Business Mathematics: Review of Arithmetic - Order Of Operations

When two or more operations are involved in the same expression, they are performed in the following order:
Powers (exponents)
Multiplication and division
Addition and subtraction

Within each level, operations are performed left to right. If any modifications are to be made to this scheme, they are indicated by parentheses. Calculations within parentheses are always performed first.

Example: Compute (a) 2 + 3 · 5, (b) 3 + 23 · 5, (c) (2 + 3) · 5, (d) (3 + 2f · 7.
(a) 2 + 3 · 5 = 2 + 15 = 17
(b) 3 + 23·5 = 3 + 8·5 = 3 + 40 = 43
(c) (2 + 3)·5 = 5·5 = 25
(d) (3 + 2)2·7 = 52·7 = 25 · 7 = 175
This ordering scheme applies to fractions in a similar manner.

Example 30
Compute (a) 2/3 + 3/4 · 1/3 and (b) (2/3 + 3/4) · 1/3.



Solved Problems


1.  Explain the difference between 5 + 7·3 and (5 + 7) · 3 and compute their values.
Solution
In the expression 5 + 7·3 the multiplication is performed first to give 21. Then 5 is added to give an answer of 26. In the expression (5 + 7) · 3 the parentheses indicate that the addition is to be performed first and the sum, 12, is then multiplied by 3. The result is 36.

2.  Compute the value of 2 + 3 · 52.
Solution
The exponent is evaluated first to give 25. Then 3 is multiplied by 25 to give 75. Finally 2 is added to give 77 as the answer.

3.  Compute the value of (3 + 23) · 5.
Solution
All operations inside parentheses are performed first. The exponent is evaluated first and then the addition is performed. This gives a value of 11 (3 + 23 = 3 + 8). This is then multiplied by 5 to give an answer of 55.