Short Division: Simplifying Arithmetic

Short Division: Simplifying Arithmetic

Short division, a fundamental arithmetic operation, serves as a streamlined method for dividing numbers. Unlike long division, short division doesn’t involve writing down all the steps, making it a quicker and more efficient process, particularly for simple divisions.

Understanding the Concept

What is Short Division?

Short division is a method used to divide two numbers, where the dividend (the number being divided) is divided by the divisor (the number by which the dividend is being divided) without any remainders.

How Does Short Division Work?

Short division simplifies the process of division by breaking it down into smaller, more manageable steps. It involves dividing, multiplying, subtracting, and bringing down numbers systematically until the division is complete.

Steps for Short Division

Short division typically involves four main steps:

1. Divide

The first step is to divide the leftmost digit or digits of the dividend by the divisor, obtaining the quotient.

2. Multiply

Next, multiply the divisor by the quotient obtained in the previous step, and write the result below the dividend.

3. Subtract

Subtract the result obtained from the previous step from the digits above it.

4. Bring Down

If there are digits remaining in the dividend, bring down the next digit and repeat the process until all digits have been brought down.

Examples of Short Division

Let’s illustrate short division with a couple of examples:

Example 1: Two-Digit Dividend

Divide 72 by 6.

Step 1: 7 ÷ 6 = 1 (Quotient) Step 2: 1 × 6 = 6 Step 3: 7 – 6 = 1 Answer: Quotient = 12, Remainder = 0

Example 2: Three-Digit Dividend

Divide 315 by 5.

Step 1: 31 ÷ 5 = 6 (Quotient) Step 2: 6 × 5 = 30 Step 3: 31 – 30 = 1 Step 4: Bring down 5 Step 5: 15 ÷ 5 = 3 (Quotient) Answer: Quotient = 63, Remainder = 0

Advantages of Short Division

Short division offers several advantages, including its simplicity and efficiency, making it ideal for quick calculations and mental math exercises.

Limitations of Short Division

While short division is useful for straightforward calculations, it may not be suitable for more complex divisions involving larger numbers or decimals.

Tips for Mastering Short Division

To master short division, practice regularly, focus on understanding the steps involved, and utilize mnemonic devices or shortcuts to enhance speed and accuracy.

Practical Applications of Short Division

Short division finds applications in various real-life scenarios, such as dividing resources, calculating expenses, and distributing quantities evenly among groups.

Common Mistakes to Avoid

Avoid common mistakes in short division, such as misplacing digits, forgetting to carry over remainders, or misinterpreting the quotient.


In conclusion, short division provides a simple and efficient method for dividing numbers without remainders. By following a systematic approach and practicing regularly, anyone can master the technique and apply it to various mathematical problems

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