I really don't understand why the brackets would make a difference
in the result. I have been doing it this way and teaching my
students how to do it for years. I just put the numbers in the
calculator and it always works out fine.
You’re calculator may be just by accident doing it the right way.
But brackets make a big difference. Brackets determine what gets done
In the case of this formula, (diameter+ metal thickness) x pi, which
is the correct formula, whether you add the two numbers together and
then multiply the whole by pi is quite different from without the
brackets, or the other position of the brackes, which would multiply
pi by one number and then add the second number to the result.
For example: Just numbers for this, not realistic ones, but to
illustrate the math.
diameter = 5
metal thickness = 5
with pi x (5+5) you have the equivalent of pi x 10, or 31.4159.
if you had the brackets around pi and the diameter instead, then the
formula would be (pi x 5) + 5. That is (15.707) +5, which equals
20.707. Very different result, depending on the position of the
It’s a question of what the order of operation is. If you multiply
first, then pi gets multiplied by only one of the measurements. If
you add first, then pi gets multiplied by both.
With your calculator, you’re probably entering:
diameter + thickness x pi. No brackets. The calculator is simply
performing the operations in the order you entered them, which ends
If you entered the same numbers as:
pi x diameter + thickness, you’d get the wrong result.
But it’s intuitive in this situation to enter the measurements
first, so you got lucky and did it right by accident.
Adding brackets to the equation means there is then no longer any
ambiguity as to which operation (multiplication or addition) is done
first (within the brackets is always done first), so the results no
longer vary according to which direction you write or enter the
equation. Simpler calculators don’t have bracket keys, though, so
then you simply have to enter the numbers in the right order.