Mastering the BODMAS Rule
When solving math problems with multiple operations, things can sometimes get tricky. Should you multiply first or add first? What about brackets? That’s where the BODMAS rule comes in to help you. It’s a basic rule in mathematics that ensures you solve problems in the right order.
What is BODMAS?
BODMAS is an acronym that stands for:
- B: Brackets
- O: Orders (Exponents, including powers and square roots)
- D: Division
- M: Multiplication
- A: Addition
- S: Subtraction
The BODMAS rule gives you the exact order to follow when solving an expression that involves different mathematical operations like addition, subtraction, multiplication, and division. If you don’t follow this rule, you could end up with the wrong answer.
BODMAS Rule: Order of Operations
Let’s explore each part of the BODMAS rule in more detail:
Brackets (B):
Always start by solving anything inside brackets (parentheses). There can be multiple types of brackets, including:- Parentheses: ( )
- Curly Braces: { }
- Square Brackets: [ ]
Example:
For the expression (5 + 2) × 3, you first solve 5 + 2 = 7, then multiply by 3 to get 7 × 3 = 21.Orders (O):
Orders include exponents, like squares and square roots (for example,or √4). Deal with these after brackets but before any multiplication or division.
Example:
In the expression 3 + 2^3, solve the exponent first:
2^3 = 8, so the expression becomes 3 + 8 = 11.Division and Multiplication (DM):
Division and multiplication are done next, from left to right. These operations are of equal importance, so whichever comes first in the expression is solved first.Example:
In the expression 10 ÷ 2 × 3, divide first:
10 ÷ 2 = 5, and then multiply: 5 × 3 = 15.Addition and Subtraction (AS):
Addition and subtraction are solved last, also from left to right. Like multiplication and division, addition and subtraction have the same importance, so you solve them in the order they appear.Example:
In the expression 8 – 5 + 3, subtract first:
8 – 5 = 3, then add: 3 + 3 = 6.
Example Problems
Let’s try a few example problems to see how the BODMAS rule works.
Example 1:
Solve 7 + (6 × 5 – 2)
- Step 1: Solve the brackets first: 6 × 5 = 30, and then 30 – 2 = 28.
- Step 2: Add 7 + 28 = 35.
So, the answer is 35.
Example 2:
Solve 25 ÷ 5 + 4 × 3.
- Step 1: Solve division and multiplication first.
25 ÷ 5 = 5 and 4 × 3 = 12. - Step 2: Add them together: 5 + 12 = 17.
So, the answer is 17.
Why is the BODMAS Rule Important?
Imagine you have a math problem that looks like this: 8 + 4 × 2
If you solve it from left to right, you might think the answer is: 8 + 4 = 12
12 × 2 = 24
But that would be incorrect!
The correct way to solve it is to first deal with multiplication before addition, as per the BODMAS rule: 4 × 2 = 8
8 + 8 = 16
So, the correct answer is 16, not 24. This is why following the BODMAS rule is crucial—it ensures you get the right answer every time!
Common Mistakes with BODMAS
Here are a few common mistakes students make when using the BODMAS rule:
- Not solving brackets first: Always handle the operations inside the brackets before moving on to other operations.
- Confusing the order of operations: Sometimes, students solve addition before division or subtraction before multiplication. Remember that division and multiplication come before addition and subtraction.
- Forgetting exponents: When you see powers or square roots, don’t skip them! Exponents are solved right after brackets.
BODMAS Practice
Let’s make learning fun! Try these problem following the BODMAS rule:
15 – 3 + 2 × (6 ÷ 3) + 4^2
18 ÷ 2 × (5 + 3) – 2^3 + 7
Can you figure them out?
Answers:
- 32
- 71
FAQs on BODMAS
In BODMAS, multiplication and division are performed from left to right, whichever comes first. So, if division appears before multiplication when reading left to right, you perform the division first. Similarly, if multiplication appears first, you do it before division.
Yes, BODMAS applies even if there are only two operations. For example, in 8+4×3, you still follow the BODMAS rule by performing the multiplication first: 4×3=12, then 8+12=20.
If you have multiple levels of brackets, solve them from the innermost bracket outwards. For example:
5×[(3+2)×(6−4)]
- First, solve the inner brackets: (3+2)=5 and (6−4)=2.
- Now, multiply the results inside the square brackets: 5×2=10.
- Finally, 5×10=50
For both multiplication/division and addition/subtraction, follow the left to right rule. Whichever appears first as you read from left to right is solved first. For example, in 16÷4×2, do division first: 16÷4=4, then multiply: 4×2=8.
Brackets can appear in different forms, such as { } or [ ], but the BODMAS rule applies the same way. Start with the innermost bracket, no matter the shape, and solve outward.
The BODMAS rule applies to negative numbers the same way it does to positive numbers. You just need to keep track of the negative signs. For example, in the expression 5−(−3×2), you first perform the multiplication: −3×2=−6, so the expression becomes 5−(−6). Subtracting a negative is the same as adding, so the final result is 5+6=11.
Most calculators follow the BODMAS/PEMDAS rules, but it’s important to input the numbers and operations correctly. If in doubt, solving step by step manually helps ensure accuracy.
Yes, BODMAS applies to fractions as well.