# Operations in the right order

When faced with a mathematical expression comprising several operations or parentheses, the result may be affected by the order in which the various operations are tackled e.g.

$$4\cdot 7-2$$

the result is influenced if we take the multiplication first:

$$28-2=26$$

Or if we begin with the subtraction:

$$4\cdot 5= 20$$

To avoid misunderstandings mathematicians have established an order of operations so that we always arrive at the same result.

- Simplify the expressions inside parentheses ( ), brackets [ ], braces { } and fractions bars.
- Evaluate all powers.
- Do all multiplications and division from left to right.
- Do all addition and subtractions from left to right.

An example of this appears if we were to ask ourselves how many hours a person works over two days, if they work 4 hours before lunch and 3 hours after lunch. We first work out how many hours the person work each day:

$$4+3=7$$

and then multiply that with the number of working days:

$$7\cdot 2=14$$

if we instead were to write this as an expression, we would need to use parentheses in order to calculate the addition first:

$$\left ( 4+3 \right )\cdot 2=14$$

**Video lesson**

Evaluate the expression

$$2\cdot\left [ 4+\left (4-2 \right )^{2}-3 \right ]+\left ( \frac{14}{2} \right )$$