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.
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.
1. 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.
2. Indirect computation
When the above method doesn’t work, then the method of indirect calculation is applied.
3. Borrow method
Subtract the numbers from left to right.
For example:
4. 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.
5. Finding roots
A simpler way to find the square root of a number is by using the following equation.
6. Approximation of common logarithms
One must know the following logarithm rules.
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