SectionB.4Division
Whenever we share evenly, we are using division. Imagine there are \(18\) candies. If \(2\) people want to share them evenly, each person gets \(18 \div 2 = 9\) candies. (The symbol \(\div\) is one symbol used for division.) But there's no way to divide the \(2\) people by \(18\text{.}\) The order of division matters — division is not commutative.
The result of division is called quotient. As we wrote above, one way to denote division is with the \(\div\) symbol, as in \(18\div2\text{.}\) A fraction bar also denotes division, as in \(\frac{18}{2}\text{.}\) The first number (the number being divided into) is called the dividend and the second number (the number doing the dividing) is called the divisor.
Multiplication and division are inverse operations. For example, division by \(4\) would undo multiplication by \(4\text{:}\)
\begin{equation*}
3\multiplyright{4}=12
\end{equation*}
and then
\begin{equation*}
12\divideright{4}=3\text{.}
\end{equation*}
This implies we can often use facts we know about multiplication to do division. For example, when we calculate \(\frac{54}{9}\text{,}\) we think: \(9\) times what equals \(54\text{?}\) If we know the multiplication table and know that \(6\multiplyright{9}=54\text{,}\) then it is evident that \(\divideunder{54}{9}=6\text{.}\) This is useful when dividing with relatively small numbers.
When the result is not going to be a whole number, or larger numbers are being divided, then division is the most time-consuming of the four basic arithmetic operations. There are algorithms like the long division algorithm (detailed at en.wikipedia.org/wiki/Long_division and elsewhere) to compute a quotient by hand. Or perhaps you have access to an electronic calculator.
Here are some division exercises that most instructors would expect you to be able to do without the aid of a calculator.
CheckpointB.4.2
Perform each division by hand, then check your results.
