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

1 Answer

Answer:

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#