# Tricks in Maths to Calculate Fast: Mastering the Art of Quick Calculation

Mathematics is often viewed as a challenging subject, but with the right set of tricks, anyone can become a master of numbers. In this blog, we'll explore some ingenious techniques to help you calculate faster and with more confidence. These tricks can be applied to various mathematical operations, making your journey through numbers a breeze. Picture a scenario where the realm of mathematics becomes both effortless and captivating, thanks to your proficiency in swiftly solving problems using various mathematical tricks. Diverse arithmetic operations such as addition, subtraction, division, multiplication, squaring, roots, powers and divisions contribute to the mathematical landscape. Presented below are some of the most effective techniques designed to empower students in effortlessly executing arithmetic computations.

## Addition Tricks in maths to calculate fast

Adding two numbers from Left to Right

If we add two  2-digit numbers , then first add the tens place digit in second number with the first number, then add the units place digit in second number with the result obtained in previous step.

For example:- 48+75 = (40+70)+8+5= 110 +8 + 5 = 118 + 5 = 123

Subtract two numbers  mentally.
while subtracting we can Break the number being subtracted into its tens and ones. Then Subtract in parts. in this method we can subtract easily.

For example:- 63-35 , first 63 - (30+5 ),  63 - 30 =33, then 33-5 =  28.

Multiplication Tricks in maths to calculate fast

a. The Magic of 9:
To multiply any number by 9, simply multiply it by 10 and subtract the original number. For example, to find 6 × 9, calculate (6 × 10) - 6 = 54 , 12 x 9, calculate (12 x 10) - 12 = 108.

Break down complex multiplication problems by splitting numbers into more manageable parts. Multiply each part separately and then add the results. This technique is particularly helpful for multiplying larger numbers.

For example:- 123 x 23 = 123 x (20+3) = (123 X 20 ) + (123 X 3) = 2460 + 369 = 2829

c. Use concept of half:

10 is a base number and we know that multiplying any number by 10 is very easy. We just add one 0 at the end of that number. For example:- 25 x 10 = 250;

Note that, 10 can be written as 2 x 5.
So, any number multiplied by 5 is equivalent to multiplying the number by 10 and halving the result.

When multiplying a number by numbers like 5 or 50, it's often quicker to halve  the numbers involved. For example:- to multiply  48 by 5,  5 = 10/2, so, halve 48 = 24 then 24 x 10 = 240.

Quick Division tricks in maths to calculate fast

a. Divisibility rule:

Learn divisibility rules for common numbers. For instance, If a number is an even number and ends in 0, 2, 4, 6 or 8, it is divided by 2.  For example:- 20,42,76, 98 these all numbers are divisible by 2.

A number is divisible by 3 if the sum of its digits is divisible by 3, for example:- 15 is divisible by 3 , 1+5 = 6, 6/3 = 2;

If the last digit is 0 or 5, it is divisible by 5; For example:- 40, 85 ,90, 125 all the numbers are divisible by 5.

And a number is divisible by 9 if the sum of its digits is divisible by 9. For example:- 72 is divisible by 9, 7+2 = 9, 9/9= 1.

If the final digit of the number is 0, it is divisible by 10. Ex:- 20, 200, 40. 140 all the numbers are divisible by 10.

Shortcut for Percentage Increase/Decrease: tricks in maths to calculate fast

Percentage is relative value indicating hundredth parts

Now a % of b is mathematically expressed as  a x b / 100
The percentage increase
is equal to the subtraction of the original number from a new number, divided by the original number and multiplied by 100.
% increase = [(New number – Original number)/Original number] x 100
where,
increase in number = New number – original number

Similarly, a percentage decrease is equal to the subtraction of a new number from the original number, divided by the original number and multiplied by 100.
% decrease = [(Original number – New number)/Original number] x 100
Where decrease in number = Original number – New number.

Digit Sum: tricks in maths to calculate fast

Digit sum of a number is  the sum of all the digits of the number followed by  the addition of digits of the results till a single digit answer is obtained as below.
234156758 =  2+3+4+1+5+6+7+5+8= 41 = 4+1 = 5. We can use digit sum rule in Addition, subtraction , multiplication ,etc.

Digit sum in Multiplication

235 x 45 = 10575

We will check this using the  Digit Sum rule of Multiplication.
Digit sum of 235 = 2+3+5 = 10 = 1+0 = 1 and digit sum of 45 = 4 + 5 = 9
Product of the digit sums = 1 × 9 = 9 –> Digit-sum = 9.
Digit-sum of 10575 is = 1 + 0 + 5 + 7+ 5 = 18 = 1 + 8 = 9.

So,  Digit sum L.H.S = Digit-sum R.H.S = 9
In competitive exams this important concept is very helpful to solve questions.

We have: 58

Here, Tens digit = 5 Unit digit = 8

At first we have to multiply the digits of unit place ; 8 x 8 = 8² = 64  (R.H.S)

Now multiply the remaining digits;  5 x 5 = 25 ; now just we have to add 25 with

8(unit digit) 25+8 = 33 (L.H.S)

Now combine both sides to get the final result.

58² = 3364 ; In this way we can find out easily square of numbers like 51, 52, 56, 59... etc.

Square Roots Simplified

a. Estimation Techniques:

Approximate the square root of a number by finding the nearest perfect square and adjusting accordingly. For example, for the square root of 24, you can round it to the nearest perfect square, 25, and then make small adjustments based on the difference.

b. Digit by Digit:

Break down the square root calculation into individual digits, making it easier to manage mentally. This is especially effective for square roots of non-perfect squares.

Class 4 Mental Math: Unlocking the Power of the Mind

a. Benefits of Mental Math:

Mental math, especially when introduced at an early age like in class 4, enhances cognitive abilities, improves concentration, and boosts problem-solving skills. Students become more adept at making quick, accurate calculations without relying on pen and paper.

b. Incorporating Mental Math into Daily Practices:

Simple exercises like mental addition, subtraction, and multiplication can be introduced in class 4, setting the foundation for more complex mental math skills in the future. These practice exercises not only improve calculation speed but also foster a love for numbers.

Conclusion

Mastering these math tricks, including mental math techniques from class 4, can transform your approach to calculations, making them faster and more enjoyable. Practice is key to proficiency, so incorporate these techniques into your daily math exercises. Soon, you'll find yourself effortlessly navigating the world of numbers with confidence and speed. Happy calculating!