Order Of Operations Tutorial: BODMAS

BODMAS refers to the order of operations in a sum, which is a method of working out whether one needs to multiply before addition, solve brackets before subtracting, and so on. This is simple enough to learn and apply, but it is suprising how many students struggle with this concept throughout their school careers. A small amount of structured repetition and practice can iron out any difficulties your child has in this area and will give her yet more opportunities to succeed in maths. Once this is mastered for simple sums, the way is open for equation solving to be tackled with success which itself presents many opportunities to the budding mathematician / scientist.

B Brackets first
O Orders (Powers, Square Roots)
DM Divide and Multiply (left to right)
AS Add and Subtract (left to right)

The operations are in the order of strength; the strongest is performed first, then the next strongest and so on. One way to remember this is to picture a big strong bully shoving his way to the front of a queue. The two pairs of operations, being DM and AS, are the SAME STRENGTH and if there is more than one of these to be done at any stage, they are performed from left to right across the sum.

Note: If you just want exercises to practice this skill, go to the order of operations worksheets page.

Learning BODMAS

A few simple steps will help your child retain this concept. When problems are being solved, the following steps should be taken:

Step 1: Write the term BODMAS above the question for easy reference. This may seem tedious after several sums but it will help your child memorize the term.

Step 2: Identify the operations that are available to solve. Note that if there is more than one operation in the bracket the process has to be performed in the bracket first. This is best left until the child has a sound grasp of the basics.

Step 3: Go through the options in order: B---O---DM---AS. Identify which of these is the strongest operation, and must therefore be done first. Circle the operation and the numbers on each side of that operation.

Step 4: Perform that operation and write the answer in the place of the original operation and the numbers that were on either side of it.

Step 5: Write the other parts of the sum unchanged and in exactly the same positions as in the original sum.

Step 6: If there are still two or more operations to perform, go back to Step 2. If there is only one operation left, or only operations of the same strength, complete it to get the answer to the sum.

Examples of BODMAS

EXAMPLE 1:

Let's have a look at how these 6 steps are used to solve sums. This first example is a sum with two choices to make: do you do the addition first or the multiplication?

Here is another example, again with two operations to choose from. As shown below, following the simple steps outlined above guarantees the correct answer.

This example has three operations, one additions, one multiplication and one subtraction. Here we see that if there are two operations of the same strength to be performed during a single step, they are done from left to right:

Here is an example of order of operations in a sum with a bracket. The bracket is the strongest operation, so whatever is in it needs to be completed first.

Last is a more complex example. It includes an "order" and has several operations. While such a sum will initially seem daunting to a child just starting this topic, it is important to just take the sum one step at a time and the solution will appear. It looks a bit long-winded, but the method used in this question guarantees success.

It is also easy to see how this order of operations process can become quick and streamlined with these six steps being compressed into a minimum of work. The student will do this naturally and should be encouraged to do so as long as their working out remains clear and logical.

BODMAS Practice worksheets

Repetition is the mother of skill in mathematics, so to allow your child to practice this essential method I have made available a series of order of operations worksheets ranging from simple to complex. They are in PDF form and are free to be saved to your computer for printing and personal use.