Long Division - Steps, Examples
Long division is an essential mathematical theory which has several real-world uses in different fields. One of its primary application is in finance, where it is used to figure out interest rates and work out loan payments. It is further used to figure out taxes, investments, and budgeting, making it an essential skill for everyone involved in finance.
In engineering, long division is utilized to figure out intricate challenges in connection to development, construction, and design. Engineers utilize long division to estimate the weight which structures can endure, determine the strength of materials, and design mechanical networks. It is further utilized in electrical engineering to calculate circuit parameters and design intricate circuits.
Long division is also essential in science, where it is applied to figure out dimensions and perform scientific workings. Such as astronomers apply long division to determine the distances between stars, and physicists use it to figure out the velocity of objects.
In algebra, long division is used to factor polynomials and solve equations. It is an important tool for solving complicated challenges that consist of large numbers and need accurate calculations. It is also used in calculus to calculate integrals and derivatives.
As a whole, long division is a crucial mathematical theory that has several real-life uses in many fields. It is a rudimental arithmetic function which is used to work out complex challenges and is an essential skill for everyone interested in engineering, science, finance, or arithmetic.
Why is Long Division Important?
Long division is an important mathematical idea that has several uses in different fields, including engineering, science and finance. It is an important math function which is used to work out a wide array of challenges, for example, working out interest rates, measuring the amount of time needed to finish a project, and determining the length traveled by an object.
Long division is further utilized in algebra to factor polynomials and solve equations. It is a crucial tool for solving complicated challenges which consist of large numbers and requires precise calculations.
Steps 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 outcome of the division) above the digit or set of digits.
Step 3: Multiply the quotient by the divisor and write the outcome beneath the digit or set of digits.
Step 4: Subtract the result achieved in step 3 from the digit or set of digits in the dividend. Write the remainder (the amount remaining after the division) underneath the subtraction.
Step 5: Carry down the following 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 processed.
Examples of Long Division
Here are some examples of long division:
Example 1: Divide 562 by 4.
Solution:
140
--------
4 | 562
4
--
16
16
---
2
Therefore, 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
As a result, 1789 divided by 21 is 85 with a remainder of 11.
Example 3: Divide 3475 by 83.
Workings:
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 problematic concept to conquer, and there are numerous common mistakes which students make when working with long division. One usual mistake is to forget to note down the remainder when dividing. Another usual error is to incorrectly place the decimal point while dividing decimal numbers. Students may further forget to carry over numbers when subtracting the product within the dividend.
To circumvent making these mistakes, it is crucial to practice long division frequently and pay close attention to ever stage of the procedure. It can also be beneficial to revisit your calculations utilizing a calculator or by performing the division in reverse to ensure that your answer is correct.
Furthermore, it is important to understand the rudimental principles about long division, such as the relationship among the quotient, dividend, divisor, and remainder. By conquering the basics of long division and preventing usual errors, individuals can improve their abilities and gain self-esteem in their ability to solve intricate challenges.
Conclusion
Ultimately, long division is a fundamental mathematical idea that is important for solving complicated challenges in various domains. It is used in science, finance, engineering, and mathematics, making it a crucial skill for working professionals and learners alike. By mastering the procedure involved in long division and getting a grasp of how to utilize them to real-world challenges, individuals can gain a deeper understanding of the complicated workings of the world surrounding us.
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