Mastering the Order of Operations: A Guide to BIDMAS

Introduction to BIDMAS

In mathematics, the order in which you perform calculations is not just a suggestion; it is a fundamental rule. If you have an expression like $3 + 2 \times 5$, you might be tempted to calculate from left to right, giving you $5 \times 5 = 25$. However, the correct mathematical answer is $13$. This discrepancy occurs because multiplication takes priority over addition. To avoid such errors, we use the acronym BIDMAS.

BIDMAS provides a universal framework for solving multi-step expressions. Mastering this is essential for your KS3 maths journey, as it forms the foundation for algebra, geometry, and beyond. Understanding these rules ensures that your work is consistent, logical, and, most importantly, correct in your exams.

What is BIDMAS?

BIDMAS is an acronym that dictates the hierarchy of mathematical operations. When you encounter a calculation with multiple steps, you must follow this sequence:

• Brackets: Solve everything inside brackets first.
• Indices: Calculate powers and roots (e.g., $3^2$ or $\sqrt{16}$).
• Division and Multiplication: These have equal priority. Work from left to right.
• Addition and Subtraction: These also have equal priority. Work from left to right.

By following this order, you ensure that every mathematician arrives at the same result for any given expression.

Step 1: Brackets and Indices

Brackets are the most powerful tool in an expression. They force you to perform a specific part of the calculation before anything else. If you have nested brackets, always start with the innermost set.

Indices, or powers, are the next priority. This includes squares, cubes, and square roots. You must evaluate these before moving on to multiplication or division.

Example 1: Solve $10 - (2^2 + 1)$.

1. Brackets first: Inside the brackets, we have an index ($2^2$). $2^2 = 4$.
2. Complete brackets: $4 + 1 = 5$.
3. Final step: $10 - 5 = 5$.

Step 2: Division and Multiplication

Once brackets and indices are cleared, you move to division and multiplication. A common misconception is that division always comes before multiplication because it appears first in the acronym. In reality, they share the same priority level. If both appear in an expression, you must work from left to right.

Example 2: Solve $20 \div 4 \times 2$.

1. Left to right: Since division and multiplication are equal, we start with $20 \div 4 = 5$.
2. Multiply: Now, $5 \times 2 = 10$.

If you had multiplied first, you would have calculated $4 \times 2 = 8$, then $20 \div 8 = 2.5$, which is incorrect.

Step 3: Addition and Subtraction

Addition and subtraction are the final operations to perform. Similar to division and multiplication, they share the same priority level. Always process them from left to right to maintain accuracy.

Example 3: Solve $15 - 3 + 2$.

1. Left to right: $15 - 3 = 12$.
2. Add: $12 + 2 = 14$.

Common Mistakes to Avoid

1. Ignoring the Left-to-Right Rule: Many students assume multiplication always beats division, or addition always beats subtraction. Remember that these pairs are equal in priority and must be solved in the order they appear from left to right.
2. Misinterpreting Indices: Students often multiply the base by the exponent (e.g., thinking $3^2 = 6$ instead of $3 \times 3 = 9$). Always remember that an index represents repeated multiplication.
3. Forgetting Brackets: If you see brackets, they must be the very first thing you address. Skipping this step will almost certainly lead to an incorrect answer.

Frequently Asked Questions

Is BIDMAS the same as BODMAS? Yes. The 'I' in BIDMAS stands for Indices, while the 'O' in BODMAS stands for Orders. Both refer to powers and roots and follow the exact same rules.

What happens if there are multiple sets of brackets? Always solve the innermost brackets first and work your way outwards.

Do I always have to follow BIDMAS? Yes, it is the standard convention for all mathematical expressions to ensure consistency.

Conclusion

BIDMAS is the key to unlocking accuracy in your maths work. By consistently applying these rules, you can tackle even the most complex multi-step problems with ease. To see these concepts in action and test your skills, head over to MathInstructor AI to generate a free, narrated animated lesson tailored to your learning needs.