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Maths258Updated 14 Sept 20262 pages

Understanding the Order of Operations in Mathematics

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Ever wondered why your calculator gives different answers than your mate's when doing the same sum? It's all about following the right order when doing maths calculations. Without these rules, chaos would reign in the maths world!
Order of operations – page 1

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Order of Operations

You can't just work through a maths problem from left to right like reading a book. There's a specific order of operations that you must follow to get the right answer every time.

BODMAS (or BIDMAS) is your best mate for remembering this order. It stands for Brackets, Orders/Indices, Division/Multiplication, Addition/Subtraction. Think of it as a queue - some operations get to jump ahead of others!

Here's how it works with 3+42−10÷23 + 4^2 - 10 ÷ 2: First, tackle that power (42=164^2 = 16). Then sort out the division (10÷2=510 ÷ 2 = 5). Finally, work left to right with addition and subtraction (3+16−5=143 + 16 - 5 = 14).

Quick Tip: When you've got division and multiplication (or addition and subtraction) in the same problem, work from left to right - they're equal in the pecking order!

Order of operations – page 2

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Working with Brackets

Brackets are the VIPs of mathematical operations - they always get dealt with first, no matter what. If you spot brackets within brackets, start with the innermost ones and work your way out.

Let's tackle [40−(2+42)]×2[40-(2+4^2)] × 2 step by step. Inside those inner brackets, we've got 2+422 + 4^2. Following BODMAS, the power comes first: 42=164^2 = 16, so we get 2+16=182 + 16 = 18.

Now we can handle the outer brackets: 40−18=2240 - 18 = 22. With the brackets sorted, we finish with the multiplication: 22×2=4422 × 2 = 44. See how those brackets completely changed the order of our calculations?

Remember: Brackets are like putting a "deal with me first" sticker on part of your calculation - ignore them at your peril!

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