[Maths Class Notes] on Divisor Pdf for Exam

In Mathematics, the four fundamental operations widely used are Addition, Subtraction, Multiplication, and Division. The role of the division is to break the number into equal parts. The four terms used in the division to divide the number into equal parts are dividend, divisor, quotient, and remainder. The number which divides another number is termed as a divisor whereas the number which is being divided is termed as a dividend. A quotient is a result which we get in the process of division whereas the remainder is the portion of the dividend that is left after the division. In this article, we will study division meaning, divisor definition, divisor formula, divisor examples, etc.

Division Meaning

The Division is a basic Arithmetic operation used widely in Mathematics. Division breaks a number into an equal number of parts. It divides a given number of items into different groups.

 

For example, If you take 20 apples and place them into 4 equal-sized groups, there will be 5 apples in each group.

 

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Division Symbol

Although there are numerous division signs that people use, the most common division sign is    ( ÷ ) and in case of fraction backlash (/) is used, where the numerator is written on the top and the denominator is written on the bottom.

 

Division example sign for x divided by z

 

x ÷ z

x/z

Division Formula

Dividend  ÷ Divisor = Quotient

 

Or,

 

Quotient = Dividend/ Divisor

Divisor Meaning

In division, we divide a number by any other number to obtain another number as a result. The number which is getting divided is known as the dividend and the number which divides a given number is termed as the divisor. The number which we receive as a result is known as the quotient. The divisor which does not divide the given number completely is referred to as the remainder.

Divisor Definition

A Divisor is a Number that Divides the Other Number in the Calculation.

 

For example: when you divide 28 by 7, the number 7 will be considered as a divisor, as 7 is dividing the number 28 which is a dividend.

7) 28 (4

–   28

——–

    0

——–

Divisor Formula

Operation division can be written in the following manner:

 

Quotient= Dividend ÷ Divisor

 

The above remainder equation can also be written in the following manner

 

Divisor = Dividend ÷ Quotient

Divisor Example

You can understand the divisor meaning in a better way by looking at divisor examples given below:

 

If 33 ÷ 11= 3, then 33 is the dividend and 11 is the divisor of 33 which divides the number 33 into 3 equal parts

 

If 50 ÷ 5 = 10, then 50 is the dividend and 5 is the divisor of 50 which divides the number  50 into 10 equal parts

 

1÷ 2 = Here divisor 2 is dividing the number 1 into a fraction.

5) 46 (9

–    45

——–

    1

——-

In the above example – 5 is the divisor, 46 is the dividend, 9 is the quotient and 1 is the remainder.

General Form of Division

The division is one of the 4 primary mathematical operations. Division can also be called the process of repetitive subtraction. The division is denoted by a mathematical symbol. The symbol consists of a short horizontal line with a dot, above and below it. The general formula for the division requires the quotient, the dividend, the divisor, and the remainder. Long Division Method is one of the methods of division that is used to divide two given numbers. The general formula of division is: 

Dividend = (Divisor × Quotient) + Remainder

Verification of division can also be done to check if the process done is right or not. Division can also be seen as the reverse of multiplication and the check by substituting the values in the General form of Division.

Special Cases of Division-

• When any number is divided by 1, the quotient is always to equal the dividend and the answer will be the same as the dividend. 

• If the dividend is equal to the divisor, the same numbers (but not 0) then the answer will always be 1.

• No number can ever be divided by 0. That’s why when a number is divided by 0 the answer is always undefined.
  

Divisor in Division

In a division, the divisor is the number that divides another number. It might or might not leave a remainder. In other words, in a division with given numbers, the divisor divides the dividend into equal groups. The number getting divided in a division is called the dividend. Some properties of the divisor of a division are-

• In any division, the remainder is always less than the divisor.

• If the quotient is similar to the dividend, then number 1 will always be the divisor of all the numbers. 

• If the dividend and the divisor are equal in a situation, the quotient will always be 1. 

• If the remainder is 0, that implies that the divisor has divided the dividend, completely.

• If in a division, the divisor is greater than the dividend, then the resultant number will always be a decimal number.

• In a division, a quotient is a number that is obtained upon dividing a dividend by a divisor. When any number is left over after the division. That is called the remainder.
  

Remainder in Division

The remainder is a part of a division. Remainder is the left-over digit that is received while performing division. In case of an incomplete division after certain steps we get a remainder as a result. The remainder is left-over when a few numbers are divided into groups with an equal number of things.

Some properties of the remainder are –

• In any division, the divisor will always be greater than the remainder. If the remainder of a given division is greater than or equal to the divisor, this indicates that the division is performed incorrectly.

Solved Example

1. There are 26 men and Rs. 5876 is distributed equally among all men. How much money will each person receive?

Solution:  Money received by 26 men = Rs. 5876

Money each person will receive = 5876 ÷ 26

Divisor = 26 ,  Dividend = 5876

Quotient = 22, Remainder =0

Therefore, each man will receive = Rs. 22

 

2. If 9975 Kg of rice is packed in 95 jute bags, how much rice will each jute bag contain?

Solution: Quantity of rice packed in 95 jute bags = 9975 kg 

Quantity of rice packed in 1 bag = 9975÷ 95

Divisor = 95 , Dividend = 9975

Quotient =105,  Remainder = 0

Hence, the quantity of rice each bag will contain = 105 kg

 

Interesting Facts

• De Morgan in 1845 introduced the oblique bar used as a sign of that process in the division.

• Division of a number by 0 is not defined

• The term colon is used to represent the division in some non-English speaking countries. The colon was introduced by Gottfried Wilhelm Leibniz in his 1684 Acta eruditorum.

• “÷” also known as obelus was introduced by Swiss Mathematician Johann Rahn in 1659.
  

Quiz Time

1. The given number that we are dividing by is called

Remainder

Divisor

Quotient

Dividend

2. 456 ÷ 7

7

76

70

75

3. In a division sum, the dividend is 336, the quotient is 42 and the remainder is 0. What will be the divisor?                                

7

9

8

2