Long Division - Steps, Examples
Long division is an essential mathematical theory that has many practical applications in different fields. One of its primary application is in finance, where it is applied to figure out interest rates and work out loan payments. It is further applied to calculate budgeting, taxes, and investments, making it an important skill for everyone working in finance.
In engineering, long division is applied to figure out complex challenges in connection to design, development, and construction. Engineers utilize long division to calculate the weight which structures can hold, assess the toughness of materials, and design mechanical systems. It is further utilized in electrical engineering to determine circuit parameters and design intricate circuits.
Long division is further crucial in science, where it is used to calculate measurements and carry out scientific calculations. For example, astronomers use long division to determine the distances between stars, and physicists utilize it to calculate the velocity of objects.
In algebra, long division is utilized to factor polynomials and solve equations. It is a crucial tool for solving complex challenges that involve large numbers and need accurate calculations. It is further used in calculus to figure out derivatives and integrals.
As a whole, long division is an important math concept that has many practical uses in various domains. It is a rudimental math operation that is used to figure out complex challenges and is an important skill for everyone interested in science, finance, engineering, or arithmetic.
Why is Long Division Important?
Long division is an important math theory which has many utilization in various domains, consisting of engineering, science and finance. It is an important math function which is applied to figure out a broad array of challenges, for example, figuring out interest rates, determining the amount of time required to finish a project, and determining the length traveled by an object.
Long division is further used in algebra to factor polynomials and solve equations. It is an essential tool for solving complicated problems that involve enormous numbers and need exact calculations.
Procedures Involved in Long Division
Here are the procedures involved in long division:
Step 1: Note the dividend (the number being divided) on the left and the divisor (the number dividing the dividend) on the left.
Step 2: Determine how many times the divisor can be divided into the first digit or set of digits of the dividend. Write the quotient (the outcome 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 achieved in step 3 from the digit or set of digits in the dividend. Note down the remainder (the value left over 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 until all the digits in the dividend have been processed.
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
So, 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
Therefore, 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
Therefore, 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 many ordinary mistakes which learners make when working with long division. One general error is to forget to note down the remainder when dividing. One more usual error is to wrongly put the decimal point when dividing decimal numbers. Learners might also forget to carry over values while subtracting the product from the dividend.
To circumvent making these mistakes, it is essential to practice long division daily and ready carefully ever step of the process. It can also be beneficial to revisit your calculations utilizing a calculator or by working the division in reverse to make sure that your solution is correct.
Furthermore, it is essential to get a grasp of the fundamental principles about long division, for example, the relationship among the dividend, divisor, quotient, and remainder. By mastering the essentials of long division and avoiding usual errors, individuals can enhance their abilities and obtain self-esteem in their skill to solve intricate problems.
Conclusion
Finally, long division is a fundamental mathematical theory that is important for solving complicated challenges in several fields. It is used in engineering, science, finance, and math, making it a crucial skill for professionals and students alike. By conquering the stages involved in long division and comprehending how to use them to real-life challenges, anyone can gain a deeper comprehension of the complex workings of the world around us.
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