Table of Content

• What is Division in Math’s?
• Division Symbol
• Parts of Division
• Division Formula
• How To Do Division – Rule
• Division with Remainders
• Division of Fractions
• Division Properties
• Division of 2 Digit Number
• Division of 3 Digit Number
• Division Sum
• Long Division in Math’s
• Division Tricks and Divisibility Check
• Division Solved Examples
• Division Worksheet Class 2 and 3

Parts of Division Process
Terms	Description	Example
Dividend	The number that is to be divided is called the Dividend.	52
Divisor	The value of the portion which is taken out is called the Divisor	6
Quotient	The number of equal portions in which the dividend is divided is called the Quotient.	8
Remainder	The remaining value left is called the remainder.	4

Division Formula

The equation or the technique used to find the division of the number is called the division formula sometimes also known as division algorithm.

The division algorithm or the division in math formula is,

Dividend = (Divisor × Quotient) + Remainder

This algorithm is used to verify the results of the division process, the division of two numbers yields a quotient and the remainder which when used verified the results of the division.

This can be understood using the following example of division,

Example: Divide math 22 by 3.

22 divided by 3 will give us 7 as the quotient and 1 as the remainder.

Dividend = (Divisor × Quotient) + Remainder

22 = (3 × 7) + 1

22 = 21 + 1

22 = 22

Hence verified.

How To Do Division – Rule

The division of one digit number can be directly performed using the tables of various numbers, such as suppose we have to find the division of 24 by 4 then we know that by the table of 4,

4×6 = 24, thus

24/4 = 6

For two-digit or three-digit numbers division is performed using the steps discussed below, here we use the example of division, 77 divided by 4 to get the steps of division.

Step-by-Step Guide to Division

Here is a stepwise method of doing division in math’s.

Step 1: Using the symbol ⟌  write the divisor (here 4) on its left side and the dividend (here 77) enclosed under the division symbol(⟌).

Step 2: Starting from the left-hand side take one digit of the dividend at a time and check whether it is smaller or greater than the divisor. If the digit is smaller, then take two digits at a time. (here, 7 is greater than 4).

Step 3: Take the multiple of the divisor that is equal to or less than the digits in step 2. (here 4×1 = 4, i.e. less than 7). Write the number in the Quotient.

Step 4: Subtract the multiple of the divisor from the digits in Step 2 and write the remainder and then carry the next digit from the dividend.

If the number is less than the divisor adds zero in the quotient and bring the next digit down, repeat this process till the divisor is greater than the number. (here 7 – 4 = 3)

Step 5: Now again find the suitable multiple of the quotient and repeat the above process till the remainder so obtained is less than the divisor.

Step 6: When the remainder obtained is less than the divisor the Quotient and the remainder so obtained are the result of the division.

Division with Remainders

The number left at the end of the division process is called the remainder of the division and it is not always zero. But it is always less than the divisor. This can be understood by the example discussed below,

Example: 14 ÷ 2

• Quotient = 7
• Remainder = 0

Example: 15 ÷ 2

• Quotient = 7
• Remainder = 1

Division of Fractions

Fractions can also be easily divided and the divisibility rules for dividing the fractions are different from dividing natural numbers. If we in math divide a fraction from another fraction, then the latter is multiplied with the former by taking its reciprocal.

This can be understood as,

a/b ÷ c/d = a/b × d/c

For example, Divide 2/5 by 4/3

= (2/5) ÷ (4/3)

Now, converting “÷” into “×” and taking the reciprocal of the divisor

(2/5) × (3/4)

= 6/20

= 3/10

Thus, the division 2/5 by 4/3 gives 3/10

Division Properties

Some of the most important + properties of the math division operation are,

Property of Division by 1: If we divide any number by 1 then the quotient is the number itself. This can be understood by the example, 23 divided by 1 then the result is 23, thus,

If Divisor = 1, then Dividend = Quotient

Property of Division by 0: If we divide maths any number by 0 then the quotient is undefined as the division of zero is not possible. This can be understood by the example, 23 divided by 0 then the result is undefined, thus,

If Divisor = 0, then Quotient = Undefined (Division is not possible), i.e.

n/0 = Undefined, for any number n (n ≠ 0)

Property of Division by Itself: If we divide any number by itself then the quotient is the 1. This can be understood by the example, 23 divided by 23 then the result is 1, thus,

If Divisor = Dividend then, Quotient = 1

Property of Division of 0 by Any Number: If we divide the sums any number by 0 then the quotient is always 0. This can be understood by the example, 0 divided by 23 then the result is 0, thus,

If Dividend = 0 for any Divisor, Quotient = 0

Property of Division by 10: If we divide any number by 10 then the quotient is the number itself without the one’s digit and the remainder is one’s digit. This can be understood by the example, 237 divided by 10 then the result is 23, and 7 is the remainder, thus,

If Divisor = 10, then Quotient = Dividend without the One’s Digit and Remainder = One’s Digit

Property of Division by a Power of 10: If we divide any number by the Power of 10 then the quotient is the number obtained by removing the digits (from the right-hand side) from the number as there are a number of zeroes or exponent in the divisor. This can be understood by the example, 2376 divided by 100 now here there are two zeroes in the divisor then the result is 23, and 76 is the remainder, thus,

If Divisor = 10ⁿ, then Quotient = Dividend without the n digit from last and Remainder = Last n digits of the number.

Division of 2 Digit Number

In division 2 digits we study how to divide a two digit number by one digit number. The same can be studied by the examples added below,

Example: Divide 96 by 4

Using Division Algorithm,

• Quotient = 24
• Remainder = 0

Example: Divide 56 by 5.

Using Division Algorithm

• Quotient = 11
• Remainder = 1

Division of 3 Digit Number

In division 3 digits we study how to divide a three digit number by one digit number. The same can be studied by the examples added below,

Example: Divide 196 by 6

Using Division Algorithm

• Quotient = 32
• Remainder = 4

Example: Divide 546 by 5

Using Division Algorithm

• Quotient = 129
• Remainder = 1

Division Sum

Division sum contains the sums, or the problems related to the division. Some example problems of division sums are,

Division Sum Problem 1. If we have to distribute 20 mangoes among 5 boys then each boys gets how many mangoes?

Solution:

Total mangoes = 20

Number of boys = 5

Each boy gets mangoes = 20/5

= 4 mangoes

Thus, each boys gets 4 mangoes.

Division Sum Problem 2. Krisha has 45 sweets to distribute in his class if there are 15 students in his class then how many sweets each student of the class gets?

Solution:

Total sweets = 45

Number of students in class = 15

Each student gets sweets = 45/15

= 3 sweets

Thus, each boys gets 3 sweets.

Long Division in Math’s

Long division is a method of dividing one number (the dividend) by another number (the divisor) to find the quotient (the result) and, optionally, the remainder.

It is called “long division” because it often involves writing out the division problem with multiple steps and carrying out the division process one digit at a time, working from left to right.

Division Tricks and Divisibility Check

If a number can be divided by a single-digit number without any remainder, it is considered divisible. There are quick methods to determine divisibility without performing the actual division.

Some of the most important tricks of the math division operation, including divisibility, shortcuts of division, and tricks of division, are:

• Divisible by 2: If a number is even, meaning it ends in 0, 2, 4, 6, or 8. Example: 746 is divisible by 2.
• Divisible by 3: Sum of its digits is a multiple of 3. Example: 471 is divisible by 3 because 4 + 7 + 1 = 12, and 1 + 2 = 3.
• Divisible by 4: Last two digits form a multiple of 4. Example: 7,324 is divisible by 4 because 24 is a multiple of 4.
• Divisible by 5: Last digit is 0 or 5. Example: 285 is divisible by 5.
• Divisible by 6: Divisible by both 2 and 3. Example: 438 is divisible by 6 because it is even, and the digit sum is a multiple of 3.
• Divisible by 8: Last three digits form a multiple of 8. Example: 42,976 is divisible by 8 because 976 is a multiple of 8.
• Divisible by 9: Sum of its digits is a multiple of 9. Example: 7,281 is divisible by 9 because 7 + 2 + 8 + 1 = 18, and 1 + 8 = 9.
• Divisible by 10: Last digit is 0. Example: 91,420 is divisible by 10.

Division Solved Examples

Here are some solved examples on Division for you help.

Example 1: Divide 45 by 6 and verify using Division Algorithm.

Solution:

• Dividend = 45
• Divisor = 6
• Quotient = 7
• Remainder = 3

Division Algorithm

Dividend = (Divisor × Quotient) + Remainder

45 = 6 × 7 + 3

45 = 42 + 3

45 = 45

Hence verified.

Example 2: Divide 145 by 9 and verify using Division Algorithm.

Solution:

• Dividend = 145
• Divisor = 9
• Quotient = 16
• Remainder = 1

Division Algorithm

Dividend = (Divisor × Quotient) + Remainder

145 = 9 × 16 + 1

145 = 144 + 1

145 = 145

Hence verified.

Example 3: Divide 48 by 4 and verify using Division Algorithm.

Solution:

• Dividend = 48
• Divisor = 4
• Quotient = 12
• Remainder = 0

Division Algorithm

Dividend = (Divisor × Quotient) + Remainder

48 = 4 × 12 + 0

48 = 48 + 0

48 = 48

Hence verified.

Division Worksheet Class 2 and 3

Here are some practice problems on Division in Math’s for you to solve.

Problem 1. If we divide 25 pencils among 5 students. How many pencils will each student receive?

Problem 2. If a farmer has has harvested 368 apples, and he distributes them in 4 baskets. How many apples will be in each basket?

Problem 3. A bakery bakes 72 breads and needs to distribute it among 12 different persons. How many bread each person gets?

Problem 4. In a garden there are 45 different flowers equally distributed in 5 rows then each row has how many flowers?