**Title: Understanding Long Division with Base-Ten Pieces****Introduction:**Learn how to use base-ten pieces to illustrate the long division algorithm. This exercise helps you understand how each digit in the quotient corresponds to specific base-ten pieces. Follow the steps below to fill out the provided questions.**Exercise: Long Division Step-by-Step****Problem: 378 ÷ 7**1. **Initial Setup**: - Divide 378 by 7.2. **Step 1: Dividing Hundreds**: - Determine how many groups of 7 fit into the first digit(s). In this case, identify how 7 fits into 37 (from the number 378). 3. **Calculation**: - Place the number determined (5) above the 8 to indicate 54 group(s) of 7 in 378, and calculate 7 multiplied by 5 to get 35 long(s) as the first part of the division process. - Subtract 35 from 37 to get a remainder of 2.4. **Step 2: Dividing Tens**: - Bring down the next digit (8) to result in 28. - Determine how many groups of 7 fit into 28.5. **Calculation**: - Place the number determined (4) above the 8 to represent 4 more groups of 7 unit(s) in 28. - Calculate 7 multiplied by 4 to get 28 unit(s). - Subtract 28 from 28 to finish with a remainder of 0.**Conclusion:**Through this detailed breakdown using base-ten pieces, you can see how the quotient is derived digit by digit. The final result of 378 ÷ 7 is 54, with the process clearly showing how each step contributes to the overall division.

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Description: **Title: Understanding Long Division with Base-Ten Pieces****Introduction:**Learn how to use base-ten pieces to illustrate the long division algorithm. This exercise helps you understand how each digit in the quotient corresponds to specific base-te

When 378 is divided by 7, 54 is the quotient and 0 is the remainder. 378 is represented by 3 flats,…

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Use base-ten pieces to illustrate the long–division algorithm. In separate steps, show which base-ten pieces correspond to each digit in the quotient by filling out the provided questions. 54 group(s) of long(s), group(s) of unit(s) 7)378 35 long(s) 28 long(s) unit(s) 28 unit(s)

Use base-ten pieces to illustrate the long–division algorithm. In separate steps, show which base-ten pieces correspond to each digit in the quotient by filling out the provided questions. 54 group(s) of long(s), group(s) of unit(s) 7)378 35 long(s) 28 long(s) unit(s) 28 unit(s)

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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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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**Title: Understanding Long Division with Base-Ten Pieces**

**Introduction:**
Learn how to use base-ten pieces to illustrate the long division algorithm. This exercise helps you understand how each digit in the quotient corresponds to specific base-ten pieces. Follow the steps below to fill out the provided questions.

**Exercise: Long Division Step-by-Step**

**Problem: 378 ÷ 7**

1. **Initial Setup**:
- Divide 378 by 7.

2. **Step 1: Dividing Hundreds**:
- Determine how many groups of 7 fit into the first digit(s). In this case, identify how 7 fits into 37 (from the number 378).

3. **Calculation**:
- Place the number determined (5) above the 8 to indicate 54 group(s) of 7 in 378, and calculate 7 multiplied by 5 to get 35 long(s) as the first part of the division process.
- Subtract 35 from 37 to get a remainder of 2.

4. **Step 2: Dividing Tens**:
- Bring down the next digit (8) to result in 28.
- Determine how many groups of 7 fit into 28.

5. **Calculation**:
- Place the number determined (4) above the 8 to represent 4 more groups of 7 unit(s) in 28.
- Calculate 7 multiplied by 4 to get 28 unit(s).
- Subtract 28 from 28 to finish with a remainder of 0.

**Conclusion:**
Through this detailed breakdown using base-ten pieces, you can see how the quotient is derived digit by digit. The final result of 378 ÷ 7 is 54, with the process clearly showing how each step contributes to the overall division.

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