Lesson 11
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 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
Tyler reasoned: “\(\frac{9}{25}\) is equivalent to \(\frac{18}{50}\) and to \(\frac {36}{100}\), so the decimal of \(\frac{9}{25}\) is 0.36.”

Use long division to show that Tyler is correct.

Is the decimal of \(\frac{18}{50}\) also 0.36? Use long division to support your 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 \((1.24) \boldcdot (0.15)\).