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Basic Operators

1. Addition
In addition, we add the numbers as given and carry forward the digit that comes in the tens place. Direct questions on addition may not be asked. However, the questions can call for an understanding, as the following example shows.

 

Example:
If a, b, c are non-zero numbers, then what can be inferred from the equation:
aa + bb = cc0?
We see that a + b ends in zero, so it must be 10. Also ‘c’ (in the hundreds place) must be 1, as it is carried forward.
Hence the sum is 110.

By trial and error, we find that ‘a’ must be 6 and ‘b’ is 4, since their sum is 110.
Sums based on the above reasoning are frequently asked. That is why the student must be familiar with basic operators.

 

Subtraction

Short cut: While subtracting numbers care must of the ‘carrying over’ from the previous digit.
To subtract (2163 – 869) we subtract 2100 – 800 and get 1300.
Now look at the figures 63 and 69. These imply that after subtracting, the actual number must be reduced by (63 – 69) = -6.
Hence the answer is: 1300 – 6 = 1294.
 

Multiplication

There are several methods of multiplication. One method we have been taught in school. We can try to make things slightly faster.
To multiply 23 × 17 we can write the number as
(20 + 3) × 17 = (17×20 + 17×3) = 340 + 51
= 391.
By doing this, the multiplication becomes an oral task.
In this section we discuss some other methods too.
 

Time Saver - Short Cuts of Multiplication

1. To multiply by 9, 99, 999 etc.
To multiply a number α by 9, multiply a by 10 and subtract α from the result. Algebraically, α × 9 = α × (10 - 1) = 10 α - α.
Similarly, for 99, 999 etc multiply a by 100, 1000 respectively.

e.g 745 × 99 = (745 × 100 – 745) = 74500 - 745 = 73755.

2. To multiply by 5 or powers of 5
1. To multiply by 5, multiply by 10 and divide by 2. e.g 137 × 5 = 1370/2 = 685
2. To multiply by 25, multiply by 100 and divide by 4. e.g 24 × 25 = 24 × 100 / 4 = 2400/4 = 600
3. To multiply by 125, multiply by 1,000 and then divide by 8 e.g. 48 × 125 = 48 × 1000/8 = 48000/8 = 6000
4. To multiply by 625, multiply by 10,000 and then divide by 16 e.g 64 × 625 = 64 × 10000 / 16 = 40,000

3. To multiply any two numbers a and b close to a power of 10
(a) To multiply by 5, divide by 2 and shift a decimal point (or add zero) e.g. 262 × 5 = [262/2 = 131] = 1310
Take as base for the calculations that power of 10 which is nearest to the numbers to be multiplied.

(b)  Put the two numbers a and b above and below on the left hand side.

(c)  Subtract each of them from the base (nearest power of 10) and write down the remainders r1 and r2 on the right hand side either with a connecting minus sign between a & r1 and b & r2 if the numbers a and b are less than the closest power of 10.
Otherwise, use a connecting plus sign between the numbers and the remainders.

(d) The final answer will have two parts. One on the left hand side and the other on the right hand side. The right hand side is the multiplication of the two remainders and the left hand side is either the difference of a and r2 or b and r1 if the numbers are less than the closest power of 10. Otherwise, it is the sum of a and r2 or b and r1.

4. Division: If we divide 126 by 5, we will get 25 as the answer with 1 remainder. Here 5 is the divisor, 25 is the quotient, 126 is the dividend and 1 is the remainder. We can express this in the form:
Dividend = (Divisor × Quotient) + Remainder.




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