Lesson 19: Practice Problems

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.

$99 \div 12$
$216 \div 5$
$1, 988 \div 8$

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.

A base ten diagram of a number divided by 5.

If a large rectangle represents 1,000, what division problem did the second diagram show? What is its answer?
If a large rectangle represents 100, what division problem did the second diagram show? What is its answer?
If a large rectangle represents 10, what division problem did the second diagram show? What is its answer?

Problem 5

Complete the calculations so that each shows the correct difference.

Problem 6

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