BODMAS stands for:
- Brackets
(…) - Orders
√ , x2 - Division or Multiplication
÷ ,x
- Addition or Subtraction
+, –
In order to complete any mathematic calculation, we must follow BODMAS. This mnemonic helps us remember the order of operations for these sets of mathematical equations. BODMAS is extremely important to understand as it applies to harder equations with multiple operations. Here, BODMAS focuses on order within an equation rather than solving from purely left to right. In addition, it allows us to remember how to evaluate mathematical operations in a certain mathematical expression.
The word BODMAS tells us the order we must follow to correctly answer complex questions with multiple steps.
Brackets
Orders (Square roots, indices or powers)
Division
Multiplication
Addition
Subtraction
We must follow the order by completing any calculations inside brackets first. Then, we apply any orders which include square roots, indices or powers. Thirdly, divisions or multiplication are to be completed from left to right, followed by addition or subtractions that are also completed from left to right.
Examples of BODMAS
For example, let’s take a look at this equation: 4 – 3 x 7
In any equation, we must incorporate BODMAS. To do this, we need to multiply 3, and 7 first as M (multiplication) appears in the word BODMAS before S (subtraction). Only once we have done the multiplication can we move on to subtract it from 4 such that the final answer would be – 17.
3 x 7 = 21
4 – 21 = – 17
Let’s take a look at another example: 42 – 3 x 5
When we check BODMAS, we can see O (Orders) need to be completed before M (multiplication). Here, we need to consider the 42, as there is a power in it. As a result, the equation becomes: 16 – 3 x 5
Then we must multiply 3 by 5 to get 15. From there, we take 15 away from 16 to result in 1.
16 – 15 = 1
In our final example: (15 + 6) x 4 =
Once again, checking BODMAS, we know we must look at the brackets first.
15 + 6 = 21
Then we multiply this result of 21 by 4, resulting in 84.
21 x 4 = 84
Using BODMAS helps us remember the order of mathematical operations to solve problems and give us and everyone else consistency in our answers. BODMAS, in general, helps us make mathematical expressions and equations easier to solve, especially when there are multiple operations involved. By using brackets or parentheses, BODMAS can set up certain conventions such that algebraic expression is no longer ambiguous and has meaning in regards to priority and meaning.
Practice questions for you
Here are some practice questions for you. Remember to follow BODMAS!
9 x 4 – 3 =
Click to reveal the answer
33
2 ( 6 + 7 x 3) =
Click to reveal the answer
54
22 + 32 – 9 =
Click to reveal the answer
4
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