What is the quotient and remainder of division?

Division is a calculation expressed as follows

\[a\div b\]

\(a\) is called the dividend and \(b\) is called the divisor.

Suppose also that the following equation holds

\[ a=b\times c+d \]

In this case, \(c\) is called the quotient and \(d\) the remainder.

This relationship can be expressed by division as follows

\[ a\div b=c\ \text{R}\ d \]

Example

Example 1

Calculate the quotient and remainder of 100 divided by 30.

Solution

\[ 100\div30=3\ \text{R}\ 10 \]

Example 2

Calculate the quotient and remainder of 22 divided by 7.

Solution

\[ 22\div7=3\ \text{R}\ 1 \]