Strategies to do Mental Division Fast

Out of the 4 most basic arithmetic operations – addition, subtraction, multiplication and division, generally the most feared one is division. However, you can learn few simple division tricks and shortcuts to become comfortable with divisions.

How do you mentally divide?

You generally find multiplication more effortless as compared to division, right? So to mentally solve division, simply convert the division into multiplication. Yes, you heard me right. Hold on to see how this makes things relatively easier for you.

In this article, I will share with you the trick to divide any number by 5, 25 and 125 by converting these into single digit multiplications. You can refer to an earlier article where certain Vedic Mathematics trick are used for division of more difficult numbers.

Believe me, you will be amazed at the simplicity of this method. So stay tuned and read ahead.

How do you divide by 5?

To divide any number by 5, you don’t actually need to perform any division. You will get your answer in 2 simple steps.  

First step, you simply need to multiply the given number by 2.

Let us take some examples to understand this further.

2323/5 = 2323×2 = 4646

Second step, put place a decimal just before one digit from the right. So in this case the decimal will come before 6. Hence the answer would be 464.6

Thus, 2323/5 = 464.6

Isn’t that simple? You just need to know multiplication or table of 2.

Another example,

Step 1: 23487/5 = 23487×2 = 46974

Step 2: placing the decimal before one digit from right: 4697.4    

Did you ever think it could be this easy?                                                                                                                                      

How do you divide by 25?

To divide any number by 25, you simply need to multiply the given number by 4 and then place a decimal before 2 digits from the right.

Let’s try with an example, 5830/25

Step 1: multiply the given number by 4

5830×4 = 23320

Step 2: placing a decimal point before 2 digits from the right

Another example, 719835/25

Step 1: Multiplying by 4:

719835*4 = 2879340

Adjusting the decimal by 2 places

28793.40, that’s the answer.

This is fun.

How do you divide by 125?

To divide any number by 125, multiply the number by 8 and then put a decimal point before 3 digits from the right. Let’s take an example, 2650/125

Step 1: Multiplying by 8:

2650*8 = 21200

Adjusting the decimal by 3 places

21.200 = 21.2, that’s the answer.

Another example, 348847/125

Step 1: Multiplying by 8:

348847*8 = 2790776

Adjusting the decimal by 3 places

2790.776, that’s the answer.

Don’t you love this?

Explanation of the shortcut trick for division

For those who’re interested in understanding what’s going on here, you can read further.

Let us first understand for 5.

x/5 = x*2/10 = (x/10) * 2 = 0.x * 2

thus, to divide any number by 5, we can multiply the same number by 2 and adjust the decimal point by one place.

Similarly, we can understand shortcut we adopted above for multiplication by 25.

x/25 = x * 4/100 = (x/100) * 4 = 0.0x * 4

Thus, to divide any number by 25, we can multiply the same number by 4 and adjust the decimal point by 2 places.

Stretching the method further, to divide anything by 125 we multiply the number by 8 because –

x/125 = x*8/1000 = (x/1000) * 8 = 0.00x * 8

Once you understand the logic explained above, you don’t have to memorize the steps in these tricks. In fact, by using the same logic you can do quick division by numbers like 50, 250, 500 and so on. So please don’t memorize, please understand and then apply.

If you’ve slightest doubt, ask your questions in the comments below.

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Vineet Patawari

Hi, I'm Vineet Patawari. I fell in love with numbers after being scared of them for quite some time. Now, I'm here to make you feel comfortable with numbers and help you get rid of Math Phobia!

One thought to “Strategies to do Mental Division Fast”

  1. It is critical that students develop trusted, efficient and flexible methods for multiplying and
    dividing whole numbers and decimals. Students’ ability to solve multiplication and division
    problems confidently and efficiently will often rely on their use of a mental strategy.

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