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 30mile 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 baseten 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.

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