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:


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.

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


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

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