Lesson 19

Dividing Numbers that Result in Decimals

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

Here is a diagram representing a base-ten number. The large rectangle represents a unit that is 10 times the value of the square. The square represents a unit that is 10 times the value of the small rectangle.

Here is a diagram showing the number being divided into 5 equal groups.

1. If a large rectangle represents 1,000, what division problem did the second diagram show? What is its answer?

2. If a large rectangle represents 100, what division problem did the second diagram show? What is its answer?

3. If a large rectangle represents 10, what division problem did the second diagram show? What is its answer?

Solution

(From Unit 3, Lesson 20.)

Problem 5

Complete the calculations so that each shows the correct difference.

Solution

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 $$(1.24) \boldcdot (0.15)$$.