Division Formulas

Division in Maths

There are four mathematical operations in Maths namely, Addition, Subtraction, multiplication, and Division. Division in Maths is considered as the most difficult among the four basic mathematical operations. The division is a method of splitting a number into an equal number of parts. For example, 20 ÷ 4, it states that 20 apples are split into 4 equal groups which further implies that 5 apples are there in one group. The diagram given below shows that there are 20 apples which are divided into 4  equal groups and each group has 5 apples.


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In this article, we will discuss, division in maths, division formulas, division symbols, division examples, division rules etc.


Division Symbol

There are various division symbols that are used to represent division. The most commonly used division symbol is ÷, but sometimes the backslash / is also used to represent the division in the form of a fraction, where a Numerator value is written on the top and Denominator value on the bottom.


Example

“p divided by q”:

p÷q

Or

p/q

Dividend, Divisor, Quotient and Remainder Mean in Division in Maths.


When any number is divided by another number, we get the terms namely dividend, divisor, quotient and remainder.

  • The dividend is defined as the number to be divided by another number.

  • The divisor is a number that divides another number without leaving any remainder.

  • The quotient is the result which is obtained after division.

  • The remainder is the number that is left after division.

The above concept can be clearly understood through the image given below:


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The division formula is :


Division Formula

Dividend ÷ Divisor = Quotient

Or,

Dividend / Divisor = Quotient


In the above division formula,

  • The dividend is the number to be divided by another number.

  • The divisor is a number that divides another number without leaving any remainder.

  • The quotient is the result which is obtained after division.

  • The remainder is the number that is left after division.

Division Rules

Some of the division rules are given below:

  1. When the digit 0 is divided by another number, the result obtained is always 0. For example, 0 ÷ 3 = 3. This sentence means that 0 chocolates is distributed among 3 girls. 

  2. When any number is divided by 0, it means that we are not dividing the number at all. For example, 3 ÷ 0 = is not possible in Mathematics. This sentence means that we have 3 chocolates but no girls to distribute the chocolates because we cannot divide any number by 0.

  3. When any number is divided by 1, we always get the same number. For example, 3 ÷ 1 = 3. This sentence means that 3 chocolates are distributed among 3 girls. Each girl received 1 chocolate.

  4. When any number is divided by the same number, we always get the number as 1. For example, 3 ÷ 3 = 1.

  5. Numbers should always be divided in the precise order. For example, 15 ÷ 3 = 5 and 3 ÷ 15 = 0.2 are two different cases. 15 chocolate divided by 3 girls is different from 3 sweets divided by 15 girls.

The fractions such as ½, ⅓, 1/4 etc are considered as division sums. For example, 1/3 is 1÷3.  It means one chocolate divided by 3 girls.


Division Examples

Some of the division examples are given below:


1. Find the value of 60000 ÷ (- 10).


Solution:

60000 ÷ (-10)

= (60000 ) / (-10)

= (-60000) /(10)

= - 6000


2. Find the quotient value of 516 ÷ 12.


Solution:


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Hence, the quotient value of 516 12 = 43


Solved Example

Some of the division examples with its solutions are given below:

1. Find the value of (-15625) ÷ (-125).


Solution:

(-15625) ÷ (-125)

=  (-15625) / (-125)

=  15625/125

 = 125


2. Divide -112 by -14.


Solution: 

-112 ÷ (-14) 

=  (-112) /(-14)

 = 112 / 14 

 = 8 


3. Divide and find the quotient value of (-1728) ÷ 12.


Solution:


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Hence, the quotient value of 1728 ÷ 12 = 144


Quiz Time

1. If 6 girls share 145 chocolates equally, how many sweets will be left?

  1. 24

  2. 0

  3. 6

  4. 1

2.  (25 ÷ 5) ÷ ( 6-1)

  1. 5

  2. 1

  3. 625

  4. 25

3.  What is the value of 323 ÷ 1

  1. 323

  2. 1

  3. 0

  4. Cannot find the answer

FAQ (Frequently Asked Questions)

1. Example Simple Division and Long Division.

Ans. Simple Division - The simple division in Maths is a method used to divide small numbers into equal groups or parts. Simple division sums help in dividing easier and simple division questions into divisible terms. The simple division example is given below:


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Long Division - The long division in Maths is a method used to divide larger numbers into small equal groups or parts. It helps in splitting the long division sums into a sequence of straightforward and easy steps. In long division, a larger number which is known as the dividend is divided by another number known as divisor which obtains the results quotient. The number which is left after division is known as the remainder. The long division example is given below:


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2. Explain the Relationship Between Multiplication and Division?

Ans. Multiplication and division are both closely related to each other. The division is basically an inverse process of multiplication. The division is a method of splitting a number into an equal number of parts while multiplication joins equal groups. For example,


3 × 5 = 15 , its inverse relation( in the division form will be the following)

15  ÷  5 = 3

15 ÷ 3 = 5


Similarly, if we divide 40 ÷ 4 = 10, its inverse relation (in the multiplication form  will be the following)

4 * 10 = 40

10 * 4 = 40


In the above example, we can see there are three numbers. It is because when we multiply two numbers ( which are known as factors), the result we get is called a product of two numbers whereas if we divide two numbers we get the factors as a result.