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6. Felicia is working on the following problem: There are 730 balls to be put into packages of 3. How many packages can be made, and how many balls will be left over? Here are Felicia's ideas: One hundred packages of balls will use 300 balls. After another 100 packages, we will have used up 600 balls. Another 30 packages will use another 90 balls, for a total of 690 balls used. Ten more packages brings us to 720 balls used. Three more packages will bring us to 729 balls used. Then there is 1 ball left over. All together we could make 100 + 100 + 30 + 10 + 3 = 243 %3D packages of balls with 1 ball left over.

6. Felicia is working on the following problem: There are 730 balls to be put into packages of 3. How many packages can be made, and how many balls will be left over? Here are Felicia's ideas: One hundred packages of balls will use 300 balls. After another 100 packages, we will have used up 600 balls. Another 30 packages will use another 90 balls, for a total of 690 balls used. Ten more packages brings us to 720 balls used. Three more packages will bring us to 729 balls used. Then there is 1 ball left over. All together we could make 100 + 100 + 30 + 10 + 3 = 243 %3D packages of balls with 1 ball left over.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Understanding the Common Long Division Algorithm** **Write equations like Equations (6.3) and (6.4) that correspond to Felicia’s work. Explain how your equations show that 730 ÷ 3 = 243, remainder 1.** In this exercise, you are tasked with creating equations similar to given examples that align with a specific division process. The goal is to express the division of 730 by 3, resulting in a quotient of 243 with a remainder of 1, using the long division method. To do this, follow these steps: 1. Break down the division process step by step. 2. Create equations that represent each step of the operation. 3. Indicate how the remainder fits into the final result. This exercise will enhance your understanding of the mechanics behind the long division algorithm and its application in solving mathematical problems.
Transcribed Image Text:**Understanding the Common Long Division Algorithm** **Write equations like Equations (6.3) and (6.4) that correspond to Felicia’s work. Explain how your equations show that 730 ÷ 3 = 243, remainder 1.** In this exercise, you are tasked with creating equations similar to given examples that align with a specific division process. The goal is to express the division of 730 by 3, resulting in a quotient of 243 with a remainder of 1, using the long division method. To do this, follow these steps: 1. Break down the division process step by step. 2. Create equations that represent each step of the operation. 3. Indicate how the remainder fits into the final result. This exercise will enhance your understanding of the mechanics behind the long division algorithm and its application in solving mathematical problems.
6. Felicia is working on the following problem: There are 730 balls to be put into packages of 3. How many packages can be made, and how many balls will be left over? Here are Felicia’s ideas: One hundred packages of balls will use 300 balls. After another 100 packages, we will have used up 600 balls. Another 30 packages will use another 90 balls, for a total of 690 balls used. Ten more packages bring us to 720 balls used. Three more packages will bring us to 729 balls used. Then there is 1 ball left over. All together we could make 100 + 100 + 30 + 10 + 3 = 243 packages of balls with 1 ball left over.
Transcribed Image Text:6. Felicia is working on the following problem: There are 730 balls to be put into packages of 3. How many packages can be made, and how many balls will be left over? Here are Felicia’s ideas: One hundred packages of balls will use 300 balls. After another 100 packages, we will have used up 600 balls. Another 30 packages will use another 90 balls, for a total of 690 balls used. Ten more packages bring us to 720 balls used. Three more packages will bring us to 729 balls used. Then there is 1 ball left over. All together we could make 100 + 100 + 30 + 10 + 3 = 243 packages of balls with 1 ball left over.
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