Dhristi JEE 2022-24

What is Division?

The division or the process of the divide is one of the four basic arithmetic operations, the additional three mathematical operations being addition, subtraction, and multiplication. In other words, divide or dividing can be defined as the splitting of a huge group into equal smaller groups. For example, if we divide an apple into 4 slices, we do the process of division. Thus, 1 ÷ 4 = 0.25. This implies that every piece of the slice of this apple is around 0.25times the total apple. 

In this article, we will learn to divide, divide meaning, division math definition, and what is division process along with the solved division examples.


Divide Meaning

In Mathematics, the process of division can be depicted as a method of repetitive subtraction. Thus divide meaning can be generally defined as the deduction of large fractions into small fractions. The dividing process is indicated by a mathematical symbol that includes a short horizontal line with a dot each above and below the line (÷).

The divide meaning is to split into two or more equal parts, classes, items, types, groups, or splits. Simply put, the divide meaning is just to spread the group into equal or equal parts. Suppose the diagonal of a square divides it into two triangles of equal area. The result of the division may or may not be an integer. The result may be decimal.


Do You Know the Meaning of Division?

Now, let us have a look at what is division? The divide meaning or division meaning enables us to understand that the division process is basically a primary arithmetic operation in which numbers are united and divided in such a way that it results in an entirely new number. This means that we will divide a particular number with another, and an entirely new - third number will be generated. It implies that in mathematics division is a process of grouping objects equally in groups, such as arranging some fruits in rows while selling.

The formula of division or the division formula, which is one of the four basic four mathematical operations of arithmetic used to equally split the factor into many parts. Division Formula mathematically can be expressed as:

\[\Rightarrow \frac{Divident}{Divisor}=Quotient\]

The division formula is applied for dividing a number into equal parts or sometimes unequal parts. Symbols used to represent the division process are ÷ and /. Thus, “p divided by q” will be expressed using the division symbol as follows:

p ÷ q or p/q.

There are a few special cases of division to which we must pay attention:

  • Any number when divided by 1(the quotient equals the dividend), then it will result in an answer which will be the same as the dividend. For example: 120 ÷ 1 = 120.

  • Any number can not be divided by 0 and the obtained answer will be undefined. For example: 10000 ÷ 0 = undefined. But at the same time, 0 divided by any number will be zero i.e., 0 ÷ n = 0.

  • If the dividend is equal to the divisor, it implies the same numbers but not 0, then the corresponding answer will always be equal to 1. For example, 2 ÷ 2 = 1.


General Formula For Division

The general formula for the process division will need us to have the dividend, the quotient, the divisor, and the remainder. The meaning of each of these terms can be understood from the example given below. 


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Thus, the general formula of division is:

dividend = (divisor x quotient) + remainder

We can easily verify whether the obtained answer is correct or wrong. As we know that the process of division is just the reverse of multiplication, let us understand how we can verify our answer using the general formula for division. For example,12 ÷ 6 = 2, remainder = 0. In other words, 12 = (6 x 2) + 0. 

For instance, re-consider the above example where the dividend is 126, divisor and quotient are 5 and 25 respectively followed by the remainder 1.

Then using the general formula for division we write:

126 = (5 x 25) + 1

Now let us have a look at the terms related to the division. As we have seen the division process includes the terms such as divisor, dividend, quotient, and the remainder. 

  • Divisor: The divisor can be defined as the total number of equal groups that are to be made. 

  • Dividend: The dividend can be defined as the total number of parts that are to be grouped.

  • Quotient: The quotient can be defined as the total number of parts in each group.

  • Remainder: The remainder can be defined as the remaining parts that are not shared by any group.


Long Division Method

There are many types of division. The long method is the most frequently used method of division. In the long division method, the divider is usually written outside the closing parenthesis and the dividend is written inside. The quotient is written on the top bar above the dividend. The quotient in Mathematics can be defined as the result of dividing a number and any divisor. Thus, the quotient is basically the number of times the divisor is included in the dividend where the remainder is negative.

Let us have a look at the steps included in the long division method:

a. Step 1: 

Consider the first digit of the dividend, for instance from the above example 1 is the first digit of the dividend. Check whether this digit is greater than or equal to the divisor.

b. Step 2:  

If it is greater than the divisor, then divide it by the divisor and write the answer on top. If the considered digit is less than the dividend, then consider the first two digits of the dividend and divide them by the divisor.


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c. Step 3: 

Subtract the obtained result from the considered digit and write below.

d. Step 4: 

Then, repeat the same process until we obtain the remainder which further can not be divided.


Division of Fractions

We can also use the division operations on fractions. While dividing the fractions, the division operator requires it to be changed into multiplication. This can be understood in a better way with the help of an example as mentioned below:

Divide 20/4 by 5/16 we get:

\[\Rightarrow \frac{20}{4}\div \frac{5}{16}\]

\[\Rightarrow \frac{\frac{20}{4}}{\frac{5}{16}}=\frac{20\times16}{4\times5}\]

\[\Rightarrow \frac{20}{4}\div \frac{5}{16}=16\]

Divide Examples:

1. Rita had baked a few cookies for her kid Eva. Sam and Andy, best friends of Rita’s kid. They decided to give him a surprise by visiting him unannounced. If there were 12 cookies, how many did Rita give to Eva, Sam, and Andy so that they were equally distributed between them? Use the division method to verify your answer.

Sol:

Given,

The number of cookies prepared = 12

Cookies divided equally among Eva, Sam, and Andy = 12 ÷ 3 = 4

To verify our answer, we will substitute in the general formula for division.

Here,

Dividend = 12

Divisor = 3

Quotient = 4

Remainder = 0

The general formula for division is given by:

dividend= (divisorquotient)+remainder

12 = (3 x 4) + 0

Hence, Eva’s mother gave 4 cookies each to Eva, Sam, and Andy.


2. How many candies does each student get when 200 candies are distributed among 40 students equally.

Sol:

Given,

The number of candies available = 200

The total number of students among which 200 candies are distributed = 40

Here, we are asked to calculate how 200 candies are distributed among 40 students evenly, which implies that we have to calculate how many candies each student will get.

200/40=5

Thus, 200 candies are distributed among 40 students and each student will get 5 candies respectively.

FAQs on Division

1. What is Meant By Division?

Answer: The division meaning in math and division class meaning is to split a huge part into a number of parts. It is one of the four basic arithmetic operations in mathematics.

2. What is the Division Formula?

Answer: The division formula is given by:

dividend = (divisor x quotient) + remainder

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