Long Division - Steps, Examples
Long division is an important math theory that has many real-life uses in various fields. One of its main application is in finance, where it is applied to figure out interest rates and determine loan payments. It is further applied to calculate budgeting, taxes, and investments, making it an important skill for everyone engaged in finance.
In engineering, long division is applied to figure out complex problems linked to design, development, and construction. Engineers employ long division to calculate the loads which structures can bear, evaluate the toughness of materials, and design mechanical networks. It is further utilized in electrical engineering to figure out circuit parameters and design intricate circuits.
Long division is further crucial in science, where it is utilized to figure out dimensions and carry out scientific workings. For instance, astronomers utilize long division to calculate the length between stars, and physicists utilize it to determine the velocity of objects.
In algebra, long division is applied to factor polynomials and solve equations. It is an essential tool for working out complicated problems that consist of large values and need accurate calculations. It is further applied in calculus to figure out integrals and derivatives.
As a whole, long division is an important mathematical theory which has multiple real-world utilizations in several fields. It is a rudimental math function which is used to solve complex problems and is an essential skill for anyone keen in finance, engineering, science, or mathematics.
Why is Long Division Important?
Long division is a crucial math idea that has several applications in distinguished domains, including finance, engineering, and science. It is an important math operation that is applied to work out a broad range of challenges, for instance, figuring out interest rates, determining the length of time needed to complete a project, and finding the length traveled by an object.
Long division is also utilized in algebra to factor polynomials and work out equations. It is an important tool for working out complex problems that consist of large values and requires exact calculations.
Stages Involved in Long Division
Here are the steps involved in long division:
Step 1: Note the dividend (the number being divided) on the left and the divisor (the value dividing the dividend) on the left.
Step 2: Calculate how many times the divisor can be divided into the first digit or set of digits of the dividend. Write the quotient (the result of the division) prior the digit or set of digits.
Step 3: Multiply the quotient by the divisor and note down the result below the digit or set of digits.
Step 4: Subtract the outcome achieved in step 3 from the digit or set of digits in the dividend. Write the remainder (the value remaining after the division) below the subtraction.
Step 5: Bring down the next digit or set of digits from the dividend and append it to the remainder.
Step 6: Repeat steps 2 to 5 unless all the digits in the dividend have been refined.
Examples of Long Division
Here are handful of examples of long division:
Example 1: Divide 562 by 4.
Workings:
140
--------
4 | 562
4
--
16
16
---
2
Thus, 562 divided by 4 is 140 with a remainder of 2.
Example 2: Divide 1789 by 21.
Solution:
85
-----
21 | 1789
21
---
158
147
---
11
Thus, 1789 divided by 21 is 85 with a remainder of 11.
Example 3: Divide 3475 by 83.
Solution:
41
-----
83 | 3475
3326
----
149
124
---
25
So, 3475 divided by 83 is 41 with a remainder of 25.
Common Mistakes in Long Division
Long division can be a challenging concept to master, and there are several general errors that learners make when working with long division. One general mistake is to forget to note down the remainder when dividing. One more common error is to incorrectly place the decimal point when dividing decimal numbers. Learners may further forget to carry over numbers when subtracting the product from the dividend.
To prevent making these mistakes, it is essential to practice long division frequently and pay close attention to each stage of the process. It can further be helpful to revisit your calculations utilizing a calculator or by performing the division in reverse to ensure that your solution is right.
In addition, it is important to comprehend the basic principles about long division, for instance, the link among the quotient, dividend, divisor, and remainder. By mastering the basics of long division and avoiding usual mistakes, individuals can improve their skills and obtain self-esteem in their skill to figure out complicated challenges.
Conclusion
Finally, long division is a fundamental mathematical theory that is essential for figuring out complicated challenges in various domains. It is applied in science, finance, engineering, and mathematics, making it an essential skill for working professionals and students alike. By mastering the procedure consisted in long division and comprehending how to use them to practical challenges, individuals can get a detailed understanding of the complex functions of the world around us.
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