Start here

Use the model to solve the first problem. Then try these quick review questions from earlier lessons.

1. 1

   Same stepsFinish what the group started. Use the model above, step for step. 🔊 Listen 💡 Hint

   Try it together — then prove it:

   1. Find 21/2 ÷ 1/2. Then explain why the answer is greater than 21/2.
   2. Change 21/2 to an improper fraction. (5/2)
   3. Rewrite the division as multiplication by the reciprocal. (5/2 × 2/1)
   4. Multiply and simplify. (10/2 = 5)
   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

   Quick reviewWhat is the reciprocal of 3/5? 🔊 Listen 💡 Hint

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

   How do you know?
3. 3

   Quick reviewWhat is 2/3 ÷ 1/3? 🔊 Listen 💡 Hint

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

   How do you know?
4. 4

   Quick reviewWhat is 1/2 ÷ 1/4? 🔊 Listen 💡 Hint

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

   How do you know?

Try these on your own

Choose an answer. Then explain how you know.

1. 5

   Think it throughWrite 5 1/4 as an improper fraction. 🔊 Listen 💡 Hint

   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 = ? 🔊 Listen 💡 Hint

   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? 🔊 Listen 💡 Hint

   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? 🔊 Listen 💡 Hint

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 mistakeRead the mistake. Explain what went wrong, then show the correct step. 🔊 Listen 💡 Hint

   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. 🔊 Listen 💡 Hint
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. 🔊 Listen 💡 Hint

   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? 🔊 Listen 💡 Hint

   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? 🔊 Listen 💡 Hint

   1. A1/27
   2. B3
   3. C12
   4. D27

   How do you know?
3. 14

   From Lesson 6.9A student answered 2.5. What did they do wrong? 🔊 Listen 💡 Hint

   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?

Check your progress

Choose the box that best describes how you feel about each skill.