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An arithmetic expression that involves multiple operations such as addition, subtraction, multiplication, and division are not easy to solve as compared to operations involving two numbers. In this article, we will discuss Tips to Solve BODMAS Questions.
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BODMAS RULE
The BODMAS acronym is for:
- Brackets (the parts of expression inside brackets and always come first).
- Orders (numbers involving powers or square roots).
- Division.
- Multiplication.
- Addition.
- Subtraction.
In certain regions, PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction) is employed, which is also the synonym of BODMAS.
It explains the order of operations to be performed while solving an expression. According to the BODMAS rule, if an expression contains brackets ((), {}, []) we have first to solve or simplify the bracket followed by “Orders” (numbers involving powers or square roots)., then division, multiplication, addition and subtraction from left to right. Solving the expression in the wrong order will result in a wrong answer.
The “Order” in the BODMAS full form is also called “of”, which means the numbers which involve powers, square roots, etc. Check the Conditions and Rules in the below table to have a better understanding of using the BODMAS rule.
Conditions and Rules
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|
Condition |
Rule |
| a +(b + c) = a + b + c | Open the bracket and only then add the terms. |
| a – (b + c) = a – b – c | Open the bracket and multiply the negative sign with each term inside the bracket. (All positive terms will be negative and vice-versa) |
| a (b + c) = ab + ac | Multiply the outside term with each of the numbers inside of the bracket |
Simplification of Brackets
Simplification of brackets in expression means the expansion of brackets. We can remove brackets from an expression by using multiplication. We use multiplication over addition or subtraction. Generally, it can be written as:
x (y + z) = xy + xz
Notes: The order of brackets that can be simplified is (), {}, [].
Example 2: Expand and simplify
9 (5+3)
11 (2x + 3)
Solution:
(i) The terms inside the bracket are called like terms. We can solve this by two methods.
Method 1: Add the terms inside the bracket and multiply the number outside the bracket with the sum of the numbers inside the bracket.
9 (5 + 3) = 9 * 8 = 72
Method 2: Multiply the outside terms with each number inside the bracket and add the products.
9 (5 + 3) = (9 * 5) + (9 * 3)= 45 + 27 = 72
(ii) Here the terms are unlike terms. This expression can be simplified by multiplying the number outside the bracket with the terms inside the bracket and by adding their product, you will find the solution.
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Simplification using Orders
Do anything involving orders that is the numbers involving powers or square roots, again working from left to right if there is more than one.
Example:
32 + 5 = ?
You need to calculate the power first before you can add 5.
32 = 3 × 3 = 9
9 +5 = 14
Simplification using Division and Multiplication
Once you have done any parts of the calculation involving brackets or powers the next step is division and multiplication.
Multiplication and division rank equally, so you work from left to right within the sum, doing each operation within the order in which it appears.
Example:
6 ÷ 2 + 7 × 4 = ?
You need to do division and multiplication first, but you have one of each of them in this expression.
Start from the left and work across to the right, which means that you start with 6 ÷ 2 = 3. Then do the multiplication, 7 × 4 = 28.
Your calculation is now 3 + 28.
Complete the operation to find the answer, 31.
Addition and Subtraction
The final step is to solve addition or subtraction. Again, subtraction and addition rank equally, and you simply work from left to right.
Example:
4 + 6 − 7 + 3 = _?
You start on the left and work your way across.
4 + 6 = 10
10 − 7 = 3
3 + 3 = 6
The answer is 6.
Bringing It All Together
This final example includes all elements of BODMAS.
Example:
4 + 82 × (30 ÷ 5) = _?
Start with the calculation inside the brackets.
30 ÷ 5 = 6
This gives you 4 + 82 × 6 = _?
Then calculate the orders – in this case, the square of 8.
82 = 64
Your answer is now 4 + 64 × 6
Then move to the multiplication 64 × 6 = 384
Finally perform the addition. 4 + 384 = 388
The answer is 388.
In this blog, we discussed Tips to Solve BODMAS Questions. Keep visiting us for updates on various government jobs.
