Mathematics: Division Methods Beyond Long Division

Every student learns to perform long division as part of the standard curriculum. It is a method for dividing big numbers and is applied to solve difficult issues in many areas. The long division is a fundamental operation, but there are more modern methods that can make dividing numbers much less tedious and time-consuming. We’ll take a look at how some of these high-tech approaches may make division quicker and more precise.

Vedic Practices

The Vedic method of division is an old Indian approach that may be used to divide very large numbers efficiently. One must continually divide, multiply, and subtract to solve problems using Vedic methods. To use this approach, divide the Divisor by 2, multiply the resulting Dividend by 2, and remove the result from the original Dividend. Finally, the rest is cut in half, and the resulting amount is added to the payout. After the rest is at zero, the operation is repeated.

Fragmentary Quotations

When the Divisor is bigger than the Dividend, a partial quotient can be used as an alternative way of division. Step one is to divide the Dividend by the Divisor, and step two is to keep removing the Divisor from the payout until the Dividend is less than the Divisor. As the Divisor may be split into two or more pieces, each of which can then be divided by the Dividend, partial quotients are very helpful when dealing with situations requiring a large number of digits.

Remaining Portion

Dividing by the remainder is a straightforward method that involves repeatedly subtracting the Divisor from the payout until the result is zero. Any number of digits and decimal places can be utilized using remainder division.

Arithmetic Division Using Decimals

Whenever an issue calls for the usage of a decimal, division by decimals is a helpful tool to have at your disposal. To convert a fractional Divisor to a whole number, we multiply it by a power of 10 until we get a whole integer. Then, we divide the Dividend by this absolute amount and multiply the resulting number by the power of 10.

Divisor = 0

Typically, you can’t divide by zero. However, there are certain exceptional cases. For example, the answer is zero if the Dividend is zero and the Divisor is a non-zero integer. Similarly, the answer is undefined if the Divisor is 0 and the Dividend is a non-zero value.

Subtracting By Using Multiplication As a Division Tool

Calculating a dividend is multiplying the Divisor by the quotient, which is the result of a division operation. The inverse of multiplication is another name for this method. To utilize this method to determine the Dividend, we need access to both the Divisor and the quotient. Take the division of 48 by six as an illustration. The following equation can be used:

Profit Sharing: Quotient Divisor

Yield to Investors = 6 times 8

Payout = $48

The Dividend here is 48, which is the product of 6×8. When splitting big numbers, long division can be a tedious waste of time. Thus this method can be quite helpful.

Subdividing by Factors

A further sophisticated method of numerical division is the use of factors. Numbers that may be multiplied to form another number are called “factors.” For instance, 1, 2, 3, 4, 6, and 12 are all factors of 12. We may apply this method by determining the factors of both the Dividend and the Divisor and then canceling out the components that are shared between the two. As an illustration, suppose we need to divide 84 by 6. For this, we may utilize the following procedures:

Figure out what the numbers 1, 2, 3, and 6 represent.

Subtract any shared elements: As 6 is divisible by 6, it cancels out on both ends.

The remaining variables may be simplified as follows: 84/6 = 14

In this situation, dividing 84 by 6 yields 14, as expected. This method can be time-saving by lowering the total amount of computations required, and it is especially helpful when working with huge numbers that have numerous elements.

Using Decimals for Division

If you need to divide a number that contains a decimal, you can use another complicated method called division by decimals. To use this method, round off the Divisor and the Dividend to the nearest whole integer before dividing. After performing a division, the decimal point should be reset to its previous position. Take the division of 0.80 by 0.04, for instance. For this, we may utilize the following procedures:

Flip the decimal point two places to the right, such that 0.8 becomes 80 and 0.04 becomes 4.

To get the answer, divide 80 by 4, or 80/4, and get 20.

Change the position of the decimal point back to where it was: A value of 20 is converted to a value of 0.20.

Thus, we can see that 0.20 is the result of dividing 0.08 by 0.04. When working with decimal numbers, doing long division might be difficult, but this method can be quite helpful.

How to Divide by an Exponent

Using the concept of dividing with exponents, powers of numbers may be broken down into their parts. Numbers with the same base are ideal candidates for this method of division. A new exponent can be obtained by subtracting the exponents of two integers divided by the same factor. Take the division of 84 by 82 as an illustration. For this, we may utilize the following procedures:

Just take the exponents away: (4 – 2) * = 2

New exponent with base 2: (8 2)

From this, we know that 84 / 82 = 82. This method can be quite helpful for working with big exponents, where long division can be tedious.

The Logarithmic Method of Division

Divisors based on logarithms are a sophisticated method for dividing huge numbers. To use this method, first, the numbers are logarithmized, then the logarithms are subtracted, and finally, the result is back-converted to the original form. Take the division of 10,000 by 100 as an illustration. For this, we may utilize the following procedures:

Take the logarithm of both numbers: log (10,000) and log (100)

Take away one of the logarithms: log (10,000) – log(100) = 4 – 2 = 2.

Back-convert the answer to its original format: 10^2 = 100

Thus, we can see that 100 results from dividing 10,000 by 100. If you’re working with really huge numbers that are challenging to split in any other way, this method may come in handy.


In conclusion, a wide variety of cutting-edge methods exist. Many strategies exist for making quick work of the division, including multiplying by factors, dividing by decimals, dividing by exponents, and dividing by logarithms. Although long divisions are necessary for anybody, these more sophisticated methods may make splitting numbers much less tedious and time-consuming. Our problem-solving skills and mathematical self-assurance will benefit from a deeper familiarity with these methods.

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