[Maths Class Notes] on Division Formulas Pdf for Exam

There are four mathematical operations namely, addition, subtraction, multiplication, and division. Division in Maths is considered 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 things are split into 4 equal groups, which further implies that 5 things are there in one group. The diagram given below shows that there are 20 things which are divided into 4  equal groups and each group has 5 things.

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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 the division in Mathematics. 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 the numerator value is written at the top and the denominator value at the bottom.

Example

“p divided by q”:

p÷q

Or

p/q

Dividend, Divisor, Quotient and Remainder 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.

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

• The quotient is the result that 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

Division Rules

Some of the division rules are given below:

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

• 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.

• 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 given to 1 girl. 

• When any number is divided by the same number, we always get the number as 1. For example, 3 ÷ 3 = 1. Each girl received 1 chocolate.

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

The fractions such as [frac{1}{2}], [frac{1}{3}], [frac{1}{4}], etc. are considered as division sums. For example, [frac{1}{4}] is 1÷3.  It means one chocolate divided by 3 girls.

Uses of Division in Real Life:

• The division is used when you have to share work among people. For example, a band singing a song divides different portions of that song among the band members.

• You can also use division when you make a project along with your classmates or your friends. This will give you clarity about who does a particular work and also avoid doubling the work.

• The division is also used in sustainability concepts. Many countries come together to pledge for a sustainable future. They divide the target to be achieved based on their capacity.

• The division is used when we have to distribute goods like fruits, chocolates, rice, vegetables among “n” number of people in our daily life. This mathematical operation plays a key role in dividing property, especially land.

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 Examples

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