Number System: Basic Arithmetic operations
In this post we will discuss about some Basic Arithmetic Operations: Addition, Subtraction, Multiplication and Division.
Addition:
Addition combines two quantities into a single quantity. It can be done with numbers, decimal or fractions.
For example: If you have 3 pencils and your friend has 4 pencils. So, if we want to find total pencils with you and your friend. Just take all the pencils and count them. It will come out as total 7.
Let’s represent this operation in a mathematical expression:
3 + 4 = 7.
Subtraction:
Subtraction is the process of removing one quantity from the other quantity. Again to understand, let’s take the help of the last example.
For example: If you have 7 pencils lying on your table, A friend of yours wants some pencil and you gave him 4 pencils. So, you are left with 3 pencils now.
Let’s represent this operation in a mathematical expression:
7 – 4 = 3.
Multiplication:
Multiplication is the process of repeated addition of the same number. In a way, the multiplication of two numbers is equivalent to adding as many copies of one of them, the multiplicand, as the quantity of the other one, the multiplier and the final result of multiplication is called the product.
a x b = a + a + …………., b times.
a is the multiplicand.
b is the multiplier.
a x b is the product.
Both numbers a and b can be referred to as factors of a x b.
Let’s represent this operation in a mathematical expression:
7 x 4 = 28.
Some basic properties of Multiplication :
1. If either of multiplicand or multiplier is 0, the product is zero.
For example: 3 x 0 = 0 or 0 x 3 = 0.
2. The multiplicand and multiplier may be interchanged in the process of multiplication. The product remains the same.
For example: 7 x 4 = 4 x 7 = 28.
3. To multiply numbers ending with zeroes. Firstly, remove the zeroes from both the numbers. Multiply the remaining part and then append the total number of zeroes removed at the end.
For example: 3000 x 50000
Remove the number of at the end and multiply the remaining part 3 x 5 = 15
Now add the 7 zeroes removed. The final result now becomes 150000000.
So, 3000 x 50000 = 150000000.
Division:
Division is the method of distributing a group of items into equal parts.
In the number system, we can say that the division is the method of finding how often a given number (called as divisor) is contained in another given number (called the dividend). The number expressing it is called as the Quotient and the excess left after the process of division is called as the Remainder.
So, Dividend = (Divisor x Quotient) + Remainder
Division is an operation inverse of multiplication.
For example: 
:
83 is the dividend.
10 is the divisor.
8 is the quotient.
3 is the remainder.
So, 
Now if remainder = 0
then, divisor and quotient both becomes factor of the dividend.
also, dividend is the multiple of both divisor and quotient.
Solve questions from : Quantitative Aptitude for CAT
