May 04, 2023

Long Division - Steps, Examples

Long division is a crucial math concept which has several practical utilizations in various fields. One of its main uses is in finance, where it is applied to calculate interest rates and work out loan payments. It is further used to figure out budgeting, taxes, and investments, making it an important skill for anybody involved in finance.

In engineering, long division is utilized to solve complicated problems linked to design, development, and construction. Engineers employ long division to determine the loads that structures can endure, evaluate the toughness of materials, and plan mechanical systems. It is further utilized in electrical engineering to determine circuit parameters and design complicated circuits.

Long division is further important in science, where it is applied to figure out dimensions and execute scientific calculations. For example, astronomers apply long division to determine the length between stars, and physicists employ it to calculate the velocity of objects.

In algebra, long division is applied to factor polynomials and solve equations. It is an important tool for figuring out complex challenges that include huge values and requires precise calculations. It is also used in calculus to calculate integrals and derivatives.

As a whole, long division is a crucial math theory which has many real-life applications in various domains. It is a rudimental math operation which is used to figure out complicated problems and is a crucial skill for anyone keen in engineering, science, finance, or math.

Why is Long Division Important?

Long division is an important mathematical theory which has several utilization in distinguished domains, involving finance, engineering, and science. It is a fundamental arithmetic function that is applied to figure out a wide spectrum of challenges, for example, working out interest rates, determining the amount of time required to finish a project, and figuring out the distance traveled by an object.

Long division is further applied in algebra to factor polynomials and solve equations. It is a crucial tool for figuring out complicated challenges which consist of huge values and need exact calculations.

Procedures Involved in Long Division

Here are the stages involved in long division:

Step 1: Write the dividend (the number being divided) on the left and the divisor (the number 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. 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 outcome below the digit or set of digits.

Step 4: Subtract the outcome 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) 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.




4 | 562







Therefore, 562 divided by 4 is 140 with a remainder of 2.

Example 2: Divide 1789 by 21.




21 | 1789







Thus, 1789 divided by 21 is 85 with a remainder of 11.

Example 3: Divide 3475 by 83.




83 | 3475







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 general mistakes that students make when working with long division. One usual mistake is to forget to write down the remainder when dividing. Another usual error is to incorrectly put 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 mistakes, it is essential to practice long division daily and be mindful of each stage of the process. It can also be helpful to revisit your calculations utilizing a calculator or by performing the division in reverse to assure that your solution is right.

In addition, it is crucial to comprehend the fundamental principles behind long division, for example, the relationship between the dividend, divisor, quotient, and remainder. By mastering the basics of long division and avoiding common errors, anyone can better their abilities and gain self-esteem in their skill to solve complicated challenges.


In conclusion, long division is an essential mathematical theory which is essential for solving complicated problems in various fields. It is utilized in finance, engineering, science, and mathematics, making it a crucial ability for working professionals and students alike. By mastering the stages consisted in long division and understanding how to apply them to real-life challenges, individuals can get a detailed grasp of the complicated workings of the world surrounding us.

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