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

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

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.

Multiplication Trick for Multiples of 11

If you know how to quickly multiply any number by 11 (click on the link to read further), the short cut multiplication method for 22, 33, etc. becomes easy to grasp. It’s an extension to the earlier method and you’ve seen earlier that there is no need to remember multiplication tables.

Multiplication by 11 is easy. Start from the right, add the two adjacent digits and keep on moving left. Since you can write only one digit in each step, if there is a carryover add it to the number obtained in the next step. So let’s begin to learn multiplication by multiples of 11.

Multiplication Trick for 22

For multiplication with 22, the rule is (number +next number)*2

Let us look at it step by step –
Step 1: For sake of simplicity, assume that there are two invisible 0 (zeroes) on both ends of the given number.
Say if the number is 786, assume it to be 0 7 8 6 0

Step 2:Start from the right, add the two adjacent digits and multiply by 2. Keep on moving left.
07860
Add the last zero to the digit in the ones column (6), and multiply by 2. Write the answer below the ones column.
Then add this 6 with digit on the left i.e. 8 and multiply by 2.
Next add 8 with 7 and multiply with 2.
Next add 7 with 0 and multiply by 2.
(0+7)*2     |    (7+8)*2  |    (8+6)*2   |   (6+0)*2
=   14   |   30   |  28   |  12

Step 3: Start from right most digit. Keep only the unit’s digit. Carryover and add the ten’s digit to the next number to the left. Doing this we get the answer as 17292.
Yes, job done. Quite simple, isn’t it?

Multiplication with Other Multiples Of 11

For multiplication with 33, the rule is (number +next number)*3
For multiplication with 44, the rule is (number +next number)*4
and so on….till
For multiplication with 99, the rule is (number +next number)*9. However, their is a simpler way of multiplication trick for 99

Multiplication Examples:
56789*22 = 0567890*22= (0+5)*2  |   (5+6)*2  |   (6+7)*2  |   (7+8)*2  |   (8+9)*2  |   (9+0)*2=1249358
123678*88 = 01236780*88 = (0+1)*8  |   (1+2)*8  |   (2+3)*8  |   (3+6)*8  |   (6+7)*8  |   (7+8)*8  |   (8+0)*8=10883664

Try it yourself. Share your experience with all by posting a comment below.

Vedic Maths Tricks for Multiplication

Both the videos given below cover Vedic Maths Multiplication Trick i.e. The Criss-Cross Method or Urdhva Tiryak Sutra.

Each video is made using different tools and aids. I would request you to share your opinion on which format of the recording did you like more. Please share your views by posting a comment below. I intend to make more such videos after getting your feedback.

Vedic Maths Multiplication Tutorial: Video 2

The videos are posted without any sort of editing. Kindly ignore all kind of disturbances and aberrations. Your feedback will help me in improving the quality of future video tutorials, which will be posted for free on Quickermaths.com.

How to find the Remainder upon Division of a Very Large Number?

This is a guest post by Sudeep Shukla

The statement- “When x is divided by z, it leaves y as the remainder.” is represented in modular arithmetic as-

x=y(mod z)

It can also be interpreted as “x and y leave the same remainder when divided by z.” This is also known as the congruence relation and we can say that “x is congruent to y modulo z.”

There is a property of this relation which is very useful. Read More

Quick Multiplication by 5

Tricks for fast calculation by 5

It is a simple trick which is very intuitive and easy to understand. Many QuickerMaths.com followers might find it very simple. However, there are many who will enjoy this simple yet readily usable trick to multiply any number by five.

1. Multiplying 5 times an even number: halve the number you are multiplying by and place a zero after the number.

Example:

i. 5 * 136, half of 136 is 68, add a zero for an answer of 680.

ii. 5 * 874, half of 874 is 437; add a zero for an answer of 4370. Read More

The Criss-Cross Method: An Alternative Form of Multiplication

Traditionally, multiplication of multiple digit numbers is done as a series of multiplications that are eventually added together to form a final answer. The criss-cross method is a variation on this technique that allows for much quicker processing of the problem without the need for a calculator or extensive use of paper space. There are many situations, such as trips to the grocery store, where you will find a need to perform multiplication of odd numbers in order to stay within a budget as you shop.

This system of multiplication is adopted from Vedic Mathematics’ URDHVA-TIRYAK SUTRA, which means vertically and cross-wise.

To start with, we will look at a simple example just to get a grasp on the steps involved in the method. Later we will apply it to a slightly more advanced problem to show how to handle carrying numbers from one digit to the next. For now, we will multiply 111 by 111. Read More

Base Method of Multiplication

Base method of multiplication derived from Vedic Mathematics can be applied for multiplication of two numbers close to 100.

This post in is in continuation of an earlier post named “Vedic Multiplication of two numbers close to hundred“. Though you can understand this post stand alone, yet I’ll recommend you to read the linked post before reading this one.

In this post I’ll explain how to multiply two numbers lesser than the base (in this case 100). In the earlier post it was about both numbers more than 100.

Simplify Multiplication using Lattice Method

Multiplication tables are a pillar of growing up no matter where you are in the world. Spending most of fourth grade learning how to multiply up to 12 x 12 was a fun and exciting time, but I was never a fan of how long it took to multiply larger numbers. I didn’t learned the lattice method until later but as a fan of matrices in calculus, this alternative method of multiplication appealed to me. Here’s how it works:

Rule for multiplying any number by 21

Start from left. Double the first digit and add it to left side neighboring digit. Repeat the steps for subsequent digits. The last number will be same as the last number of the multiplied number.

This rule is very much like the shortcut for multiplying by 11. Since 21 is sum of 11 and 10, it does belong to the same family of short cuts.

Let’s understand the whole concept with an example. Let’s multiply 5392 by 21.

The first digit of the answer will be equal to twice the first digit of 5392. To make the rule consistent assume there is a zero before the number. Read More