BODMAS is an acronym designed to help children remember the order of mathematical operations. Children can put it to good use while trying to find solutions to mathematical problems and to derive mathematical statements. Keep reading to learn more about BODMAS.
What does BODMAS stand for?
BODMAS stands for brackets, orders, division, multiplication, addition, and subtraction.It serves to remind us to begin mathematical operations by resolving the brackets, then moving on to powers or roots, followed by division or multiplication, and finally addition/subtraction. Division and multiplication are grouped together and can be performed in either order. The same is true for addition and subtraction.
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Why is it important to get the BODMAS order right?
Let us look at the following question:
10 – 8 x 3 + 4 ÷ 2 = ?
Without BODMAS, where would we begin?
If we simply calculate from left to right, it would look something like this:
Firstly, 10 – 8 = 2, which is then multiplied by 3 to get 6. We then add 4 to the 6 to get 10 and divide it by 2 to get an answer of 5.
Now let us use BODMAS:
If we use BODMAS, we know that division and multiplication come first:
8 x 3 = 24
4 ÷ 2 = 2
We now insert these answers back into the equation and calculate addition and subtraction:
10 – 24 + 2 = ?
10 – 24 is -14. If we then add 2, we get an answer of -12, which is vastly different from the answer we get when not using BODMAS. This is why it is so important to get the order of operations correct!
BODMAS vs PEDMAS vs BIDMAS
There are two acronyms, other than BODMAS that are used to remember the order of operations: PEDMAS, and BIDMAS. All of these are identical, the only difference being that some terms are known by different names.
The following is a table which shows the name variations that exist across the three terms:
BODMAS PEDMAS BIDMAS
Brackets Parentheses Brackets
Orders Exponents Indices
Division Division Division
Multiplication Multiplication Multiplication
Addition Addition Addition
Subtraction Subtraction Subtraction
BODMAS Conditions
When a mathematical equation has multiple operations, BODMAS is utilized. There are, however, some conditions to adhere to when utilizing this acronym:
- Open any of the brackets and add/remove the terms:
- a + (b + c) = a + b + c
- a + (b – c) = a + b – c
- Simply open the bracket if there is a negative sign outside the bracket, and then transfer the sign’s function to each phrase that exists inside the bracket:
- a – (b + c) = a – b – c
- The term outside the bracket must be multiplied with each term within the bracket:
- ab + ac = a(b + c)
How to solve BODMAS questions
Question 1
3(4 x 10) ÷ { 2 + (2 x 5) } + 12 – 3 = ?
This is a fairly complex equation, and without the BODMAS rule, where would we even begin? Nevertheless, we know that brackets come first and so let us start there:
One thing to bear in mind is there are different types of brackets: ( ), { }, and [ ]. They essentially mean the same thing. However, you should know that they simply exist to help distinguish equations. After all [3{4+(2+1)}] is easier to understand than (3(4+(2-1))).
Let us begin by solving { 2 + (2 x 5) }
2 x 5 = 10, which when added to the 2 outside the brackets totals to 12. We can then reinsert this into the equation as follows:
3(4 x 10) ÷ (12) + 12 – 3 = ?
Then we move onto the other bracket: 3(4 x 10).
4 x 10 = 40, which when multiplied by 3 gets us 120. We can then insert this back into the equation:
(120) ÷ (12) + 12 – 3 = ?
According to BODMAS, this is followed by division:
120 ÷ 12 = 10
Reinserting this back into the equation yields the following:
10 + 12 – 3 = ?
As addition and subtraction are grouped, we can work from left to right:
10 + 12 = 22.
Subtracting 3 from this gets us 19
As such:
3(4 x 10) ÷ {2 + (2 x 5)} + 12 – 3 = 19
Question 2
{18 – 2(5 + 1)} ÷ 3 + 7 = ?
Using BODMAS, we know to tackle the brackets first:
{18 – 2(5 + 1) }
Firstly, we begin by solving the inner bracket:
5 + 1 = 6, then we multiply it by 2 to get an answer of 12. Reinserting this, we get:
{18 – (12)} = ?
Solving 18 – 12, we get 6. Returning to the original equation, we can now insert this answer:
(6) ÷ 3 + 7 = ?
Next, according to BODMAS, we divide:
6 ÷ 3 = 2
Then, we can add 7 to this to get an answer of 9.
As such:
{18 – 2(5 + 1) } ÷ 3 + 7 = 9
Question 3:
(1 + 20 – 16 ÷ 4²) ÷ {(5 – 3)² + 12 ÷ 2} = ?
As both sides of the equation contain brackets, we can solve them separately as follows:
To begin with:
(1 + 20 – 16 ÷ 4²)
According to BODMAS, we solve the power first, then the division, then the addition/subtraction:
42 = 16, and if we then divide 16 by this answer, we get 1.
Then we can add and subtract from left to right:
1 + 20 – 1 = 20
Returning to the original equation yields:
(20) ÷ {(5 – 3)² + 12 ÷ 2}
Let us now solve the other equation within the brackets:
{(5 – 3)² + 12 ÷ 2}
According to BODMAS, we begin with the inner brackets:
5 – 3 = 2
We then square this number to get 4.
The equation now reads: 4 + 12 ÷ 2
BODMAS tells us to then calculate the division:
12 ÷ 2 = 6, to which we add the 4 to get 10.
The original equation now reads:
(20) ÷ (10) =?
Dividing these numbers equals the correct answer of 2.
As such:
(1 + 20 – 16 ÷ 4²) ÷ {(5 – 3)² + 12 ÷ 2} = 2
Easy ways to remember the BODMAS rule
The following are some easy guidelines for remembering the BODMAS rule:
- First, simplify the brackets.
- Solve all terms that are exponential.
- Do either multiplication or division (go from left to right)
- Do additions and subtractions (go from left to right)
Common errors while using the BODMAS rule
There are some common errors students make when using BODMAS that yield a wrong answer. Be sure to read the following, so that you don’t make the same mistakes:
- Multiple brackets may confuse people, which could lead to the incorrect response. Therefore, if a mathematical expression has many bracket types, all of the same types can be solved at once.
- Remember that an arithmetic symbol attached to a number changes, whether it is positive or negative. As an illustration, 1-3+4 = -2+4 = 2. However, occasionally mistakes like 1-3+4 =1-7 = -6 are made that result in the incorrect answer.
- Assuming that division comes before multiplication, and addition comes before subtraction is erroneous. The right solution can be obtained by choosing these operations according to the left to right rule.
- Regardless of whatever occurs first in the statement, addition and subtraction must be performed after multiplication and division, since they are same-level operations and must also be completed in the left-to-right order. As D comes before M in BODMAS, one may get the incorrect result if they try division before multiplication.
Why is it important to follow the order of operations?
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