Long Division - Steps, Examples
Long division is an essential mathematical theory which has several real-life uses in various fields. One of its primary application is in finance, where it is used to calculate interest rates and determine loan payments. It is further applied to figure out investments, budgeting, and taxes, making it an essential skill for anybody working in finance.
In engineering, long division is utilized to figure out complex challenges linked to development, construction, and design. Engineers utilize long division to determine the loads which structures can bear, evaluate the toughness of materials, and plan mechanical systems. It is further utilized in electrical engineering to figure out circuit parameters and design complicated circuits.
Long division is also crucial in science, where it is applied to determine dimensions and perform scientific workings. Such as astronomers apply long division to calculate 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 figuring out complex problems which include large numbers and need precise calculations. It is further utilized in calculus to calculate integrals and derivatives.
Overall, long division is an essential mathematical theory that has several real-life utilizations in various domains. It is an essential mathematical operation which is applied to figure out complex problems and is a crucial skill for anyone keen in finance, engineering, science, or mathematics.
Why is Long Division Important?
Long division is a crucial mathematical concept that has many utilization in different fields, including science, finance, engineering. It is an important math operation that is applied to work out a broad spectrum of challenges, for example, calculating interest rates, measuring the amount of time required to complete a project, and determining the length traveled by an object.
Long division is further used in algebra to factor polynomials and figure out equations. It is an essential tool for solving complicated challenges that involve enormous numbers and requires accurate calculations.
Procedures Involved in Long Division
Here are the steps involved in long division:
Step 1: Write the dividend (the value being divided) on the left and the divisor (the number 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. Note down the quotient (the outcome of the division) prior the digit or set of digits.
Step 3: Multiply the quotient by the divisor and write the outcome 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) 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: Replicate steps 2 to 5 unless 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
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
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
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 mistakes which learners make when working with long division. One common 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. Learners may also forget to carry over numbers while subtracting the product within the dividend.
To circumvent making these errors, it is important to exercise long division regularly and be mindful of ever step of the procedure. It can further be helpful to check your calculations using a calculator or by working the division in reverse to assure that your solution is right.
Furthermore, it is essential to get a grasp of the rudimental principles behind long division, for example, the connection among the divisor, quotient, dividend, and remainder. By conquering the basics of long division and avoiding usual errors, anyone can enhance their skills and gain self-esteem in their skill to work out complicated problems.
Conclusion
Finally, long division is a fundamental mathematical idea that is important for working out complex problems in many domains. It is used in science, finance, engineering, and mathematics, making it a crucial ability for working professionals and learners alike. By conquering the procedure consisted in long division and understanding how to utilize them to real-life challenges, individuals can get a detailed understanding of the complicated functions of the world around us.
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