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 x 7-2

The result is influenced if we take the multiplication first:

28-2 +26

Or if we begin with the subtraction:

4x5=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 divisions from left to right.

4. Do all additions 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:

7x2 =14

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

(4+3)x2=14

Video lesson: Simplify the following expression:

2x[(8-3)+6x(2)]-3

Watch the video in the next page for the solution.

Here we have an arithmetic expression and we want to simply and solve this as best as we can. The expression is; 2x[(8-3)+6x(2)]-3. So it’s just a bit of a messy arithmetic expression. We’re going to simplify it down as much as possible using the order of operations and see what it equals. So we’re going to start with our brackets and our parentheses here. Simplify down there and then we can start to add and subtract. So if we leave the two outside of the bracket, eight minus three becomes five. Plus, six times two becomes twelve….minus three. So we’ve done the bracket first here, this parentheses and we’ve done six times two so that takes care of that bracket. No we’re going to add five and twelve. So we still have two times bracket, five plus twelve is seventeen, minus three still. Now finally we can do 2 times seventeen. Two times seventeen becomes thirty four. Thirty four minus three is just thirty one. There’s our final answer.

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