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

Lesson 6.106.10 · Part II

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can explain what dividing with mixed numbers means, rewrite them as improper fractions, find the quotient with common denominators or by multiplying by the reciprocal, 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
Mixed NumberSpanish: Número mixto	A whole number plus a fraction, like 2 1/3.	2 1/3 means 2 wholes and 1/3 more — picture 2 full circles and 1/3 of another
Improper FractionSpanish: Fracción impropia	A fraction where the top is bigger than or equal to the bottom, like 7/4.	7/3 is improper because 7 > 3. It equals 2 1/3 as a mixed number.
ConvertSpanish: Convertir	To change a number to a new form but keep the same value.	2 1/3 → multiply 2 × 3 = 6, add 1 → 7/3. Same value, different form.
SimplifySpanish: Simplificar	To write a fraction with smaller numbers that names the same amount, like 2/4 = 1/2.	8/6: GCF is 2 → 8÷2 / 6÷2 = 4/3 = 1 1/3
ReciprocalSpanish: Recíproco	A fraction turned upside down. Dividing by a fraction gives the same answer as multiplying by its reciprocal.	The reciprocal of 3/4 is 4/3. To divide by 3/4, multiply by 4/3.

Say it and write itSentence starters

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

Word bank Mixed NumberImproper FractionConvertSimplifyReciprocal

Watch outA common mistake

A common mistake in Divide Mixed Numbers is dividing the whole-number parts and fraction parts separately instead of converting first — for example, treating 4 1/2 ÷ 1 1/2 as (4 ÷ 1) + (1/2 ÷ 1/2) = 5. Always convert each mixed number to one improper fraction first, then divide using the reciprocal shortcut: 4 1/2 ÷ 1 1/2 = 9/2 ÷ 3/2 = 9/2 × 2/3 = 3.

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

Lesson 6.106.10 · Part II

Apply Day · Version ASupported practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice

Name Date Period

Learning target I can explain what dividing with mixed numbers means, rewrite them as improper fractions, find the quotient with common denominators or by multiplying by the reciprocal, and check it by multiplying.

1Complete each step, then write the final answer.

Find 1 1/4 ÷ 1/4.
Show your work
Hint Change 1 1/4 to 5/4. Then multiply by 4.
Final answer:
2Complete each step, then write the final answer.

Find 2 1/2 ÷ 1/4.
Show your work
Hint Change 2 1/2 to 5/2. Then multiply by 4.
Final answer:
3Complete each step, then write the final answer.

Find 3 1/2 ÷ 1/2.
Show your work
Hint Change 3 1/2 to 7/2. Then multiply by 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 6.106.10 · Part II

Apply Day · Version BCore practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice

Name Date Period

Learning target I can explain what dividing with mixed numbers means, rewrite them as improper fractions, find the quotient with common denominators or by multiplying by the reciprocal, and check it by multiplying.

Part 1Practice the skillshow every step

1Complete each step, then write the final answer.

Find 4 2/3 ÷ 1 1/6.
Show your work
Final answer:
2Complete each step, then write the final answer.

Find 2 2/5 ÷ 3/5.
Show your work
Final answer:

Part 2Apply itreal-world problems

3Circle the letter of the best answer. Show how you know.
Which is the correct first step for 2 3/4 ÷ 1/4?
1. AChange 2 3/4 to 11/4
2. BChange 2 3/4 to 5/4
3. CFlip 2 3/4
4. DDrop the 3/4 and find 2 ÷ 1/4
Show your work

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 6.106.10 · Part II

Apply Day · ChallengeExtension

Mastery check☐ Exceeds☐ Meets target☐ Needs practice

Name Date Period

Learning target I can explain what dividing with mixed numbers means, rewrite them as improper fractions, find the quotient with common denominators or by multiplying by the reciprocal, and check it by multiplying.

Part 1Practice the skillshow every step

1Complete each step, then write the final answer.

Find 3 1/2 ÷ 1 3/4.
Show your work
Final answer:

Part 2Apply itreal-world problems

2Circle the letter of the best answer. Show how you know.
What is the value of 3 3/4 ÷ 1 1/2?
1. A1 1/2
2. B2 1/2
3. C2
4. D5 5/8
Show your work
3Complete each step, then write the final answer.

Omar finds 5 1/2 ÷ 2 3/4. He divides 5 by 2 and 1/2 by 3/4 on their own. What is the correct quotient?
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