# What is 55\div ( 4^{2} - 5)?

5

#### Explanation:

To answer this type of question, we use the Order of Operations, also known as PEMDAS:

• $\textcolor{red}{P}$ - Parentheses (also known as Brackets)
• $\textcolor{b l u e}{E}$ - Exponents
• $\textcolor{g r e e n}{M}$ - Multiplication
• $\textcolor{g r e e n}{D}$ - Division (this has the same weight as M and so I gave it the same colour)
• $\textcolor{b r o w n}{A}$ - Addition
• $\textcolor{b r o w n}{S}$ - Subtraction - again, same weight as A and so the same colour)

$55 \div \left({4}^{2} - 5\right)$

We do $\textcolor{red}{P}$ first: $\textcolor{red}{{4}^{2} - 5}$

Now that we have this term isolated from the division, we now look to PEMDAS from the beginning again. There are no $\textcolor{red}{P}$ but we do have an $\textcolor{b l u e}{E}$: $\textcolor{b l u e}{{4}^{2} = 16}$

Now back to $\textcolor{red}{{4}^{2} - 5}$, which we can rewrite as $\textcolor{red}{16 - 5 = 11}$

Now back to the fraction $55 \div \left({4}^{2} - 5\right)$. Since we know that ${4}^{2} - 5 = 11$, let's rewrite the expression: $55 \div 11 = 5$