# 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, we arrive at the following answer:

$\\ 28-2=26 \\$

If instead we begin by substracting, 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:

1.       Simplify the expressions inside parentheses ( ), brackets [ ], braces { } and fractions bars.
2.       Evaluate all powers.
3.       Do all multiplications and divisions from left to right.
4.       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:

$\\2\cdot\left [ \left ( 8-3 \right )+6\cdot \left ( 2 \right ) \right ]-3$