# Illustrative Mathematics Unit 6.5, Lesson 11: Dividing Numbers that Result in Decimals

Learning Targets:

• I can use long division to find the quotient of two whole numbers when the quotient is not a whole number.

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Illustrative Math

#### Lesson 11: Dividing Numbers that Result in Decimals

Let’s find quotients that are not whole numbers.

Illustrative Math Unit 6.5, Lesson 11 (printable worksheets)

#### Lesson 11 Summary

The following diagram shows how to use base-ten diagrams to find quotients that are not whole numbers. The following diagram shows how to use long division to find quotients that are not whole numbers. #### Lesson 11.1 Number Talk: Evaluating Quotients

Find the quotients mentally.
400 ÷ 8
80 ÷ 8
16 ÷ 8
498 ÷ 8

#### Lesson 11.2 Keep Dividing

Here is how Mai used base-ten diagrams to calculate 62 ÷ 5.
She started by representing 62.
She then made 5 groups, each with 1 ten. There was 1 ten left. She unbundled it into 10 ones and distributed the ones across the 5 groups.
Here is her diagram for 62 ÷ 5.

1. Discuss these questions with a partner and write down your answers:
a. Mai should have a total of 12 ones, but her diagram shows only 10. Why?
b. She did not originally have tenths, but in her diagram each group has 4 tenths. Why?
c. What value has Mai found for 62 ÷ 5? Explain your reasoning.
2. Find the quotient of 511 ÷ 5 by drawing base-ten diagrams or by using the partial quotients method. Show your reasoning. If you get stuck, work with your partner to find a solution.
3. Four students share a \$271 prize from a science competition. How much does each student get if the prize is shared equally? Show your reasoning.

#### Lesson 11.3 Using Long Division to Calculate Quotients

1. Here is how Lin calculated 62 ÷ 5.
• Lin put a 0 after the remainder of 2. Why? Why does this 0 not change the value of the quotient?
• Lin subtracted 5 groups of 4 from 20. What value does the 4 in the quotient represent?
• What value did Lin find for 62 ÷ 5?
1. Use long division to find the value of each expression. Then pause so your teacher can review your work.
a. 126 ÷ 8
b. 90 ÷ 12
2. Use long division to show that:
a. 5 ÷ 4, or 5/4, is 1.25
b. 4 ÷ 5, or 4/5, is 0.8
c. 1 ÷ 8, or 1/8, is 0.125
d. 1 ÷ 25, or 1/25, is 0.04
3. Noah said we cannot use long division to calculate 10 ÷ 3 because there will always be a remainder.
a. What do you think Noah meant by “there will always be a remainder”?
b. Do you agree with his statement? Why or why not?

#### Lesson 11 Practice Problems

1. Use long division to show that the fraction and decimal in each pair are equal.
a. 3/4 and 0.75
b. 3/20 and 0.06
c. 7/25 and 0.28
2. Mai walked 1/8 of a 30-mile walking trail. How many miles did Mai walk? Explain or show your reasoning.
3. Use long division to find each quotient. Write your answer as a decimal.
a. 99 ÷ 12
b. 216 ÷ 5
c. 1,988 ÷ 8
4. To find the decimal of 9/25, Tyler reasoned: “9/25 is equivalent to 18/20 and to 36/100, so the decimal of 9/25 is 0.36.”
a. Use long division to show that Tyler is correct.
b. Is the decimal of 18/50 also 0.36? Use long division to support your answer.
5. Complete the calculations so that each shows the correct difference.
6. Use the equation 124 · 15 = 1,860 and what you know about fractions, decimals, and place value to explain how to place the decimal point when you compute (1.24) · (0.15)

The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics.

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