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 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
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.](https://cms-im.s3.amazonaws.com/xDjPPKiGvRuZ5dQxEkViv2Pt?response-content-disposition=inline%3B%20filename%3D%226-6.5.PP.Image.63.png%22%3B%20filename%2A%3DUTF-8%27%276-6.5.PP.Image.63.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240718%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240718T033103Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=accf060a26e56c3a1beac95344f97f8aaf8e95ca76dc3d1a5eb2bade67b05c0d)
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.](https://cms-im.s3.amazonaws.com/Han259pLxG2GYe2cQynRwbxb?response-content-disposition=inline%3B%20filename%3D%226-6.5.PP.Image.64.png%22%3B%20filename%2A%3DUTF-8%27%276-6.5.PP.Image.64.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240718%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240718T033103Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=336fefd9cca762370c1a467f9fc8cfa569fd787929a42b6e992bcfe00ee76fa9)
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If a large rectangle represents 1,000, what division problem did the second diagram show? What is its answer?
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If a large rectangle represents 100, what division problem did the second diagram show? What is its answer?
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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.
![3 fill in the blank subtraction problems.](https://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=AKIAXQCCIHWF3XOEFOW4%2F20240718%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240718T033103Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=55480660e619da8ffbdd86d36590d2d0fe275e97ceef892b9a1aa5eb78c0e90d)
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 \((1.24) \boldcdot (0.15)\).