10 Fast Maths Tricks and Shortcuts

List of Cool Maths Tricks

Squaring

In this simple trick we need to modify the equation and make the units digit zero. After all it is easy to multiply when units digit is zero.

For example - Find square of 43

= (43+3) × (43-3) + (3×3)
=(46×40) + 9
= (460×4) + 9
= 1840 + 9 = 1849

Multiplication

Vedic maths gave us the easiest method to do complex multiplications quickly. This method can be quickly explained with an example.

Multiply 62 with 32
Step 1

Step 2

Step 3

Multiplication with 5

Simply multiply the number by 10 and then divide it by 2.
For example 99×5= 990/2= 495

Multiplication with 4

Multiplication with 9

Multiplication with 6

Multiplication with 99

Multiply the number with 100 and then minus same number from the result. Let's take an example
Multiply 32×99 = 3200 - 32 = 3168

Mixture

Questions related to mixtures can be easily solved by alligation method. By using alligation we can wide arrange of maths questions. Let me explain this with a simple example

Example

Price of wine of $60 per liter. If Samuel is adding water with and selling the mixture for $40 per liter. Profit margin remains same. What is the ratio of water and wine in the mixture.

Square root

Best method to find square root of large numbers is by dividing the number into parts. Let's take an example
Find square √ 1936
√ 1936 = √ 4 × √ 484 = √ 4 × √ 4 × √ 121 = 2×2×11 = 44

Time and Work

Every question in in time and work chapter can be solved easily by finding efficiency of workers or subject (such as pipes).

For example - A takes 10 days to complete a job. B takes 20 days to complete the same job. In how many days they will complete the job if they work together ?

A's efficiency = 100/10 = 10% per day
B's efficiency = 100/20 = 5% per days

A and B can do 15% of the work in a day if they work together. So they can do the whole job in 100/15 = 6.66 days or 6 days and 18 hours.

Profit and Loss

In case of profit 
25% of  Cost Price (1/4 of CP) = 20% of Selling Price (1/5 of SP)
Similarly 1/3 of CP  = 1/2 of SP

In case of loss
25% of  Selling Price (1/4 of SP) = 20% of Cost Price (1/5 of CP)
Similarly 1/3 of SP  = 1/2 of CP

Estimation

That's the most important technique. This is not a secret that every successful candidate is using this technique during exams.

Example - 112 × 92
Simply 112 × 9 = 1008
Add a zero 10080 and then add 224 to 10080.
Answer is 10304

You need to do all the calculations in your brain. Don't use paper. You need to divide complex calculations in parts and solve it in your brain without paper. That's how toppers do complex calculations during exams.

Right now it will be difficult for you to use this method but with practice, you will be able to do any complicated calculation within seconds.