Lesson 19

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

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.

A base-ten number diagram. One large rectangle, three squares and two small rectangles.

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

5 groups of 4 squares, 6 small rectangles and 4 small squares.

  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?

(From Unit 3, Lesson 20.)

Problem 5

Complete the calculations so that each shows the correct difference.

3 fill in the blank subtraction problems.
(From Unit 3, Lesson 15.)

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 3, Lesson 16.)