# Lesson 11

Dividing Numbers that Result in Decimals

Let’s find quotients that are not whole numbers.

### Problem 1

Use long division to show that the fraction and decimal in each pair are equal.

$$\frac{3}{4}$$ and 0.75

$$\frac{3}{50}$$ and 0.06

$$\frac{7}{25}$$ and 0.28

### Problem 2

Mai walked $$\frac{1}{8}$$ of a 30-mile walking trail. How many miles did Mai walk? Explain or show your reasoning.

### Problem 3

Use long division to find each quotient. Write your answer as a decimal.

1. $$99\div 12$$

2. $$216 \div 5$$

3. $$1,\!988 \div 8$$

### Problem 4

Tyler reasoned: “$$\frac{9}{25}$$ is equivalent to $$\frac{18}{50}$$ and to $$\frac {36}{100}$$, so the decimal of $$\frac{9}{25}$$ is 0.36.”

1. Use long division to show that Tyler is correct.

2. Is the decimal of $$\frac{18}{50}$$ also 0.36? Use long division to support your answer.

### Problem 5

Complete the calculations so that each shows the correct difference.

(From Unit 5, Lesson 4.)

### Problem 6

Use the equation $$124 \boldcdot 15 = 1,\!860$$ and what you know about fractions, decimals, and place value to explain how to place the decimal point when you compute $$(1.24) \boldcdot (0.15)$$.

(From Unit 5, Lesson 6.)