> order of operations
Order of operations
Often we combine several operations such as addition, subtraction, multiplication and division in an algebraic expression. The order in which we carry out the operations are very important, as doing it in different orders may give different answers.
The rules are:
- First, perform all operations within parentheses.
- Next, perform all multiplications and divisions in order from left to right.
- Finally, perform all additions and subtractions in order from left to
right.
The example below illustrate how important the order of operations is.
A museum charges a $5 admission fee for each person aged 18 years or older, $2 for person under 18. A group of visitors consists of 4 adults aged 18 years or older and 3 children under 18. How much will they need to pay?
One way of solving this problem is to work it out in three steps.
Step A: Admission fees for adults = 5 x 4 = 20
Step B: Admission fees for children = 2 x 3 = 6
Step C: The total costs = 20 + 6 = 26
Another way of solving this problem is to combine all operation in one
expression and then calculate.
The total costs = 5 x 4 + 2 x 3.
The right way to evaluate 5 x 4 + 2 x 3 is doing 5 x 4 and 2 x 3 first, and then
add the two products.
5 x 4 + 2 x 3
= 20 + 6
= 26
The following calculations are wrong!
5 x 4 + 2 x 3
= 20 + 2 x 3
= 22 x 3
= 66
5 x 4 + 2 x 3
= 5 x 6 x 3
= 90
In the next page, we will deal with parentheses.