# How do you simplify 5(4+7)=20+35 using PEMDAS?

Jul 6, 2016

55

#### Explanation:

PEMDAS represents the 'initial' letters being used in $\textcolor{b l u e}{\text{order of operation}}$ for a mixed operation expression.

P - Parenthesis (brackets)
E - Exponents (powers)
M - Multiplication
D - Division
S- Subtraction

In this expression $\textcolor{red}{\text{P"cancel(E)color(red)"M}} \cancel{D} \cancel{A} \cancel{S}$

we only have the 2 operations $\textcolor{red}{\text{P"" and "color(red)"M}}$

Evaluating Parenthesis : ( 4 + 7 ) = 11

Evaluating Multiplication : $5 \times 11 = 55$

$\Rightarrow 5 \left(4 + 7\right) = 55$

Which agrees with the $\textcolor{b l u e}{\text{distributive property}}$ you have included in the question

$\Rightarrow 5 \left(4 + 7\right) = \left(5 \times 4\right) + \left(5 \times 7\right) = 20 + 35 = 55$