Chapter 3: Order of Operations and Integers 35Now work on the problem inside the brackets: 120 – 2(7)^2 + 12. Follow the order of
operations and don’t worry about anything else until you finish with this part.
7[120 – 2(7)^2 + 12] z 2
= 7[120 – 2(49) + 12] z 2
= 7[120 – 98 + 12] z 2
= 7[120 – 98 + 12] z 2
= 7[22 + 12] z 2
= 7[34] z 2
Now you can finish up, starting from the left.
7[34] z 2
= 238 z 2
= 119Although a problem may look complicated, using the order of operations can break it down into
manageable steps.
WORLDLY WISDOM
A number written in front of parentheses or other grouping symbols without an opera-
tion sign in between tells you to multiply that number by the result of the work in
parentheses. For example, 3(4 – 2) = 3(2) = 3 v 2 = 6.
A minus sign in front of parentheses tells you to subtract the result of the parentheses
from the number that precedes the minus sign. For example, 10–(5 + 1) = 10– (6) =
10–6 = 4.Try applying the order of operations to some problems.
CHECK POINT
Complete each arithmetic problem.- 9 – 4 v 2
- 3^2 – 2 v 4 + 1
- (2^3 – 5) v 2 + 14 z 7 – (5 + 1)
4. [(2^3 – 5) v 2 + 14] z 5 – 3 + 1
5. [(3^2 – 2 v 4) + 1]2 + [11 – 8 + 5(3 + 1)]