Overview
The order of operations is a set of rules in algebra to define what operations must be done first in order to obtain the correct answer to a problem. Without sequencing rules, it would be possible to work problems and get different answers depending on the way the numbers and variables are combined. Instead, conventions ensure that a particular answer to a problem is the correct one.
Why Is Order of Operations Important?
Suppose the problem is as simple as 85 +9 X 2. Without an order of operations, one person might calculate the problem as (85 +9) X 2 or 94 X 2 = 188, while another might calculate it as 85 + (9 X 2) or 85 + 18 =103. Similarly, does 2 X 34 mean 64, or 1296, or does it mean to work the 34and then multiply by 2, or 81 X 2 = 162?
What Is the Order of Operations?
By convention, exponents are solved first, then multiplications or divisions, from left to right, then additions or subtractions, from left to right. Therefore, the correct answer to 85 + 9 X 2 is not 188, but 103. There are no exponents in the problem, but there is a multiplication, 9 X 2, equaling 18. Working from left to right, the last step is adding 85 + 18, to equal 103. Similarly, in 2 X 34, the exponent is worked first, then the multiplication.
What Do Parentheses Do?
Parentheses in mathematical sentences take priority over all other operations, so they are solved first, from left to right. Suppose the problem really were (85 +9) X 2. In that case, the correct answer would be to solve within the parentheses first, then the multiplication. Similarly, (4x)3 does not mean the same as 4x3. Within the order of operations, if x equals 2, (4x)3would equal 83 or 512. If x equals 2, 4x3 would equal 4 X 23 or 32.
Does Your Calculator Follow Order of Operations?
When they are buying school supplies, students may wonder why their teachers specify certain types of calculators. That is because scientific calculators follow the algebraic order of operations, while other calculators do not. A scientific calculator will calculate the problem 85 +9 X 2 by doing the multiplication first, coming up with the answer 103, while a regular calculator will do the operations from left to right only, answering 188.
Interested in math tutoring services? Learn more about how we are assisting thousands of students each academic year.
SchoolTutoring Academy is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Middlebury, VT visit: Tutoring in Middlebury, VT