciprocal of 1/2: 4 × 2/1 = 8. Dividing by 1/2 doubles the count, because every whole holds 2 halves.
- Check by multiplying: 8 bags × 1/2 pound = 4 pounds. So 4 ÷ 1/2 = 8. He can fill 8 bags.
Now you trySame steps, your turn
The steps are the same as the worked example. The numbers are yours. Do the work.
Let's try 3 ÷ 1/4 together. How many 1/4s fit in 3? Each whole holds 4 fourths.
Say it and write itSentence starters
Finish each sentence out loud with a partner. Then use them in your writing.
- 3 ÷ 1/4 = 12 because it takes jumps of to get from 0 to .
Word bank Whole NumberFractionReciprocalKeep, Change, FlipQuotient12fourthjumps3four timeseach whole
Watch out!A common mistake
A common mistake in Divide Whole Numbers by Fractions is doing 'Keep, Change' but skipping the 'Flip'
Lesson 6.9Divide Whole Numbers by Fractions
Version ASupported practice
Learning target I can explain what dividing a whole number by a fraction means — how many pieces fit, or how much is in one whole — find the quotient with a model or by multiplying by the reciprocal, and check it by multiplying.
Why This Matters Agent Park has 4 pounds of evidence powder. Each testing bag holds exactly 1/2 pound. He needs to prepare as many testing bags as possible before the lab deadline. How many bags can he fill?
-
1Mark and label each value on the number line.
How many jumps of 1/4 does it take to get from 0 to 2?
Hint Each jump is exactly 1/4, and your goal is to land right on 2.
Show your thinking
-
2Circle the letter of the best answer. Show how you know.
What is 6 ÷ 1/3?
- A2
- B3
- C1/18
- D18
Hint 6 ÷ 1/3 asks how many 1/3-size pieces fit into 6 wholes. Predict: bigger or smaller than 6?
Show your work -
3Circle the letter of the best answer. Show how you know.
What is 3 ÷ 1/5?
- A3/5
- B5/3
- C8
- D15
Hint The total is 3 wholes and each piece is 1/5 — every whole holds several fifths.
Show your work -
4Circle the letter of the best answer. Show how you know.
What is 10 ÷ 1/4?
- A2.5
- B1/40
- C14
- D40
Hint You're counting 1/4-size pieces inside 10 wholes — every whole holds more than one.
Show your work -
5Circle the letter of the best answer. Show how you know.
What is 5 ÷ 1/2?
- A2.5
- B1/10
- C7
- D10
Hint How many 1/2-size pieces fit into 5 wholes? Each whole holds more than one half.
Show your work
-
6Find the mistake. Explain it, then show the correct work.
Spot the Common Mistake
- 1Problem4 ÷ 1/5
- 2Multiply by the reciprocalKept the 4 and changed ÷ to ×, but forgot to flip: 4 × 1/5
- 3Multiply4 × 1/5 = 4/5
Which step has the mistake? Explain what went wrong, then show the correct work.
Hint After 'Change,' you still have to 'Flip' the second fraction.
Correct workCorrect answer:
Explain your thinkingWhy does 3 ÷ 1/4 = 12? How does the number line show this?
Sentence starter 3 ÷ 1/4 = 12 because it takes ___ jumps of ___ to get from 0 to ___.
Lesson 6.9Divide Whole Numbers by Fractions
Version BCore practice
Learning target I can explain what dividing a whole number by a fraction means — how many pieces fit, or how much is in one whole — find the quotient with a model or by multiplying by the reciprocal, and check it by multiplying.
Why This Matters Agent Park has 4 pounds of evidence powder. Each testing bag holds exactly 1/2 pound. He needs to prepare as many testing bags as possible before the lab deadline. How many bags can he fill?
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1Complete the table. Show how you found each value.
Complete the table: Whole Number ÷ Fraction. Use the reciprocal shortcut.
Expression Rewrite as Multiplication Quotient 5 ÷ 1/4 8 ÷ 1/2 3 ÷ 1/6 7 ÷ 1/3 Show your work -
2Write the letter of the matching item on each line.
Match each division expression to its quotient.
- 4 ÷ 1/3
- 7 ÷ 1/2
- 5 ÷ 1/6
- 2 ÷ 1/8
- 9 ÷ 1/4
- 6 ÷ 1/5
- A12
- B14
- C30
- D16
- E36
- F30
-
3Use the model to solve. Show your work.
How many groups of 2/3 fit into 3?
Show your workAnswer:
-
4Circle the letter of the best answer. Show how you know.
What is 6 ÷ 2/3?
- A2/18
- B4
- C9
- D12
Show your work
-
5Circle the letter of the best answer. Show how you know.
Agent Park's 6 pounds of evidence powder fill 3/4 of a storage tub. How many pounds fill a WHOLE tub? (6 ÷ 3/4 asks how much is in one whole tub.)
- A4 1/2 pounds
- B8 pounds
- C2 pounds
- D6 3/4 pounds
Show your work
-
6Find the mistake. Explain it, then show the correct work.
Spot the Common Mistake
- 1Problem8 ÷ 3/4
- 2Multiply by the reciprocalFlipped the wrong number — wrote 1/8 × 3/4 instead of 8 × 4/3
- 3Multiply1/8 × 3/4 = 3/32
Which step has the mistake? Explain what went wrong, then show the correct work.
Correct workCorrect answer:
Explain your thinkingWhy does 3 ÷ 1/4 = 12? How does the number line show this?
Lesson 6.9Divide Whole Numbers by Fractions
ChallengeExtension
Learning target I can explain what dividing a whole number by a fraction means — how many pieces fit, or how much is in one whole — find the quotient with a model or by multiplying by the reciprocal, and check it by multiplying.
Why This Matters Agent Park has 4 pounds of evidence powder. Each testing bag holds exactly 1/2 pound. He needs to prepare as many testing bags as possible before the lab deadline. How many bags can he fill?
-
1Complete the table. Show how you found each value.
Compare: what happens when you divide the same whole number by different fractions?
Expression Quotient Observation 12 ÷ 1/2 12 ÷ 1/3 12 ÷ 1/4 12 ÷ 2/3 12 ÷ 3/4 Show your work
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2Find the mistake. Explain it, then show the correct work.
Find the Division Error
- 1Problem6 ÷ 2/3
- 2Multiply by the reciprocal6 × 2/3
- 3Multiply12/3
- 4Simplify4
Which step has the mistake? Explain what went wrong, then show the correct work.
Correct workCorrect answer: -
3Answer in complete sentences.
A pizza shop has 8 whole pizzas. Each serving is 2/3 of a pizza. How many servings can they make? Write and solve an equation, then explain why the answer is greater than 8.
Write your answer