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You did these with your group. Now do them on your own — the model above is yours to copy.

1. 1

   Same stepsFinish what the group started. Use the model above, step for step.

   Try it together — then prove it: Find 21/2 ÷ 1/2. Then explain why the answer is greater than 21/2. Change 21/2 to an improper fraction. (5/2) Rewrite the division as multiplication by the reciprocal. (5/2 × 2/1) Multiply and simplify. (10/2 = 5) Why is 5 greater than 21/2? (We count halves. Each whole has 2 halves, so there are more halves than wholes.)

   Show your work
2. 2

   Warm restartWhat is the reciprocal of 3/5?

   1. A1/3
   2. B3/5
   3. C5/5
   4. D5/3

   How do you know?
3. 3

   Warm restartWhat is 2/3 ÷ 1/3?

   1. A1/2
   2. B2/9
   3. C2
   4. D6

   How do you know?
4. 4

   Warm restartWhat is 1/2 ÷ 1/4?

   1. A1/8
   2. B1/2
   3. C2
   4. D4

   How do you know?

You answered these out loud. Now write them.

Answer, then say how you know — the reason is the part that counts.

1. 5

   Think it throughWrite 5 1/4 as an improper fraction.

   1. A9/4
   2. B20/4
   3. C21/4
   4. D51/4

   Why is that the answer?
2. 6

   Think it through5 1/4 ÷ 3/4 = ?

   1. A3 3/4
   2. B4
   3. C6
   4. D7

   How do you know? Give a second reason as well.
3. 7

   Think it throughCheck the answer: how long are 7 pieces of 3/4 foot?

   1. A3/4 foot
   2. B5 1/4 feet
   3. C5 3/4 feet
   4. D7 feet

   Explain your thinking. What would have to change for a different choice to be right?
4. 8

   Back to the modelWhy is converting to an improper fraction the first step when dividing mixed numbers?

Use the words

Fill each blank with a word from the bank.

• A number with a whole number and a fraction, like 2 1/3, is a ___.
• A fraction whose numerator is greater than or equal to its denominator, like 7/3, is an ___.
• Changing a mixed number into an improper fraction is to ___ it.
• Writing a fraction with smaller numbers that names the same amount, like 4/8 = 1/2, is to ___ it.

Explain the thinking

1. 9

   Find the mistakeAnother student made this exact mistake in this lesson. Explain why it is wrong, then write what they should have done.

   The 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.
2. 10

   Say moreWalk your partner through how you changed the mixed numbers before dividing.
3. 11

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: Agent Chen maps a 3 1/2-mile suspect route and splits it into equal 1/4-mile segments so she can place a surveillance marker at each segment.

   Show your work

Last check

These two come from Lesson 6.9. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowExplain your thinking — What is 2 2/3 ÷ 2/3?

   1. A1 7/9
   2. B2/3
   3. C4
   4. D8/3

   Explain your choice.
2. 13

   From Lesson 6.9Explain your thinking — What is 9 ÷ 1/3?

   1. A1/27
   2. B3
   3. C9/3
   4. D27

   How do you know?
3. 14

   From Lesson 6.9A student answered 2.5. What did they do wrong?

   1. AThey multiplied by 4
   2. BThey added 1/4
   3. CThey used the wrong rope length
   4. DThey divided by 4 instead of by 1/4

   How do you know?

Be honest — this tells your teacher what to do next