Long Division - Steps, Examples
Long division is an important mathematical idea that has several real-life uses in different domains. One of its primary uses is in finance, where it is applied to calculate interest rates and work out loan payments. It is further used to work out investments, budgeting, and taxes, making it an essential skill for everyone working in finance.
In engineering, long division is applied to figure out intricate challenges linked to construction, design, and development. Engineers employ long division to estimate the weight which structures can hold, assess the toughness of materials, and plan mechanical systems. It is also utilized in electrical engineering to figure out circuit parameters and design complex circuits.
Long division is also essential in science, where it is utilized to figure out dimensions and carry out scientific calculations. Such as astronomers utilize 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 a crucial tool for solving complicated challenges which consist of huge values and need precise calculations. It is also used in calculus to calculate integrals and derivatives.
As a whole, long division is an essential mathematical theory which has several real-life uses in various fields. It is an essential arithmetic operation that is utilized to work out complicated problems and is an essential skill for anyone keen in science, finance, engineering, or arithmetic.
Why is Long Division Important?
Long division is an essential math idea which has many utilization in various fields, including finance, engineering, and science. It is an important arithmetic function which is used to work out a broad spectrum of challenges, for instance, figuring out interest rates, determining the amount of time needed to finish a project, and figuring out the distance traveled by an object.
Long division is further used in algebra to factor polynomials and work out equations. It is an essential tool for figuring out intricate challenges which involve large numbers and need exact calculations.
Procedures Involved in Long Division
Here are the procedures involved in long division:
Step 1: Write 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 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 write the outcome beneath 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. Note down the remainder (the value remaining after the division) below the subtraction.
Step 5: Carry down the next digit or set of digits from the dividend and append it to the remainder.
Step 6: Replicate 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.
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.
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
Thus, 3475 divided by 83 is 41 with a remainder of 25.
Common Mistakes in Long Division
Long division can be a difficult theory to conquer, and there are many ordinary mistakes which learners make when working with long division. One common mistake is to forget to note down the remainder when dividing. Another common error is to incorrectly position the decimal point while dividing decimal numbers. Learners might further forget to carry over values while subtracting the product from the dividend.
To avoid making these errors, it is crucial to practice long division frequently and be mindful of each step of the process. It can further be beneficial to revise your work using a calculator or by working the division in reverse to make sure that your result is right.
Additionally, it is important to get a grasp of the rudimental principles behind long division, such as the relationship among the dividend, divisor, quotient, and remainder. By conquering the basics of long division and avoiding usual errors, individuals can better their abilities and gather confidence in their ability to solve intricate challenges.
Conclusion
In conclusion, long division is a fundamental mathematical concept that is crucial for solving complicated problems in various domains. It is applied in engineering, science, finance, and math, making it an important skill for working professionals and learners alike. By mastering the procedure consisted in long division and understanding how to utilize them to real-life problems, individuals can get a detailed understanding of the complicated functions of the world around us.
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