# How do you solve (10^2-4*8)-:(8+9)?

Aug 10, 2016

$4$

#### Explanation:

Rather than just blindly following PEDMAS/PEMDA/BODMAS etc, just realise that the operations we do with numbers are not equally strong. The strongest operations are done first.

Powers and roots have the biggest effect on a number and are thetherefore the strongest, then comes multiplication and division, and the weakest operations are addition and subtraction.

If a weaker operation must be done first, parentheses are used to show this.

Always count the number of terms first. Each term must simplify to a single answer and these are added or subtracted in the LAST step.

$\left({10}^{2} - 4 \cdot 8\right) \div \left(8 + 9\right)$ has one term, but there are different operations.
Note that they can be done at the same time because they are independent from each other.

$\left(\textcolor{red}{{10}^{2}} \textcolor{b l u e}{- 4 \times 8}\right) \div \textcolor{m a \ge n t a}{\left(8 + 9\right)}$

=$\left(\textcolor{red}{100} \textcolor{b l u e}{- 32}\right) \div \textcolor{m a \ge n t a}{\left(17\right)}$

=$68 \div \textcolor{m a \ge n t a}{17}$

=$4$