Long Division - Steps, Examples
Long division is a crucial mathematical idea that has many real-world utilizations in various fields. One of its primary application is in finance, where it is used to calculate interest rates and work out loan payments. It is further used to figure out taxes, investments, and budgeting, making it a crucial skill for anybody engaged in finance.
In engineering, long division is used to figure out intricate challenges linked to construction, design, and development. Engineers use long division to calculate the weight that structures can endure, evaluate the strength of materials, and plan mechanical systems. It is also utilized in electrical engineering to calculate circuit parameters and design intricate circuits.
Long division is further crucial in science, where it is utilized to calculate measurements and execute scientific calculations. For instance, astronomers use long division to determine the distances between stars, and physicists employ it to determine the velocity of objects.
In algebra, long division is applied to factor polynomials and solve equations. It is a crucial tool for working out complex challenges which include large values and need accurate calculations. It is further utilized in calculus to calculate derivatives and integrals.
As a whole, long division is an important mathematical concept which has many practical uses in many fields. It is a rudimental mathematical function that is applied to work out complicated challenges and is a crucial skill for anyone keen in engineering, science, finance, or arithmetic.
Why is Long Division Important?
Long division is an important mathematical concept which has many applications in distinguished fields, including finance, engineering, and science. It is a fundamental mathematics operation which is applied to figure out a broad array of challenges, for example, calculating interest rates, measuring the length of time required to complete a project, and finding 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 figuring out complex challenges which consist of huge values and requires precise calculations.
Procedures Involved in Long Division
Here are the procedures involved in long division:
Step 1: Write the dividend (the number being divided) on the left and the divisor (the value dividing the dividend) on the left.
Step 2: Figure out how many times the divisor can be divided into the first digit or set of digits of the dividend. Note down the quotient (the result of the division) above 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. Note down the remainder (the amount left over after the division) underneath the subtraction.
Step 5: Bring down the next 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 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
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
So, 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
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 several general errors which learners make when performing long division. One common mistake is to forget to note down the remainder when dividing. One more usual mistake is to incorrectly place the decimal point when dividing decimal numbers. Students might further forget to carry over values when subtracting the product from the dividend.
To circumvent making these errors, it is crucial to exercise long division frequently and be mindful of ever step of the process. It can also be helpful to check your calculations using a calculator or by performing the division in reverse to assure that your result is correct.
In addition, it is essential to get a grasp of the rudimental principles behind long division, for example, the link among the dividend, divisor, quotient, and remainder. By mastering the basics of long division and avoiding common mistakes, individuals can enhance their abilities and gather confidence in their ability to work out intricate problems.
Conclusion
Ultimately, long division is a fundamental math idea that is important for figuring out complicated problems in many domains. It is used in science, finance, engineering, and math, making it an essential ability for working professionals and students alike. By mastering the steps involved in long division and comprehending how to utilize them to real-life challenges, individuals can gain a detailed comprehension of the complex workings of the world surrounding us.
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