Question

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

Answer 1

5

Explanation:

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

• `color(red)(P)` - Parentheses (also known as Brackets)
• `color(blue)(E)` - Exponents
• `color(green)(M)` - Multiplication
• `color(green)(D)` - Division (this has the same weight as M and so I gave it the same colour)
• `color(brown)(A)` - Addition
• `color(brown)(S)` - Subtraction - again, same weight as A and so the same colour)

`55-:(4^2-5)`

We do `color(red)(P)` first: `color(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 `color(red)(P)` but we do have an `color(blue)(E)`: `color(blue)(4^2=16)`

Now back to `color(red)(4^2-5)`, which we can rewrite as `color(red)(16-5=11)`

Now back to the fraction `55-:(4^2-5)`. Since we know that `4^2-5=11`, let's rewrite the expression: `55-:11=5`