How do you simplify #3(7 + 4 - 2) ÷ 9 - 7# using order of operations?

1 Answer
Feb 19, 2016

#3(7+4-2)-:9-7 = -4#


The order of operations is parentheses, exponents, multiplication and division, and then addition and subtraction.

First, we evaluate any parts of the expression within parentheses. In this case, the only operations within parentheses are addition and subtraction, so we can just go from left to right.

#3color(red)((7+4-2))-:9-7 = 3color(red)((11-2))-:9-7#

#= 3color(red)((9))-:9-7#

There are no more expressions within parentheses which we need to evaluate, meaning we can move on to the next step.

This expression contains no exponents, and so we move on.

Multiplication and Division:
Now we evaluate any multiplication or division operations, going from left to right.

#color(red)(3(9))-:9-7 = color(red)(27)-:9-7#

#color(red)(27-:9)-7 = color(red)(3)-7#

There are no more multiplication or division operations, and so we move to the final step.

Addition and Subtraction:
Finally, we evaluate any remaining addition and subtraction, going from left to right.

#color(red)(3-7) = color(red)(-4)#

Thus, our final result is

#3(7+4-2)-:9-7 = -4#