# Question ec859

Dec 23, 2016

$18$

#### Explanation:

$\frac{48}{2} + {4}^{2} - \left(6 + 2\right) \times 3$

$= \frac{48}{2} + 16 - \left(6 + 2\right) \times 3$

$= \frac{48}{2} + 16 - \left(8 \times 3\right)$

$= \frac{48}{2} + 16 - 24$

$= \frac{48}{2} - 8$

$= 24 - 8$

$= 16$

Dec 23, 2016

$16$

#### Explanation:

In any calculation involving multiple operations, you have to know the correct order in which to do them. This is usually known as PEDMAS, BODMAS or similar.

I prefer to work with the concept of TERMS. Terms are separated by single PLUS or MINUS signs.

Each term is simplified separately to give a single answer and these are added or subtracted in the last step.

Within each term, the order is brackets, then indices, and then multiplication and division.

$\text{ "color(red)(48/2)color(lime)(+4^2)color(blue)( -(6+2)xx3)" }$ has 3 terms. Work out each:
$\textcolor{w h i t e}{\ldots .} \downarrow \textcolor{w h i t e}{\ldots} \downarrow \textcolor{w h i t e}{\ldots \ldots} \downarrow$
=color(red)(24)color(lime)(+16)" "color(blue)( -(8xx3)
$\textcolor{w h i t e}{\ldots .} \downarrow \textcolor{w h i t e}{\ldots} \downarrow \textcolor{w h i t e}{\ldots \ldots \ldots} \downarrow$
=color(red)(24)color(lime)(+16)" "color(blue)( -24#

It is a good idea to write the ADD terms at the front and the SUBTRACT terms at the end.

This expression is already in this order.

$= 24 + 16 - 24 \text{ } \leftarrow$ work from left to right

$= 40 - 24$

$= 16$

You could also have noticed that:

in $\textcolor{red}{24} \textcolor{\lim e}{+ 16} \textcolor{b l u e}{- 24}$ there are additive inverses.

$\textcolor{red}{+ 24} \textcolor{b l u e}{- 24} = 0$

Therefore $= \textcolor{red}{\cancel{24}} \textcolor{\lim e}{+ 16} \textcolor{b l u e}{\cancel{- 24}} = 16$