# What Is A Quotient

There are different types of numbers and various operations can be performed on it. The most basic operations are addition, subtraction, multiplication, and division. When two numbers are divided the result is the quotient. A quotient is derived from the Latin word ‘quotiens’ and means ‘how many times’. The process of finding the quotient is called a division. The number which gets divided is called the dividend and a divisor is a number which divides it.

As mentioned earlier, the result of division is a quotient and are also called as factors. The dividend can be smaller or larger than the divisor and can also be represented as fractions. Dividing a fraction gives a decimal number as quotient.

Dividend÷Divisor = Quotient

20÷4 = 5

20 is the dividend

4 is the divisor

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5 is the Quotient

÷ or / is the division symbol

Types Of Division

1. Dividing a whole number: Ex: 20÷4 where 20 is a dividend which is a whole number.
2. Fractions: Ex- 134/120; 134 where the divided 134 is a fraction number and 120 is a divisor which is a fraction number
3. Dividing a negative number: -18/-3 where -18 is a dividend with a negative number and -3 is a divisor which is also a negative number.
4. Diving a positive number: 12/3 where 12 is a dividend which is a positive number and 3 which is a positive divisor.

Properties Of Division:

1. The quotient is zero when 0 is divided by a number. Ex: 0 ÷ 4 = 0, 0 ÷ 12 = 0
2. Dividing a number by 0 is not possible
3. The quotient is the number itself when we divide the number by 1. Ex: 28 ÷ 1 = 28, 558 ÷ 1 = 558
4. Dividing the number by itself the quotient is 1. Ex: 45 ÷ 45 = 1, 98 ÷ 98 = 1
5. Division of a whole number by a decimal of less than 1, the quotient is greater than the whole number as the smaller the portions you divide it with the more portions will become available to you
6. If both dividend and the divisor are multiplied or divided  by the same number then the quotient will not change
7. The quotient is the total number of times the divisor is present in the dividend. If the dividend is increased and the divisor is not changed then division of the number results in decrease or increase the same number of times as the dividend. The reverse happens if you increase or decrease the divisor – the dividend is unchanged.

Relationship Between Divisor And Quotient

The standard way of stating this relationship is dividend is the number by which it is divided and the quotient is the result of this division.

The relationship is well defined by Euclid division lemma. Consider a and b as factors of division and if a divides and gives q as quotient and r as remainder then b=aq+r. The quotient and divisor get multiplied the result is added to the reminder to get the dividend.