# Dividing by 5

Mastering the doubling operation will enable us to divide by 5 easily. This technique is well discussed in Chapter 9 of our best-selling book “25 Math Short Cuts”

Since 5 is equal to 10/2, dividing by 5 is the same as multiplying by 2/10. This means we can multiply the number by 2 and then divide it by 10. This means we can double the number and then move the decimal point one place to the left. If the number ends in zero(es), we can drop the ending zero first before doubling the number. This produces the same result.

From this technique, we can develop techniques for dividing by 0.5, 50 500 and similar numbers.

Questions about multiplying and dividing by 5, as well as the quick methods we featured in our featured in our weekly** Math Tips** are often included in Vedic Math competitions like the 2^{st} MATH-Inic Vedic Mathematics National Challenge which will be held on April 24, 2022.

But how do we double long numbers?

The answer is in **number splitting**. In our example we can split the long number into 4 two digit groups which can be doubled easily: 19283645 can be split into 19|28|36|45 and then can easily be doubled into 38|56|72|90. Dividing by 10 is easily done by removing the ending zero.

Thus 19283645 ÷ 5 = 3856729.

When the number is composed mainly of large digits like 87696889, doubling can be a little bit harder but still manageable. We can double digit by digit starting from the left as follows:

- Doubling 8 will give 16 but seeing that the next digit, 7, is big, we will anticipate the carry operation by adding 1. So we have 17 instead of 16.
- Double 7 is 14 but we have already carried the leading 1, so only 4 remains. But again the next digit in the number, 6, is also big so we have 5 instead of 4. Thus far we have 175.
- We will follow the procedure in steps1 and 2 whenever we have large digits.

Let’s have some practice exercises. Divide the following numbers by 5:

- 280
- 670
- 325
- 745
- 1230
- 5670
- 2345
- 8345
- 18340
- 23635

Here are the answers to last week’s exercises:

- 64 x 5 = 320
- 83 x 5 = 415
- 284 x 5 = 1420
- 348 x 5 = 1740
- 4268 x 5 = 21340
- 1234 x 5 = 6170
- 32, 456 x 5 = 162,280
- 75, 678 x 5 = 378,390
- 243, 556 x 5 =1,217,780
- 975, 531 x 5 = 4,877,655