How To Calculate The Remainder Of A Division Without Doing It

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Introduction

Have you ever needed to calculate the remainder of a division, but didn't want to go through the tedious process of actually performing the division? Well, you're in luck! In this article, we'll explore a few methods for calculating the remainder of a division without actually performing the division itself.

Method 1: Modular Arithmetic

Modular arithmetic is a type of arithmetic that involves working with remainders. To use this method, simply take the number you're dividing and divide it by the divisor. Then, take the remainder and subtract it from the dividend. The result will be the remainder of the division.

Example:

If we want to find the remainder of 23 divided by 5, we can use modular arithmetic. First, we divide 23 by 5 to get 4 with a remainder of 3. Then, we subtract 3 from 23 to get 20, which is the remainder of the division.

Method 2: Multiplication

Another way to find the remainder of a division is to use multiplication. To do this, simply multiply the divisor by the quotient of the division. Then, subtract the result from the dividend. The result will be the remainder of the division.

Example:

If we want to find the remainder of 37 divided by 6, we can use multiplication. First, we divide 37 by 6 to get 6 with a remainder of 1. Then, we multiply 6 by 6 to get 36. Finally, we subtract 36 from 37 to get 1, which is the remainder of the division.

Method 3: Shortcut Method

The shortcut method is a quick and easy way to find the remainder of a division. To use this method, simply look at the last digit of the dividend and divide it by the divisor. The result will be the remainder of the division.

Example:

If we want to find the remainder of 142 divided by 7, we can use the shortcut method. The last digit of 142 is 2, which we divide by 7 to get 2. Therefore, the remainder of the division is 2.

Conclusion

Calculating the remainder of a division can be a time-consuming process, but with these methods, you can easily find the answer without doing the actual division. Whether you prefer modular arithmetic, multiplication, or the shortcut method, you can save time and effort by using these techniques. So the next time you need to find the remainder of a division, try out one of these methods and see how easy it can be!

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