# 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.

*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.*

For example:

For example:

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**