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BIDMAS - Order of Operations

🎬 Video: Understanding BIDMAS

What are Mathematical Expressions? (0:01)

A mathematical expression is a combination of numbers, variables, and operators. It does not have an equals sign (=), unlike an equation.

For example, $$(300 + 3 \times 20) \div 12$$
Parts of a Mathematical Expression:

  • Terms: The individual numbers in the expression (300, 3, 20, 12).
  • Operators: The symbols that tell us what to do (+, ×, ÷).

Mathematical expressions help us write real-life problems in a structured way so we can calculate them easily!

What are Orders of Operations (BIDMAS)? (0:23)

The order of operations is the rule that tells us the correct sequence to follow when solving a mathematical expression. We can use BIDMAS to remember the order:

  • BBrackets (Solve anything inside brackets first)
  • IIndices (Powers and roots)
  • DDivision
  • MMultiplication
  • AAddition
  • SSubtraction

For example:

$$ (300 + 3 \times 20) \div 12 $$

Brackets come first, but inside the brackets, you must still follow BIDMAS rules. Since multiplication (M) comes before addition (A), you do multiplication first:

$$ 3 \times 20 = 60 $$

So the expression simplifies to:
$$ (300 + 60) \div 12 $$

Solve the addition inside the brackets:
$$ 300 + 60 = 360 $$

Finally, you divide:
$$ 360 \div 12 = 30 $$

How to Solve Expressions with Same-Level Operations? (1:22)

If a calculation only contains operations of the same level (such as only division and multiplication, or only addition and subtraction), solve from left to right.

However, if there are brackets, you must solve inside the brackets first.

💡 Example 1:

  • Only division and multiplication, solve from left to right:

$$ 20 \div 5 \times 2 = 4 \times 2 = 8 $$

  • However, if there are brackets, solve inside first:

$$ 20 \div (5 \times 2) = 20 \div 10 = 2 $$

💡 Example 2:

  • Only addition and subtraction, solve from left to right:

$$ 10 – 6 + 3 = 4 + 3 = 7 $$

  • However, if there are brackets, solve inside first:

$$ 10 – (6 + 3) = 10 – 9 = 1 $$

How to Handle Multiple Brackets? (2:05)

If there are multiple sets of brackets, solve the innermost brackets first, then work outwards.

For example,

$$
\begin{aligned}
50 – (2 \times (2 + 4 \times 5) – 3) &= 50 – (2 \times (2 + 20) – 3) \\[1em]
&= 50 – (2 \times 22 – 3) \\[1em]
&= 50 – (44 – 3) \\[1em]
&= 50 – 41 \\[1em]
&= 9
\end{aligned}
$$

📂 Flashcards: Revising BIDMAS

🍪 Quiz: Test Your BIDMAS Skills

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