Division

One of the four basic math operations is division. The other three are adding, subtracting, and multiplying. In simple terms, the division is breaking up a large group into smaller groups so that each group has the same number of things. In math, it is a way to make sure that everyone gets the same amount of something. Let’s learn more about the math operation of division in this article.

What is Division? 

One of the most basic ways to do math is to divide a larger number into smaller groups with the same number of things in each group. For example, if 30 students need to be split into 5 groups for a sports event, how many groups will be made in total? Using division, it’s easy to solve these kinds of problems. We need to divide 30 by 5 in this case. 30 ÷ 5 = 6, which is the answer. So, there will be 6 groups, each with 5 students. You can check that this number is correct by multiplying it by 6 and 5, which gives you the original number, 30.

Division Methods : 

1. Division as Equal Distribution 

The division is the process of equal sharing or Dividing into Equal Groups. 

We took an example of 12 pencils and divided them into four groups.

So we divided the pencils into four groups of three pencils each, as illustrated in the diagram below.

So if we divide 12 in 4 groups, each will have 3 pencils We can Also Divide 12 into 3 groups and then each group will have 4 pencils.

2. Division by Repeated Subtraction 

The process of dividing is to subtract over and over again. It is the opposite of the operation of multiplying. It is the act of putting people into groups of the same size. When dividing numbers, we break a larger number into smaller numbers so that multiplying the smaller numbers adds up to the original larger number. For instance, We have taken an example of 12 apples and On Subtracting 3 Apples Repeatedly 4 Times we get our Answer. 

So 12 Apples – 3 Apples = 9 Apples ( First Time Subtraction )  

9 Apples – 3 Apples = 6 Apples (Second Time Subtraction ) 

6 Apples – 3 Apples = 3 Apples ( Third Time Subtraction ) 

3 Apples – 3 Apples = 0 ( Fourth Time Subtraction ) 

So We Subtracted 3 Apples, 4 times , So on Dividing 12 Apples ÷ 3 Apples = 4 

The Below Diagram Explain the Concept perfectly: 

Division Symbols 

The division is represented by a mathematical symbol consisting of a small horizontal line with a dot above and below it. The division of two numbers is represented by two basic division symbols. They are both and. For instance, 4 ÷ 2 Equals 2, and 4/2 = 2.

Parts of Division 

The names of the phrases connected with the division process are referred to as division parts. Dividend, divisor, quotient, and remainder are the four parts of the division. Let’s look at an example of the division below and figure out what these four elements of division mean.

Dividend = ( Divisior × Quotient ) + Remainder 

139 = ( 4 × 34 ) + 3 

Here, when we divide 139 by 4, we get the values of a divisor, dividend, quotient, and remainder. Look at the table below to understand the meaning of these terms.

Terms	Descriptions	Values
Dividend	The number that is to be divided	139
Divisor	The number of equal groups that are to be made, or the number by which we divide the dividend	4
Quotient	The value/answer obtained after performing the division	34
Remainder	The remaining or left out the value that is not a part of any group	3

“Dividend = Divisor Quotient + Remainder” is written in the image above. This equation fulfills the above values, but will it satisfy dividend, divisor, quotient, and remainder values in all divisions? Let us investigate.

Division Algorithm 

The division algorithm is an equation that connects all four parts of the division. In every division fact, the product of the divisor and the quotient added to the remainder is always equal to the dividend amount. Thus, the universal division formula is: 

Dividend = (Divisor Quotient) + Remainder. This is referred to as the division algorithm.

The above formula allows us to check the values of the quotient and remainder produced after division. In the preceding equation, we can substitute the values of the quotient, remainder, and divisor to see if the outcome is the same as the dividend. If we get the dividend, it means we followed the division stages correctly. If not, it indicates that there is an issue in our computations that we must correct. 

Let’s look at an example to check if it meets the above formula and Satisfies the division procedure. 139 divided by 4 equals When we divide 139  by 4, we get 34 as the quotient and 3 as the remainder.

Dividend = (Quotient Divisor) + Remainder

139 = (4 × 34) + 3

139 = 136 + 3

139 = 139

Hence verified.

How to do Division?

One-digit division can be done using multiplication tables. For example, to solve 35÷ 7, we just need to see what we need to multiply by 7 to get 35 as the answer. Clearly, 7 × 5 = 35, therefore 35÷ 7 = 5. 

When it comes to the division of numbers with greater numbers, then we can use the long division method. Let us take the example of 139 divided by 4 to understand it. Follow the steps below to learn how to do division:

Step 1: Draw the division symbol ⟌ and write divisor (4) on its left side and dividend (139) enclosed under this symbol.

Step 2: Take the first digit of the dividend from the left (1). Check if this digit is greater than or equal to the divisor. [If the first digit of the dividend is less than the divisor, then we consider the first two digits of the dividend]

Step 3: Then divide it by the divisor and write the answer on top as the quotient. Here, the quotient of 13 ÷ 4 is 3.

Step 4: Subtract the product of the divisor and the digit written in the quotient (4 × 3) from the first digit of the dividend and write the difference below. Here, the difference is 13 – 12 = 1.

Step 5: Bring down the next digit of the dividend (if present). The next digit in the dividend is 9.

Step 6: Repeat the same process until you get the remainder, less than the divisor.

Look at the image given below showing the above steps of division.

Division with Remainders

It is not always required to have a remainder equal 0. The remainder is not zero if the dividend is not a multiple of the divisor. When dividing one integer by another and obtaining a non-zero remainder, we speak about a division with remainders.

Let us take an example if Nancy wants to Distribute 14 Chocolates equally among her 3 friends. How many chocolates will each of her friend get? 

After Dividing 14 with 3 we get 2 as a Remainder.

Properties of Division

1. Dividing a Number by 1 

Any Number Is Divided by 1 gives the number itself as the quotient.

Example: If we divide 10 ÷ 1 = 10 

2. Dividing a Number by itself

 If we divide a number by itself, we will always get 1 as the answer. 

Example:  If we divide 10 ÷ 10 = 1 

3. Dividing 0 by any number 

Zero Divided by any number ( except 0 ) gives 0

Example : 0 ÷ 4 = 0, 0 ÷ 9 = 0, 0 ÷ 54 = 0

4. Dividing a Number by itself

The value of a number divided by 0 is not defined, i.e. n/0 = not defined, where n is any number.

5. Dividing by 10 

If a number is divided by 10, the digit in the one’s place is always the remainder and the digits on the left are the quotient.

6. Dividing by 100 

If a number is divided by 100, the number created by the one’s place and tens place digits is always the leftover, while the remaining digits on the left are the quotient.

Division Examples : 

Example 1: 42 pencils were distributed among 16 children. How many pencils did each child get? How many pencils were left over? 

Solution: Number of pencils with 16 children = 42 

Number of pencils with one child = 42 ÷ 16 

Example 2: Divide 95 by 6 by Long Division Method and Verify it.

Solution : 

To check division, we will put the values in the formula, Dividend = (Divisor × Quotient) + Remainder. 

So, 95 = 6 × 15 + 5 = 95. Hence, verified.

Example 3: Poonam has paid $ 243 for 3 Books. How much did she pay for each book? 

Solution :

 Cost of 3 Books = $ 243 

Cost of 1 Book = $ 243 ÷ 3 

Poonam Paid $ 81 for each Book 

FAQs ( Frequently Asked Questions ) on Division