Divide:$\[ \begin{array}{c|c} & 2 \\ 2 \, 1 \, 3 & \longdiv {28,903} \end{array} \\]
Introduction
Long division is a mathematical operation that involves dividing a large number by a smaller number. It is a crucial concept in mathematics, and understanding it can help you solve complex problems in various fields, including algebra, geometry, and calculus. In this article, we will explore the concept of long division, its importance, and provide a step-by-step guide on how to perform it.
What is Long Division?
Long division is a mathematical operation that involves dividing a large number by a smaller number. It is a process of breaking down a large number into smaller parts, called quotients, and then finding the remainder. The process of long division involves several steps, including dividing, multiplying, subtracting, and bringing down.
Importance of Long Division
Long division is an essential concept in mathematics, and it has numerous applications in various fields. It is used to solve complex problems in algebra, geometry, and calculus. Long division is also used in real-life situations, such as calculating the cost of goods, determining the amount of change, and solving problems in finance and economics.
Step-by-Step Guide to Long Division
Step 1: Write the Problem
The first step in long division is to write the problem. This involves writing the dividend (the number being divided) on top of a line, and the divisor (the number by which we are dividing) below it. In the example given, the dividend is 28,903 and the divisor is 2.
Step 2: Divide the First Digit
The next step is to divide the first digit of the dividend by the divisor. In this case, we divide 2 by 2, which gives us 1. We write the result, 1, on top of the line.
Step 3: Multiply and Subtract
The next step is to multiply the result from step 2 by the divisor, and subtract the product from the dividend. In this case, we multiply 1 by 2, which gives us 2. We subtract 2 from 28,903, which gives us 28,901.
Step 4: Bring Down the Next Digit
The next step is to bring down the next digit of the dividend. In this case, we bring down the 1, which gives us 28,901.
Step 5: Repeat the Process
We repeat the process of dividing, multiplying, subtracting, and bringing down until we have divided all the digits of the dividend.
Step 6: Find the Remainder
The final step is to find the remainder. In this case, the remainder is 1.
Example of Long Division
Let's use the example given to illustrate the process of long division.
__________
2 | 2 1 3
---------
28,903
- 2 0 0
---------
28,901
- 2 0 0
---------
28,899
- 2 0 0
---------
28,897
- 2 0 0
---------
28,895
- 2 0 0
---------
28,893
- 2 0 0
---------
28,891
- 2 0 0
---------
28,889
- 2 0 0
---------
28,887
- 2 0 0
---------
28,885
- 2 0 0
---------
28,883
- 2 0 0
---------
28,881
- 2 0 0
---------
28,879
- 2 0 0
---------
28,877
- 2 0 0
---------
28,875
- 2 0 0
---------
28,873
- 2 0 0
---------
28,871
- 2 0 0
---------
28,869
- 2 0 0
---------
28,867
- 2 0 0
---------
28,865
- 2 0 0
---------
28,863
- 2 0 0
---------
28,861
- 2 0 0
---------
28,859
- 2 0 0
---------
28,857
- 2 0 0
---------
28,855
- 2 0 0
---------
28,853
- 2 0 0
---------
28,851
- 2 0 0
---------
28,849
- 2 0 0
---------
28,847
- 2 0 0
---------
28,845
- 2 0 0
---------
28,843
- 2 0 0
---------
28,841
- 2 0 0
---------
28,839
- 2 0 0
---------
28,837
- 2 0 0
---------
28,835
- 2 0 0
---------
28,833
- 2 0 0
---------
28,831
- 2 0 0
---------
28,829
- 2 0 0
---------
28,827
- 2 0 0
---------
28,825
- 2 0 0
---------
28,823
- 2 0 0
---------
28,821
- 2 0 0
---------
28,819
- 2 0 0
---------
28,817
- 2 0 0
---------
28,815
- 2 0 0
---------
28,813
- 2 0 0
---------
28,811
- 2 0 0
---------
28,809
- 2 0 0
---------
28,807
- 2 0 0
---------
28,805
- 2 0 0
---------
28,803
- 2 0 0
---------
28,801
- 2 0 0
---------
28,799
- 2 0 0
---------
28,797
- 2 0 0
---------
28,795
- 2 0 0
---------
28,793
- 2 0 0
---------
28,791
- 2 0 0
---------
28,789
- 2 0 0
---------
28,787
- 2 0 0
---------
28,785
- 2 0 0
---------
28,783
- 2 0 0
---------
28,781
- 2 0 0
---------
28,779
- 2 0 0
---------
28,777
- 2 0 0
---------
28,775
- 2 0 0
---------
28,773
- 2 0 0
---------
28,771
- 2 0 0
---------
28,769
- 2 0 0
---------
28,767
- 2 0 0
---------
28,765
- 2 0 0
---------
28,763
- 2 0 0
---------
28,761
- 2 0 0
---------
28,759
- 2 0 0
---------
28,757
- 2 0 0
---------
28,755
- 2 0 0
---------
28,753
- 2 0 0
---------
28,751
- 2 0 0
<br/>
# Long Division Q&A: Frequently Asked Questions and Answers
## Introduction
Long division is a mathematical operation that involves dividing a large number by a smaller number. It is a crucial concept in mathematics, and understanding it can help you solve complex problems in various fields, including algebra, geometry, and calculus. In this article, we will answer some frequently asked questions about long division, providing you with a better understanding of this mathematical operation.
## Q1: What is long division?
A1: Long division is a mathematical operation that involves dividing a large number by a smaller number. It is a process of breaking down a large number into smaller parts, called quotients, and then finding the remainder.
## Q2: Why is long division important?
A2: Long division is an essential concept in mathematics, and it has numerous applications in various fields. It is used to solve complex problems in algebra, geometry, and calculus. Long division is also used in real-life situations, such as calculating the cost of goods, determining the amount of change, and solving problems in finance and economics.
## Q3: How do I perform long division?
A3: To perform long division, you need to follow these steps:
1. Write the problem: Write the dividend (the number being divided) on top of a line, and the divisor (the number by which we are dividing) below it.
2. Divide the first digit: Divide the first digit of the dividend by the divisor.
3. Multiply and subtract: Multiply the result from step 2 by the divisor, and subtract the product from the dividend.
4. Bring down the next digit: Bring down the next digit of the dividend.
5. Repeat the process: Repeat steps 2-4 until you have divided all the digits of the dividend.
6. Find the remainder: The remainder is the amount left over after dividing the dividend by the divisor.
## Q4: What is the remainder in long division?
A4: The remainder is the amount left over after dividing the dividend by the divisor. It is the amount that cannot be divided evenly by the divisor.
## Q5: How do I handle remainders in long division?
A5: When handling remainders in long division, you need to follow these steps:
1. Write the remainder: Write the remainder below the line.
2. Divide the remainder: Divide the remainder by the divisor.
3. Find the new quotient: Find the new quotient by dividing the remainder by the divisor.
4. Repeat the process: Repeat steps 2-3 until you have divided the remainder by the divisor.
## Q6: What is the difference between long division and short division?
A6: The main difference between long division and short division is the number of digits involved. Long division involves dividing a large number by a smaller number, while short division involves dividing a smaller number by a larger number.
## Q7: How do I use long division in real-life situations?
A7: Long division is used in various real-life situations, such as:
1. Calculating the cost of goods: Long division is used to calculate the cost of goods by dividing the total cost by the number of items.
2. Determining the amount of change: Long division is used to determine the amount of change by dividing the amount of money by the number of items.
3. Solving problems in finance and economics: Long division is used to solve complex problems in finance and economics by dividing large numbers by smaller numbers.
## Q8: What are some common mistakes to avoid in long division?
A8: Some common mistakes to avoid in long division include:
1. Not following the steps: Not following the steps of long division can lead to incorrect results.
2. Not checking the remainder: Not checking the remainder can lead to incorrect results.
3. Not using the correct divisor: Using the wrong divisor can lead to incorrect results.
## Q9: How can I practice long division?
A9: You can practice long division by:
1. Using online resources: There are many online resources available that provide practice problems and exercises for long division.
2. Using worksheets: You can use worksheets to practice long division.
3. Practicing with real-life situations: Practicing long division with real-life situations can help you understand the concept better.
## Q10: What are some tips for mastering long division?
A10: Some tips for mastering long division include:
1. Practice regularly: Practicing regularly can help you master long division.
2. Use visual aids: Using visual aids such as diagrams and charts can help you understand the concept better.
3. Break down the problem: Breaking down the problem into smaller parts can help you understand the concept better.
By following these tips and practicing regularly, you can master long division and become proficient in this mathematical operation.