Operations in the correct order
When you are faced with a mathematical expression that has several operations or parentheses, the solution may be affected by the order in which you tackle the operations. For example, take the expression
$$4\cdot 7-2$$
If we do the multiplication first \(4\cdot 7 = 28\), we arrive at the following answer:
$$28-2=26$$
If instead we begin by substracting \(7-2 = 5\), we get:
$$4\cdot 5= 20$$
In order to avoid confusion and to ensure that everyone always arrives at the same result, mathematicians established a standard order of operations for calculations that involve more than one arithmetic operation. Arithmetic operations should always be carried out in the following order:
- Simplify the expressions inside parentheses ( ), brackets [ ], braces { } and fractions bars.
- Evaluate all powers.
- Do all multiplications and divisions from left to right.
- Do all additions and subtractions from left to right.
Example
Suppose you want to figure out how many hours a person works in two days assuming that they work 4 hours before lunch and 3 hours after lunch each day. First, work out how many hours the person works each day:
$$4+3=7$$
and then multiply that by the number of days the person worked:
$$7\cdot 2=14$$
If we were to write this example as one expression, we would need to use parentheses to make sure that people calculate the addition first:
$$\left ( 4+3 \right )\cdot 2=14$$
Video lesson
Simplify the following expression:
$$2\cdot\left [ \left ( 8-3 \right )+6\cdot \left ( 2 \right ) \right ]-3$$