Special Cases Order of Operations Practice Problems

When we come to use the order of operations, we can encounter various special cases.
Sometimes, these cases will affect the order of operations, and in other cases we can use them to make the solution path easier for ourselves.

The number $0$

Addition and subtraction do not affect the number.
Multiplication by $0$ = $0$
Number divided by $0$ = $0$
Division by $0$ is undefined

number $1$

Multiplication by $1$ does not change the number
Division by $1$ does not change the number

when $a$ is not equal to $0$

$a\cdot\frac{1}{a}=1$

Division and multiplication of reciprocal numbers

$\frac{a}{\frac{1}{b}}=a\cdot b$

Let's treat the arithmetic operation in the numerator as if the numerator is in parentheses.

Example
$(5:0)+\frac{10-2}{4}\cdot2=$

Solution:
Let's start by solving the numerator:
$(5:0)+\frac{8}{4}\cdot2=$
Let's continue with the parentheses:
$0+\frac{8}{4}\cdot2=$
Let's continue with multiplication and ignore adding $0$:
$\frac{16}{4}=4$