Introduction
Arithmetic has four fundamental operations: addition, subtraction, multiplication and division. A number is divided evenly when it is broken down into an equal number of parts. We use the arithmetic operation of division in day to day life to divide a specified number of objects into various categories.
An illustration is 10 divided by 2
Ten bananas divided into two groups of a similar size will yield five bananas in each group.
People may display a variety of signs to denote division. The most typical one is ‘\(\div\)’ the commonly used symbol for division. However, a horizontal line (–) with values on the top and bottom, or even a backslash (/), can also be used. Apart from the usual symbols in division operations, another common representation of this operation is to represent it in the form of a fraction, where the denominator is placed at the bottom and the numerator is written on top of the horizontal line, mentioned earlier.
Formula for the Division Operation
We can write the division formula for a given value in three ways.
For example, let us consider the value ‘p’ divided by the value ‘q’.
p \(\div\) q (or) \(\frac{p}{q}\) (or) p/q
Dividend \(\div\) Divisor = Quotient
(Or)
\(\frac{Dividend}{Divisor}\) = Quotient
In which,
- The quantity that must be shared is known as the dividend
- The number to be divided by is known as the divisor
- The outcome is the quotient
Properties of the Division Operation
There are three important properties of division operations that are:
- When an integer is divided by 1 the result will always be the same integer. In other words, the quotient and dividend are equal if the divisor is 1.
- When the dividend and the divisor are equal the result of division is always 1.
- When the dividend is an integer and the divisor is zero, we can not perform the division operation as it is not defined.
Solved Examples
Example 1: Joey shared the 26 cookies he had equally among 13 of his friends. Calculate the number of cookies that each friend receives.
Solution:
As stated in the question,
Number of cookies Joey had = 26
Number of friends = 13
Joey has to distribute 26 cookies equally to 13 friends, to perform this task we have to apply the division operation.
Number of cookies each friend receives = \(\frac{26}{13}\) = 2
Hence, Joey gives 2 cookies to each of his 13 friends.
Example 2: Rosy gave three of her friends an equal share of the 60 candies she had. Find out the number of candies each friend will receive.
Solution:
As stated in the question,
Number of candies Rosy had = 60
Number of friends = 3
Rosy has to divide 60 candies equally among three of her friends, to perform this task we have to apply the division operation.
Equal number of candies = \(\frac{60}{3}\) = 20.
Hence, each of Rosy’s friends will get 20 candies.
Example 3: Find the quotient, when 640 is divided by 5 using the division formula.
Solution:
As stated in the question,
Dividend = 640.
Divisor = 5.
Using the basic division formula,
Quotient = \(\frac{Dividend}{Divisor}\)
= \(\frac{640}{5}\)
= 128
Hence, the quotient after division will be 128.
We frequently use the division method of verification to double-check the solution of a division operation. The formula for this method of verification is ‘Dividend = Divisor times Quotient added to the Remainder’.
The division formula is typically used to divide a value or quantity into equal parts. Let’s look at an illustration. For instance, Joseph has 20 chocolates and wants to share them evenly with his two brothers. How is he going to divide the treats equally?
There are 20 chocolates in total and there are two friends.
Each of the two friends will receive 20 divided by two, which is ten chocolates.
These division-related words are regarded as components of the division formula – Dividend, Divisor, Quotient and Remainder.