Long Division - Steps, Examples
Long division is an important math theory that has many real-life uses in various domains. One of its main application is in finance, where it is applied to figure out interest rates and work out loan payments. It is also used to calculate budgeting, taxes, and investments, making it a crucial skill for everyone working in finance.
In engineering, long division is used to solve complex problems related to development, construction, and design. Engineers use long division to calculate the weight that structures can endure, determine the strength of materials, and design mechanical systems. It is also used in electrical engineering to calculate circuit parameters and design complex circuits.
Long division is further essential in science, where it is applied to figure out dimensions and execute scientific workings. For example, astronomers use long division to calculate the length between stars, and physicists employ it to determine the velocity of objects.
In algebra, long division is utilized to factor polynomials and solve equations. It is a crucial tool for working out complex challenges that involve large values and requires accurate calculations. It is further utilized in calculus to work out integrals and derivatives.
Overall, long division is a crucial mathematical concept that has several real-life uses in several domains. It is a rudimental arithmetic function that is utilized to figure out complex problems and is an important skill for anyone interested in engineering, science, finance, or math.
Why is Long Division Important?
Long division is an essential mathematical theory that has several applications in distinguished fields, involving engineering, science and finance. It is an important arithmetic operation which is used to work out a broad spectrum of problems, such as figuring out interest rates, determining the length of time needed to finish a project, and figuring out the length traveled by an object.
Long division is further utilized in algebra to factor polynomials and figure out equations. It is an essential tool for working out intricate problems which include large numbers and requires precise calculations.
Stages Involved in Long Division
Here are the steps involved in long division:
Step 1: Note the dividend (the value being divided) on the left and the divisor (the value dividing the dividend) on the left.
Step 2: Determine how many times the divisor could 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 result obtained in step 3 from the digit or set of digits in the dividend. Write the remainder (the value left over after the division) below the subtraction.
Step 5: Bring down the following digit or set of digits from the dividend and append it to the remainder.
Step 6: Repeat steps 2 to 5 until all the digits in the dividend have been refined.
Examples of Long Division
Here are few examples of long division:
Example 1: Divide 562 by 4.
Workings:
140
--------
4 | 562
4
--
16
16
---
2
So, 562 divided by 4 is 140 with a remainder of 2.
Example 2: Divide 1789 by 21.
Workings:
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
As a result, 3475 divided by 83 is 41 with a remainder of 25.
Common Mistakes in Long Division
Long division can be a difficult idea to conquer, and there are many common errors that students make when working with long division. One common error is to forget to note down the remainder when dividing. Another common error is to incorrectly place the decimal point when dividing decimal numbers. Students may further forget to carry over numbers while subtracting the product within the dividend.
To avoid making these errors, it is important to practice long division frequently and be mindful of ever stage of the procedure. It can further be helpful to revisit your calculations using a calculator or by working the division in reverse to assure that your result is correct.
In addition, it is essential to understand the rudimental principles behind long division, such as the connection between the dividend, divisor, quotient, and remainder. By conquering the basics of long division and avoiding usual mistakes, everyone can better their abilities and obtain self-esteem in their ability to solve complex problems.
Conclusion
Ultimately, long division is a fundamental mathematical concept that is essential for solving complicated challenges in various fields. It is utilized in science, finance, engineering, and mathematics, making it an important skill for working professionals and students alike. By mastering the procedure involved in long division and getting a grasp of how to use them to real-life problems, individuals can gain a detailed comprehension of the complicated functions of the world around us.
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