# How do you simplify 5 + (5 times 40 / 2 + 5) - 20 / (4 - 2) + 100 using PEMDAS?

May 1, 2018

$110$

#### Explanation:

Before you blindly follow the PEDMAS process, (or BODMAS, BEDMAS or similar) count the number of TERMS first. They are separated by $+ \mathmr{and} -$ signs.

Each term will simplify to a single answer which can be added or subtracted in the last step.

Within each term the order is :

• Parentheses
• exponents - the powers and roots
• multiply and divide

$5 + \left(5 \times \frac{4}{2} + 5\right) - \frac{20}{4 - 2} + 100 \text{ } \leftarrow$ there are $4$ terms

=color(green)(5)" "color(blue)(+" "(5xxcancel4^2/cancel2+5))" "color(red)( -" "20/(4-2))color(purple)(" "+" "100)

=color(green)(5)" "color(blue)(+" "(10+5))" "color(red)( -" "20/(2))color(purple)(" "+" "100)

=color(green)(5)" "color(blue)(+" "15)" "color(red)( -" "10)color(purple)(" "+" "100)

=color(green)(5)color(blue)(" "+" "15)" "color(purple)(" "+" "100)color(red)( " "-" "10)" "larr# subtract at end

$= 110$