GCSE Maths

Numbers
32 Topics | 2 Quizzes
Integers
Integers Quiz
Prime Numbers and Composite Numbers
Positive and Negative Numbers
Order of Operations
Square Numbers and Cube Numbers
The Laws of Indices
Square Roots and Cube Roots
Triangular Numbers
The Fibonacci Sequence
Factors
Multiples
The Highest Common Factor
Fractions
Adding and Subtracting Fractions
Multiplication of Fractions
Division of Fractions
Fractional Indices
Decimal Places
Fractions and Decimals
Expressing Fractions as Decimal Numbers
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Algebra
29 Topics | 1 Quiz
Algebraic Notation
Algebraic Vocabulary
Collecting Like Terms
Substituting Values into Formulae
Rearranging Equations
Algebraic Fractions
Expanding Brackets and Simplifying
Expanding Double Brackets
Factorisation
Factorising Quadratic Expressions
Factorising Quadratics with a Coefficient of x Squared Greater than 1
The Quadratic Formula
The Difference of Two Squares
Subject of Formula
Solving Linear Equations
Quadratic Equations
Completing the Square
Sequences and Nth Term
Arithmetic and Geometric Sequences
Quadratic Sequences
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Ratio, Proportion and Rates of Change
7 Topics
Ratios
Scaling Ratios
Direct Proportion
Inverse Proportion
Reverse Percentages
Units and Conversions
Scale Factors
Geometry and Measures
16 Topics | 3 Quizzes
2D Shapes
2D Shapes Quiz
3D Shapes
3D Shapes Quiz
Types of angles
Angle Properties
Angle in Parallel Lines
Triangles
Triangles Quiz
Angles in Triangles
Polygons
Lines of Symmetry
Bearings
Loci and constructions
Constructing Triangles
Transformations
Enlargement
Plans and elevations
Areas and Volumes in Map Scale Problems
Probability
10 Topics
Introduction to Probability
Relative Frequency
Sample Space
Probability of Single Events
Probability of Combined Events
Probability Trees
Conditional probability
Set Notation
Venn diagrams
The Complement of a Set
Statistics
2 Topics
Population and samples
Representing data
Vectors
Mensuration and Calculation
7 Topics
Area
Volume
Congruence and similarity
Pythagoras’ theorem
Sine and cosine rule
Area of a triangle
Standard units of measure
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Order of Operations

GCSE Maths Numbers Order of Operations

To evaluate expressions with multiple operations, we need to perform these operations in the correct order. The order of operations can be remembered using the acronym BIDMAS:

Brackets, Indices, Division and Multiplication, Addition and Subtraction.

Let’s look at an expression:

2+3\times 4-3^{2}+25\div 5+(2^{2}-1)\times 2

To evaluate this expression, we’ll follow the BIDMAS rule:

1. Brackets: (2^{2}-1), which gives us 4-1=3

2. Indices: 3^{2}, which is 9

3. Division: 25\div 5, which is 5

4. Multiplication: 3\times 4=12 and 3\times 2=6

5. Addition: 2+12+5+6=25

6. Subtraction: 25-9=16

Therefore, 2+3\times 4+3^{2}+25\div 5+(2^{2}-1)\times 2=16

Let’s look at some more examples.

Examples

Example 1:

Evaluate the following expressions:

a) 36-(5+(3^{2}-2)\times 3)\div 13

b) (54\div 9\times 3-10)^{2}+15

a) 36-(5+(3^{2}-2)\times 3)\div 13=36-(5+7\times 3)\div 13

=36-26\div 13

=36-2

=34

b) (54\div 9\times 3-10)^{2}+15=(6\times 3-10)^{2}+15

=(18-10)^{2}+15

=8^{2}+15

=64+15

=79

Example 2:

Find the value of 6+8\times 9\div 3

6+8\times 9\div 3=6+8\times 3, since 9\div 3=3 is done first.

=6+24

=30

Example 3:

Find the value of \frac {1}{1+\frac {2}{3}}

First, 1+\frac {2}{3} =\frac {3}{3} +\frac {2}{3} =\frac {5}{3}

Next, \frac{1}{1+\frac{2}{3}} = \frac{1}{\frac{5}{3}}

To simplify, multiply the numerator and denominator by 3: \frac{1 \times 3}{\frac{5}{3} \times 3} = \frac{3}{5}

Example 4:

Evaluate the expression, giving your answer as simple as possible:

1+2^{2}-1\times 3+(4^{2}\div 2\times 3)

First, evaluate the power: 4^{2}=16

Next, perform the division and multiplication: 16\div 2\times 3=8\times 3=24

Now, simplify the expression: 1+2^{2}-1\times 3+24=1+4-1\times 3+24

=1+4-3+24

=26

Example 5:

Evaluate { (2^{2}-3) }^{100}-({ 2^{3}-7) }^{200}

({ (2^{2}-3) }^{100}-({ 2^{3}-7) }^{200})=({ 1 }^{100}-({ 1 }^{200})

=1-1

=0

Example 6:

When there are more brackets within brackets, perform the innermost brackets first and move outwards. For example, to evaluate:

2+5-(2^{2}+(6^{3}\div 12))^{2}\times 3

1. First, evaluate the innermost bracket: 6^{3}\div 12=216\div 12=18

2. Now, the expression becomes: 2+5-(2^{2}+18)^{2}\times 3

3. Evaluate the power: 2^{2}=4

4. Simplify the expression within the bracket: 4+18=22

5. The expression becomes: 2+5-(22)^{2}\times 3

6. Evaluate the power: (22)^{2}=484

7. Finally, simplify the expression: 2+5-484\times 3=7-1452

8. The result is: -1445

Example 7:

Evaluate 3\times 5^{2}-12\div 4

1. First, evaluate the power: 5^{2}=25

2. Next, perform the division: 12\div 4=3

3. Now, simplify the expression with multiplication: 3\times 25=75

4. Finally, simplify the expression with subtraction: 75-3=72

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