Order Of Operations Bidmas Quizzes

Introduction

The order of operations, often remembered by the acronym BIDMAS (Brackets, Indices, Division/Multiplication, Addition, Subtraction), is a fundamental concept in GCSE Maths. It tells us the correct sequence to perform operations in a calculation to get the right answer. Without following BIDMAS, the same expression can produce different answers.

For example, $$2 + 3 × 4$$ equals 14 if we follow BIDMAS (multiply first, then add), but 20 if we add first (incorrect). Understanding BIDMAS ensures accuracy in calculations involving multiple operations, algebra, fractions, decimals, and directed numbers.

Core Concepts

The BIDMAS Acronym

• B - Brackets: Solve anything inside brackets first.
• I - Indices: Powers and roots (e.g., $$3^2, \sqrt{16}$$).
• D/M - Division and Multiplication: Perform from left to right.
• A/S - Addition and Subtraction: Perform from left to right.

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Brackets

Brackets indicate that the operations inside must be done first. Types include:

• Parentheses: ( )
• Square brackets: [ ]
• Curly braces: { }

Example:

$$ (2 + 3) × 4 $$

Step 1: Solve inside brackets: 2 + 3 = 5

Step 2: Multiply: 5 × 4 = 20

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Indices

Indices include powers and roots. Always calculate powers before division, multiplication, addition, or subtraction.

• Example: $$3^2 + 4 = 9 + 4 = 13$$
• Example: $$2 × 5^2 = 2 × 25 = 50$$

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Division and Multiplication

These are performed from left to right. Multiplication and division are of equal priority.

Example:

$$20 ÷ 4 × 3$$

Step 1: Divide first (from left): 20 ÷ 4 = 5

Step 2: Multiply: 5 × 3 = 15

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Addition and Subtraction

Performed from left to right, after brackets, indices, division, and multiplication.

Example:

$$10 - 4 + 2$$

Step 1: Left to right: 10 - 4 = 6

Step 2: Add 2: 6 + 2 = 8

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Combining All Operations

When multiple operations are present, always follow BIDMAS strictly:

Example:

$$ 5 + (3 × 2)^2 - 8 ÷ 4 $$

• Step 1: Brackets: 3 × 2 = 6
• Step 2: Indices: 6^2 = 36
• Step 3: Division: 8 ÷ 4 = 2
• Step 4: Addition/Subtraction from left: 5 + 36 - 2 = 39

Answer: $$39$$

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Nested Brackets

For brackets within brackets, start from the innermost bracket and work outward.

Example:

$$ [2 + (3 × 4)]^2 $$

• Innermost bracket: 3 × 4 = 12
• Next bracket: 2 + 12 = 14
• Indices: 14^2 = 196

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Directed Numbers in BIDMAS

When calculations involve positive and negative numbers, apply BIDMAS carefully and watch signs:

Example:

$$ -3 + 5 × (-2) $$

• Step 1: Multiplication: 5 × -2 = -10
• Step 2: Addition: -3 + (-10) = -13

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Fractions and Decimals in BIDMAS

Operations with fractions and decimals follow the same order. Always convert fractions to a common denominator if adding/subtracting:

Example:

$$ \frac{1}{2} + \frac{3}{4} × 2 $$

• Step 1: Multiplication first: $$\frac{3}{4} × 2 = \frac{6}{4} = 1.5$$
• Step 2: Addition: $$\frac{1}{2} + 1.5 = 0.5 + 1.5 = 2$$

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Worked Examples

Example 1 (Foundation): Simple BIDMAS

Calculate $$2 + 3 × 4$$

Step 1: Multiplication first: 3 × 4 = 12

Step 2: Add 2: 2 + 12 = 14

Answer: $$14$$

Example 2 (Foundation): Brackets and indices

Calculate $$ (2 + 3)^2 $$

Step 1: Brackets: 2 + 3 = 5

Step 2: Indices: 5^2 = 25

Answer: $$25$$

Example 3 (Higher): Mixed operations

Calculate $$ 5 + 6 × 2^2 - 8 ÷ 4 $$

• Step 1: Indices: 2^2 = 4 → 6 × 4
• Step 2: Multiplication: 6 × 4 = 24
• Step 3: Division: 8 ÷ 4 = 2
• Step 4: Addition/Subtraction: 5 + 24 - 2 = 27

Answer: $$27$$

Example 4 (Higher): Nested brackets

Calculate $$ [3 + (2 × 4)]^2 - 5 $$

• Step 1: Innermost bracket: 2 × 4 = 8
• Step 2: Next bracket: 3 + 8 = 11
• Step 3: Indices: 11^2 = 121
• Step 4: Subtract 5: 121 - 5 = 116

Answer: $$116$$

Example 5 (Higher): Directed numbers

Calculate $$ -4 + 3 × (-2) $$

• Step 1: Multiplication: 3 × -2 = -6
• Step 2: Addition: -4 + (-6) = -10

Example 6 (Higher): Fractions and BIDMAS

Calculate $$ \frac{2}{3} + \frac{1}{2} × 6 $$

• Step 1: Multiplication: 1/2 × 6 = 3
• Step 2: Addition: 2/3 + 3 = 3 + 0.666… ≈ 3.666

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Common Mistakes

• Ignoring BIDMAS and calculating from left to right
• Not handling brackets correctly
• Forgetting the order of indices before multiplication/division
• Incorrect signs with directed numbers
• Adding or subtracting fractions/decimals before multiplication or division

Tips to avoid errors:

• Always identify brackets first and solve inside them
• Handle indices before multiplication or division
• Perform multiplication and division from left to right
• Perform addition and subtraction last, from left to right
• Double-check negative numbers and fractions

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Applications

• Algebra: Simplifying expressions with multiple operations
• Directed numbers: Bank balances, temperature changes
• Fractions and decimals in BIDMAS: Science, finance, and engineering calculations
• Exam questions often test multi-step BIDMAS problems

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Strategies & Tips

• Memorize BIDMAS order and follow strictly
• Use parentheses to clarify complex calculations
• Work left to right for multiplication/division and addition/subtraction
• Practice with integers, fractions, decimals, and directed numbers
• Check your answer using estimation

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Summary / Call-to-Action

BIDMAS is essential to perform accurate calculations in GCSE Maths. Mastery of brackets, indices, division, multiplication, addition, and subtraction ensures correct results for complex expressions. Always apply BIDMAS, handle negative numbers carefully, and practice multi-step calculations regularly.

Next Steps:

• Attempt quizzes on BIDMAS to reinforce learning
• Practice multi-step calculations with brackets, indices, fractions, and directed numbers
• Apply BIDMAS rules to real-life problems and algebraic expressions
• Challenge yourself with nested brackets and mixed operations for higher-level practice

Consistent practice will build confidence and accuracy in all areas of GCSE Maths involving the order of operations.