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

Lesson 6.1Dividing a Fraction by a Whole Number

Start hereWords, worked example, and sentence starters

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.

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

Word	What it means	Example
ReciprocalSpanish: Recíproco	A fraction turned upside down.	10 → 1/10
QuotientSpanish: Cociente	The answer when you divide.	3/4 ÷ 2 = 3/8
DividendSpanish: Dividendo	The total number being divided into equal groups (the number inside the division bracket).	In 3 ÷ 1/4 = 12, the dividend is 3 — it is the total being split
DivisorSpanish: Divisor	The number of equal groups you are dividing into (the number outside the division bracket).	In 3/4 ÷ 2, the divisor is 2.
Unit fractionSpanish: Fracción unitaria	A fraction with 1 on top, like 1/4.	1/2, 1/3, 1/4, 1/5 — each represents one equal part of a whole
Multiplicative inverseSpanish: Inverso multiplicativo	Two numbers whose product is 1; each is the reciprocal of the other.	4 and 1/4 · 2/3 and 3/2

How it worksWorked exampledividing a fraction by a whole number

These numbers are not on your problems. The steps are. Follow them with your own numbers.

A 3/4-pound bag of almonds is split evenly into 6 snack cups. How much is in each cup?

Write the whole number over 1. 3/4 ÷ 6 = 3/4 ÷ 6/1
Keep, Change, Flip. 3/4 × 1/6
Multiply across. (3 × 1) over (4 × 6) = 3/24
Simplify. 3/24 = 1/8 pound in each cup

Answer: Each snack cup holds 1/8 pound of almonds.

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

A 2/3-liter bottle of juice is poured evenly into 9 glasses. How much is in each glass?

Write the whole number over 1. 2/3 ÷ 9 = 2/3 ÷ /
Keep, Change, Flip. 2/3 × /
Multiply across. /
Simplify if you can. liter in each glass

Answer:liters of juice in each glass

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

To divide by a whole number, I multiply by over that number.
I split into equal shares.
Each share is , which is smaller than what I started with.
I can check my quotient by multiplying it by .

Word bank reciprocalmultiplicative inversequotientdivisortape diagramequal sharessplitflipmultiplysimplifysmallerproduct

Watch outA common mistake

A common mistake in Interpret Division of Fractions is assuming that dividing always makes the answer smaller. For 4 ÷ 1/3, students reason 'dividing shrinks the number' and compute 4 ÷ 3 ≈ 1.3 instead of asking how many 1/3-foot pieces fit into 4 feet (each whole foot holds 3 thirds, so 4 × 3 = 12). Before you submit, check: if the divisor is a fraction smaller than 1, the quotient must be BIGGER than the dividend, not smaller.

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

Lesson 6.1Dividing a Fraction by a Whole Number

Apply Day · Version ASupported practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice

Name Date Period

Part 1Practice the skillshow every step

1Complete each step, then write the final answer.

Find 3 ÷ 1/5.
Show your work
Hint Put a 1 under the 3. Then keep, change, flip.
Final answer:
2Complete each step, then write the final answer.

Find 4/7 ÷ 3.
Show your work
Hint Write 3 as 3/1. Flip only the 3/1.
Final answer:

Part 2Apply itreal-world problems

3Complete each step, then write the final answer.

A bag holds 6 cups of rice. One scoop is 1/2 cup. How many scoops of rice are in the bag?
Show your work
Hint Find how many 1/2-cup scoops fit in 6 cups. Find 6 ÷ 1/2.
Final answer:

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help

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

Lesson 6.1Dividing a Fraction by a Whole Number

Apply Day · Version BCore practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice

Name Date Period

Part 1Practice the skillshow every step

1Complete each step, then write the final answer.

Find 4 ÷ 1/5.
Show your work
Final answer:

Part 2Apply itreal-world problems

2Complete each step, then write the final answer.

Leo says 1/2 ÷ 4 is 8. He flipped the 1/2 and multiplied: 2 × 4 = 8. Is he right? Find the correct answer.
Show your work
Final answer:
3Complete each step, then write the final answer.

Find 6/7 ÷ 3. Simplify your answer.
Show your work
Final answer:

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help

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

Lesson 6.1Dividing a Fraction by a Whole Number

Apply Day · ChallengeExtension

Mastery check☐ Exceeds☐ Meets target☐ Needs practice

Name Date Period

1Circle the letter of the best answer. Show how you know.
What is the value of 6 ÷ 1/5?
1. A1/30
2. B6/5
3. C11
4. D30
Show your work
2Complete each step, then write the final answer.

Nia says dividing always makes a number smaller. Find 7 ÷ 1/2 to test her idea.
Show your work
Final answer:
3Complete each step, then write the final answer.

Find 4/9 ÷ 6. Simplify your answer.
Show your work
Final answer:

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help