Mental Math

Mental math involves mathematical computations with the help of the human brain alone and without any devices such as calculators or any other tools. The individuals make use of mental math when the tools of calculation are not available and also the calculation time is much lesser when compared to computation time. Arithmetic operations can be solved through mental math for speedy calculations. Students of primary classes 1 to 5, can be trained for mental math by using tricks and tips to perform quick calculations.

Mental math techniques include particular methods designed for specific kinds of math problems. Few persons are named mental calculators since their ability to perform mental calculations is the best. Most of the techniques depend on the decimal numeral system. The selection of radix is what decides on which methods to make use of.

Mental Math Techniques

Let us learn the different mental math techniques or methods here.

Estimation

During the process of mental computation, it is necessary to ponder in terms of scaling. For instance, when obtaining the product of the numbers 1 531 and 19 625, the method of estimation gives the expectation of the count of digits for the final answer. One of the ways to carry out this is as follows.

1 531 is rounded to the nearest thousands = 1500

and

19 625 rounded to the nearest thousands = 20000

So, the result of 1500 × 20000 = 30 000 000

The actual result is 1531 × 19 625 = 30 045 875.

Factors

During multiplication, a thing that is important is to memorise the factors of the operands that still exist.

For instance, 14 × 15 = 201 is not reasonable.

15 is a multiple of the number 5, 14 is a multiple of the number 2.

Hence the product must be an even number.

A number that is a multiple of 5 and 2 is a multiple of the number 10.

The right answer is 210.

Finding differences

i) Direct computation

Consider two numbers a and b. When the digits of the second number are smaller than the digits of the first number, the computation is done digit by digit.

For example, find the difference of 872 – 41.

Subtract 1 from 2 in the one’s place and 4 from 7 in the 10’s place.

The final answer is 831.

ii) Indirect computation

When the above method doesn’t work, then the method of indirect calculation is applied.

iii) Borrow method

Subtract the numbers from left to right.

For example:

iv] Using square numbers

The product of smaller numerals can be found by making use of the squares of integers. To use this method, it is required to know the squares of the numbers.

v) Finding roots

A simpler way to find the square root of a number is by using the following equation.

vi) Approximation of common logarithms

One must know the following logarithm rules.

• log(a × b) = log a + log b
• log (a/b) = log a – log b
• log mⁿ = n log m
• log 1 = 0
• log 0 = undefined

Related Articles

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• Square and Square Root
• Logarithms
• Factors And Multiples