Do you like acronyms? If yes, then BODMAS is easy for you. An acronym is a short word made up of the first letters in a group of words. BODMAS is one such acronym used to remember the order of operations. BODMAS expands into Braces, Order, Division or Multiplication, and Addition or Subtraction. Different countries use different acronyms. In India, we use BODMAS whereas in the USA they use PEMDAS. LIke these acronyms differ based on the term they use to represent the order of operations.
Rules of BODMAS
These are the rules that you must follow while solving an expression.
- Braces – Always start solving an expression by simplifying the terms within the Braces or Parentheses first. Common brackets() come first in the order, followed by flower brackets { } and then in the end square brackets [ ].
- Order – at some places, the exponents’ term is used. Once braces are solved, the order or the exponent is solved.
- Division or Multiplication: While solving from left to right, the operation that comes first either division or multiplication is solved. It is performed only after solving brackets and order.
- Addition or subtraction: At last after finishing all the above-mentioned steps, addition or subtraction the operation that comes first from left is performed.
The acronym BODMAS helps you remember this order of operations easily.
Examples:
Let us work out some examples based on BODMAS
- Solve: 2) 4 – 6
Solution: According to BODMAS, Solve the Braces first.
2) = (4 2) = 2
Next is multiplication,
2) 4 = 2 4 = 8
Last subtraction
2) 4 – 6 = 8 – 6 = 2
Hence 2) 4 – 6 = 2.
- Solve: [36 – {3 (11 – 5)}]
Solution: (11 – 5) = 6
{3 (11 – 5)} = {3 6} = 18
36 = 36 2 = 18
[36 – {3 (11 – 5)}] = 18 – 18 = 0
Hence the answer is 0.
Likewise, you can make use of BODMAS to solve complicated expressions. For more information and solved examples log on to the Cuemath website.
What is an Order of Operations?
In mathematics for solving expressions involving multiple operations, braces, and exponents, we follow the order of operations. It is basically a set of rules followed uniformly throughout the world. These rules are required to get a consistent answer, as otherwise we may end up finding different answers for a single expression and we don’t know which is the correct answer.
Example: 1+5 6 3 =?
I can solve this in many ways like 1+5 = 6, 1+5 6 = 36, 1+5 6 3 = 36/3 = 12.
In other way 5 6 = 30, 5 6 3 = 30/3 = 10, 1+5 6 3 = 10+1 = 11.
In one more way 6 3 = 2, 5 6 3 = 10, 1+5 6 3 = 10+1 = 11.
So I got two same answers and one different answer. Which is the correct answer? I got 11 in 2, does it mean it is the correct answer? If yes then which order should I follow?
To avoid all these kinds of complexities, the BODMAS rule came into force. Now let us solve the same using BODMAS.
1+5 6 3 =?
According to BODMAS, you must start to solve the expression from left to right.
While solving if multiplication comes before division from left, then we have to perform multiplication first. 5 6 = 30, 5 6 3 = 30/3 = 10, 1+5 6 3 = 10+1 = 11. This is the correct order of operation.
Hence the correct answer is 11.
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