Recall the “Order of Operations” by working through these following expressions to give one numerical answer. This exercise is to refresh your knowledge on “Order of operations” and you should not use a calculator; this exercise is for your benefit!

The solutions in the above animation are repeated with a more detailed explanation below.

4 x 3 - 9

Firstly, recall the method for “Order of Operations” B.E.D.M.A.S. meaning the order from first to last in which we do our math is brackets, then exponents, then division & multiplication, then addition & subtraction. Writing this out at the top of your paper may help further on. Getting the order of operations wrong can give you completely different and incorrect results.

Note: The terms PEDMAS, BODMAS, and BIDMAS are also used to represent the order of operations.

So using this, we multiply first then subtract

4 x 3 - 9 =

12 - 9 = 3

7 + ⅓ x 9 + 18 ÷ 3

So we multiply and divide first, then add or subtract.

7 + 3 + 6 = 16

3(5 - 2) - 7(6 - 1)

Brackets first then multiply.

3(3) - 7(5) =

9 - 35 = -26

3^{2} - 5^{2} + 8

3 - 7

=

Remember, for division, brackets are implied around whatever the division line is covering, it helps if we add them in.

First we do the exponents.

9 - 25 + 8

3 - 7

=

-8

-4

= 2

Note the two negatives cancel out when dividing.

(4 - 9)(7 - 1) + 3^{2}

Brackets first, then exponents, then multiply, then addition.

(-5)(6) + 3^{2} =

(-5)(6) + 9 =

-30 + 9 =

-21

(-15 ÷ 3) + 4 x 3

3^{3}

=

So first, do the brackets and then the multiplication

-5 + 4 x 3

3^{3}

=

-5 + 12

3^{3}

=

7

3^{3}

=

Now the exponent (although that could have been done earlier as it is on it's own)

7

27

=

Make sure you have a solid understanding of the Order of Operations as it plays a key in most of mathematics!