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

1 Answer
Feb 19, 2016

Answer:

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

Explanation:

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

Parentheses:
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.

Exponents:
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#