# How do you simplify 3(8-2)² + 10 ÷ 5 - 6 * 5 using PEMDAS?

Mar 24, 2016

$3 {\left(8 - 2\right)}^{2} + 10 \div 5 - 6 \cdot 5 = 80$
(see below for PEDMAS application)

#### Explanation:

{: (color(black)("PEDMAS"),,"Expression"), (,,3(8-2)^2+10div5-6*5), (,,), (color(black)("P")"arentheses",,3color(red)((8-2))^2+10div5-6*5), (,,3*color(red)(6)^2+10div5-6*5), (,,), (color(black)("E")"xponents",,3*color(red)(6^2)+10div5-6*5), (,,3*color(red)(36)+10div5-6*5), (,,), (color(black)("D")"ivision & "color(black)("M")"ultiplication",,color(red)(3*36)+color(blue)(10div5)-color(green)(6*5)), ("left-to-right",,color(red)(108)+color(blue)(10div5)-color(green)(6*5)), (,,108+color(blue)(2)-color(green)(6*5)), (,,108+2-color(green)(30)), (,,), (color(black)("A")"ddition & "color(black)("S")"ubtraction",,color(red)(108+2)-30), ("left-to-right",,color(red)(110)-30), (,,color(blue)(110-30)), (,,color(blue)(80)) :}

Jul 31, 2016

$80$

#### Explanation:

Rather than blindly following PEDMAS, PEMDAS, BODMAS, BOMDSA, (or whatever version you know) which often leads to errors, try a different approach.

Operations are not all equally powerful.
Powers and roots are the strongest, then multiplication and division, and LASTLY addition and subtraction.

If this order is to be changed, parentheses are used to indicate that a weaker operation is to be done before a stronger one.

Count the number of TERMS first. Each TERM must simplify to a single value which are then added or subtracted in the LAST step.
Calculations may be done within each term in every line

$3 {\left(8 - 2\right)}^{2} + 10 \div 5 - 6 \cdot 5 \text{ has 3 terms}$

$\textcolor{m a \ge n t a}{3 {\textcolor{red}{\left(8 - 2\right)}}^{2}} \textcolor{b l u e}{+ 10 \div 5} \textcolor{g r e e n}{- 6 \times 5}$ "the minus is done first in the first term"

=$\textcolor{m a \ge n t a}{3 {\left(6\right)}^{2}} \textcolor{b l u e}{+ 2} \textcolor{g r e e n}{- 30}$

=$\textcolor{m a \ge n t a}{3 \left(36\right)} \textcolor{b l u e}{+ 2} \textcolor{g r e e n}{- 30}$

=$\textcolor{m a \ge n t a}{108} \textcolor{b l u e}{+ 2} \textcolor{g r e e n}{- 30}$

=$80$