Lesson 19

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

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

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

1. $99\div 12$

2. $216 \div 5$

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

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?

Complete the calculations so that each shows the correct difference.

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 $(1.24) \boldcdot (0.15)$.