1.4.5
Reciprocals
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Reciprocals
To find the reciprocal of a non-zero number x$$, calculate $$\dfrac{1}{x}
Example 1
- Find the reciprocal of 2
- Use the fact that the reciprocal is \dfrac{1}{x}$$ and substitute $$x = 2
Example 2
- Find the reciprocal of
- Use the fact that the reciprocal is \dfrac{1}{x}$$ and substitute $$x = \dfrac{1}{4}
Example 3
- Find the reciprocal of
- Use the fact that the reciprocal is \dfrac{1}{x}$$ and substitute $$x = \dfrac{2}{5}
1Number
1.1Place Value & Ordering
1.2Numerical Operations
1.2.1Adding Integers1.2.2Subtracting Integers1.2.3Multiplying Integers1.2.4Dividing Integers1.2.5Adding & Subtracting Decimals1.2.6Multiplying Decimals1.2.7Dividing Decimals1.2.8Adding & Subtracting Negative Numbers1.2.9Multiplying & Dividing Negative Numbers1.2.10Multiplying by Powers of Ten1.2.11Dividing by Powers of Ten
1.3Fractions
1.4Numerical Operations on Fractions
1.5Roots & Powers
1.6Structure of Calculations
1.7Numerical Skills
1.8Factors & Multiples
1.9Systematic Listing
1.10Surds
1.11Standard Form
1.11.1Converting to Standard Form (Positive Powers)1.11.2Converting to Standard Form (Negative Powers)1.11.3Converting From Standard Form (Positive Powers)1.11.4Converting From Standard Form (Negative Powers)1.11.5Adding & Subtracting Standard Form1.11.6Multiplying & Dividing Standard Form1.11.7Standard Form on a Calculator
1.12Fractions, Decimals & Percentages
1.13Percentage Change
1.14Rounding & Estimation
1.15Bounds & Accuracy
2Algebra
2.1Algebraic Notation
2.2Substitution & Simplification
2.3Brackets
2.3.1Expanding Single Brackets2.3.2Expanding & Simplifying with Single Brackets2.3.3Expanding Double Brackets2.3.4Expanding Multiple Brackets2.3.5Factorising into One Bracket2.3.6Factorising Quadratics of the Form x^2 + bx + c2.3.7Factorising Quadratics - AC Method2.3.8Factorising Quadratics - Middle Term Method2.3.9Factorising the Difference of Two Squares2.3.10Completing the Square
2.4Algebraic Fractions
2.6Functions
2.7Solving Linear Equations
2.8Inequalities
2.9Solving Quadratic Equations
2.10Simultaneous Equations
2.12Sequences
2.14Linear Graphs
2.15Quadratic Graphs
2.16More Non-Linear Graphs
2.17Graph Transformations
3Ratio
3.1Unit Conversions
3.2Compound Units
3.3Ratio Fundamentals
3.4Advanced Ratio & Scale
3.5Proportion
3.6Algebraic Proportion
3.7Percentages & Growth
3.8Manipulating Ratios
3.9Percentage & Interest
4Geometry
4.1Area & Perimeter
4.2Properties of Shapes
4.3Angles
4.4Trigonometry
4.5Similarity & Congruence
4.6Circle Geometry
4.7Circle Theorems
4.93D Representations
4.10Surface Area
4.11Volume
4.13Transformations
4.14Scale Drawings
4.15Bearings
4.16Geometry Proof
4.17Introduction to Geometry
4.18Triangles & Quadrilaterals
4.19Transformations
4.20Measurements & Units
5Probability
5.1Single Events
5.2Combined Events
5.3Experimental Probability
5.4Counting Outcomes
5.5Conditional Probability
5.6Representing Probabilities
5.7Probability Calculations
6Statistics
6.1Averages & Range
6.2Bar Charts
6.3Scatter Graphs
6.4Histograms
6.5Frequency Polygons
6.6Cumulative Frequency
6.8Collecting & Presenting Data
Jump to other topics
1Number
1.1Place Value & Ordering
1.2Numerical Operations
1.2.1Adding Integers1.2.2Subtracting Integers1.2.3Multiplying Integers1.2.4Dividing Integers1.2.5Adding & Subtracting Decimals1.2.6Multiplying Decimals1.2.7Dividing Decimals1.2.8Adding & Subtracting Negative Numbers1.2.9Multiplying & Dividing Negative Numbers1.2.10Multiplying by Powers of Ten1.2.11Dividing by Powers of Ten
1.3Fractions
1.4Numerical Operations on Fractions
1.5Roots & Powers
1.6Structure of Calculations
1.7Numerical Skills
1.8Factors & Multiples
1.9Systematic Listing
1.10Surds
1.11Standard Form
1.11.1Converting to Standard Form (Positive Powers)1.11.2Converting to Standard Form (Negative Powers)1.11.3Converting From Standard Form (Positive Powers)1.11.4Converting From Standard Form (Negative Powers)1.11.5Adding & Subtracting Standard Form1.11.6Multiplying & Dividing Standard Form1.11.7Standard Form on a Calculator
1.12Fractions, Decimals & Percentages
1.13Percentage Change
1.14Rounding & Estimation
1.15Bounds & Accuracy
2Algebra
2.1Algebraic Notation
2.2Substitution & Simplification
2.3Brackets
2.3.1Expanding Single Brackets2.3.2Expanding & Simplifying with Single Brackets2.3.3Expanding Double Brackets2.3.4Expanding Multiple Brackets2.3.5Factorising into One Bracket2.3.6Factorising Quadratics of the Form x^2 + bx + c2.3.7Factorising Quadratics - AC Method2.3.8Factorising Quadratics - Middle Term Method2.3.9Factorising the Difference of Two Squares2.3.10Completing the Square
2.4Algebraic Fractions
2.6Functions
2.7Solving Linear Equations
2.8Inequalities
2.9Solving Quadratic Equations
2.10Simultaneous Equations
2.12Sequences
2.14Linear Graphs
2.15Quadratic Graphs
2.16More Non-Linear Graphs
2.17Graph Transformations
3Ratio
3.1Unit Conversions
3.2Compound Units
3.3Ratio Fundamentals
3.4Advanced Ratio & Scale
3.5Proportion
3.6Algebraic Proportion
3.7Percentages & Growth
3.8Manipulating Ratios
3.9Percentage & Interest
4Geometry
4.1Area & Perimeter
4.2Properties of Shapes
4.3Angles
4.4Trigonometry
4.5Similarity & Congruence
4.6Circle Geometry
4.7Circle Theorems
4.93D Representations
4.10Surface Area
4.11Volume
4.13Transformations
4.14Scale Drawings
4.15Bearings
4.16Geometry Proof
4.17Introduction to Geometry
4.18Triangles & Quadrilaterals
4.19Transformations
4.20Measurements & Units
5Probability
5.1Single Events
5.2Combined Events
5.3Experimental Probability
5.4Counting Outcomes
5.5Conditional Probability
5.6Representing Probabilities
5.7Probability Calculations
6Statistics
6.1Averages & Range
6.2Bar Charts
6.3Scatter Graphs
6.4Histograms
6.5Frequency Polygons
6.6Cumulative Frequency
6.8Collecting & Presenting Data
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