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 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.
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\(99\div 12\)
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\(216 \div 5\)
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\(1,\!988 \div 8\)
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.”
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Use long division to show that Tyler is correct.
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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.
![3 fill in the blank subtraction problems.](https://staging-cms-im.s3.amazonaws.com/rR8TpcTK6aCnFswbAjLRrZZt?response-content-disposition=inline%3B%20filename%3D%226-6.5.PP.Image.29.png%22%3B%20filename%2A%3DUTF-8%27%276-6.5.PP.Image.29.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240703%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240703T112631Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=5da82c254cf80ebbb35f916f56e83d27cda100d3243d9177a3636f3886fa3a31)
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 \((1.24) \boldcdot (0.15)\).