Using Fractions

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Adding and Subtracting Fractions

When we add or subtract fractions, we must make sure the denominator of both fractions is the same.

Same denominator

If the denominator of both fractions is already the same we simply add or subtract the numerators.

Same denominator 2

If the denominator of both fractions is already the same we simply add or subtract the numerators.

Different denominators

If the denominators are not the same we need to make them the same using an equivalent fraction.

Different denominators 2

When finding an equivalent fraction we must multiply or divide both the top and bottom row by the same amount.

Different denominators 3

Once both the fractions have the same denominator we can add or subtract the numerators.

$What is $$\frac{3}{4} - \frac{1}{5}$$?$

What is $\frac{3}{4} - \frac{1}{5}$ ?

We cannot do the subtraction straight away because the fractions do not have the same denominator.

$What is $$\frac{3}{4} - \frac{1}{5}$$?$

What is $\frac{3}{4} - \frac{1}{5}$ ?

Using equivalent fractions, convert the fraction so that they have the same denominator.

$What is $$\frac{3}{4} - \frac{1}{5}$$?$

What is $\frac{3}{4} - \frac{1}{5}$ ?

Once both the fractions have the same denominator we can add or subtract the numerators.

Multiplying and Dividing Fractions

When we multiply or divide fractions, we do NOT have to make sure the denominator of both fractions is the same.

$Multiplying fractions$

Multiplying fractions

To multiply two fractions we multiply the two numerators and multiply the two denominators.

$Multiplying fractions 2$

Multiplying fractions 2

To multiply two fractions we multiply the two numerators and multiply the two denominators.

$Dividing fractions$

Dividing fractions

To divide one fraction by another, we first swap the numerator and denominator of the second fraction (the one we are dividing by).

$Dividing fractions 2$

Dividing fractions 2

Once we have swapped the numerator and denominator we multiply the two fractions together.

$What is $$\frac{3}{4} ÷ \frac{4}{7}$$?$

What is $\frac{3}{4} ÷ \frac{4}{7}$ ?

$What is $$\frac{3}{4} ÷ \frac{4}{7}$$?$

What is $\frac{3}{4} ÷ \frac{4}{7}$ ?

It is possible that when dividing fractions we end up with an improper fraction, such as $\frac{21}{16}$ .

Finding a Fraction of a Quantity

When finding a fraction of a quantity, we are effectively just multiplying fractions.

$What is $$\frac{2}{5}$$ of 90?$

What is $\frac{2}{5}$ of 90?

90 can be written as $\frac{90}{1}$ to make the multiplication easier.
- We multiply the two numerators and the two denominators.

$What is $$\frac{1}{6}$$ of 72?$

What is $\frac{1}{6}$ of 72?

Remember to write the starting amount as a fraction.

Numbers

1.1

Integers

1.1.1Integers 1.1.2Ordering Numbers 1.1.3The Four Rules of Operations 1.1.4Hierarchy of Operations 1.1.5Definitions & Terms 1.1.6HCF & LCM 1.1.7Standard Form 1.1.8Standard Form 2 1.1.9Prime Numbers 1.1.10End of Topic Test - Standard Form

1.2

Fractions

1.2.1Fractions 1.2.2Using Fractions 1.2.3Conversion 1.2.4Reciprocals

1.3

Decimals

1.3.1Decimals 1.3.2Decimals 2 1.3.3Exam-Style Questions - Recurring Decimals 1.3.4Comparing & Converting Decimals 1.3.5End of Topic Test - Fractions & Decimals

1.4

Powers & Roots

1.4.1Square Numbers 1.4.2Index Notation 1.4.3Exam-Style Questions - Index Notation 1.4.4Advanced Indices 1.4.5Surds 1.4.6End of Topic Test - Powers & Roots

1.5

Set Language & Notation

1.5.1Sets

1.6

Percentages

1.6.1Percentages 1.6.2Percentage Change 1.6.3Percentages in Finance 1.6.4Compound Interest

1.7

Ratio & Proportion

1.7.1Manipulating Ratios 1.7.2Proportion

1.8

Degree of Accuracy

1.8.1Rounding & Significant Figures 1.8.2Estimation 1.8.3Upper & Lower Bounds 1.8.4Limits of Accuracy 1.8.5Limits of Accuracy 2 1.8.6End of Topic Test - Rounding & Estimation

Equations, Formulae & Identities

2.1

Algebraic Manipulation

2.1.1Algebra Basics 2.1.2Power Rules & Collecting Terms 2.1.3Expanding Brackets 2.1.4Expanding Brackets 2 2.1.5Factorising Quadratics 2.1.6Algebraic Fractions 2.1.7Proofs 2.1.8End of Topic Test - Algebra & Proofs 2.1.9Exam-Style Questions - Algebraic Proof

2.2

Expressions & Formulae

2.2.1Rearranging Formulae 2.2.2Simple Formulae 2.2.3End of Topic Test - Algebra Manipulation & Formula

2.3

Linear Equations

2.3.1Solving Linear Equations 2.3.2Simultaneous Linear Equations

2.4

Quadratic Equations

2.4.1Solving Quadratics 2.4.2Solving Quadratics 2 2.4.3End of Topic Test - Solving Equations 2.4.4Simulateous Quadratic Equations 2.4.5Exam-Style Questions - Simultaneous Equations 2.4.6Graphs of Simultaneous Equations 2.4.7End of Topic Test - Simultaneous Equations

2.5

Proportion

2.5.1Graphs & Proportion

2.6

Inequalities

2.6.1Solving Inequalities 2.6.2Graphs of Inequalities 2.6.3Exam-Style Questions - Inequalities 2.6.4End of Topic Test - Inequalities

Sequences, Functions & Graphs

3.1

Sequences

3.1.1Sequence Rules 3.1.2Finding Terms 3.1.3Exam-Style Questions - Sequences 3.1.4End of Topic Test - Sequences

3.2

Functions

3.2.1Functions 3.2.2Composite & Inverse 3.2.3End of Topic Test - Functions

3.3

Graphs

3.3.1Plotting Graphs 3.3.2Straight Line Graphs 3.3.3Properties of Graphs 3.3.4Quadratic Graphs 3.3.5Practical Graphs 3.3.6Graphs of Polynomials 3.3.7End of Topic Test Graphs

3.4

Common Graphs

3.4.1Graphs of Common Functions 3.4.2Transformations of Graphs 3.4.3End of Topic Test - Transformations and Graph

3.5

Calculus

3.5.1Derivatives of Functions 3.5.2Maxima & Minima

Geometry

4.1

Angles, Lines & Triangles

4.1.1Angles & Lines 4.1.2Angle Rules 4.1.3Angles in Triangles 4.1.4Exam-Style Questions - Angles

4.2

Polygons

4.2.1Polygons 4.2.2Quadrilaterals 4.2.3Congruence 4.2.4Scale Factor 4.2.5Exam-Style Questions - Enlargements 4.2.6End of Topic Test - Geometry

4.3

Symmetry

4.3.1Symmetry 4.3.2Exam-Style Questions - Reflection

4.4

Measures

4.4.1Measurements 4.4.2Time 4.4.3Bearings 4.4.4Speed

4.5

Circle Properties

4.5.1Properties of a Circle 4.5.2Circle Theorems 4.5.3Circle Theorems 2 4.5.4Circle Theorems 3 4.5.5Exam-Style Questions - Circle Theorems

4.6

Trigonometry & Pythagoras’ theorem

4.6.1Pythagoras' Theorem 4.6.2Trigonometry 4.6.3Sine & Cosine for Obtuse Angles 4.6.4Triangle Formulae 4.6.5Exam-Style Questions - Trigonometry & Area

4.7

Mensuration of 2D Shapes

4.7.1Standard Units 4.7.2Perimeter of 2D Shapes 4.7.3Area of 2D Shapes 4.7.4Area & Circumference of Circle 4.7.5End of Topic Test - Trigonometry & Shapes

4.8

3D Shapes & Volume

4.8.13D Shapes 4.8.2Surface Area 4.8.3Volume 4.8.4Exam-Style Questions - Volume

Vectors & Transformation Geometry

5.1

Vectors

5.1.1Vectors 5.1.2Vectors 2 5.1.3Exam-Style Questions - Vectors

5.2

Transformation Geometry

5.2.1Transformations 5.2.2Rotations 5.2.3Translations & Reflections 5.2.4Enlargements 5.2.5Effects of Transformations

Statistics & Probability

6.1

Statistical Measures

6.1.1Basic Statistics 6.1.2Frequency Table

6.2

Graphical Representation of Data

6.2.1Pictograms, Bar Charts & Pie Charts 6.2.2Histograms 6.2.3Cumulative Frequency 6.2.4Cumulative Frequency 2 6.2.5Exam-Style Questions - Cumulative Frequency 6.2.6End of Topic - Datasets

6.3

Probability

6.3.1Probability 6.3.2Theoretical Probability 6.3.3Experimental Probability 6.3.4Venn Diagrams 6.3.5Sample Space Diagrams 6.3.6Tree Diagrams 6.3.7Independent Events 6.3.8Conditional Probability 6.3.9End of Topic Test - Probability 6.3.10Exam-Style Questions - Probability

Jump to other topics

Numbers

1.1

Integers

1.2

Fractions

1.2.1Fractions 1.2.2Using Fractions 1.2.3Conversion 1.2.4Reciprocals

1.3

Decimals

1.3.1Decimals 1.3.2Decimals 2 1.3.3Exam-Style Questions - Recurring Decimals 1.3.4Comparing & Converting Decimals 1.3.5End of Topic Test - Fractions & Decimals

1.4

Powers & Roots

1.4.1Square Numbers 1.4.2Index Notation 1.4.3Exam-Style Questions - Index Notation 1.4.4Advanced Indices 1.4.5Surds 1.4.6End of Topic Test - Powers & Roots

1.5

Set Language & Notation

1.5.1Sets

1.6

Percentages

1.6.1Percentages 1.6.2Percentage Change 1.6.3Percentages in Finance 1.6.4Compound Interest

1.7

Ratio & Proportion

1.7.1Manipulating Ratios 1.7.2Proportion

1.8

Degree of Accuracy

1.8.1Rounding & Significant Figures 1.8.2Estimation 1.8.3Upper & Lower Bounds 1.8.4Limits of Accuracy 1.8.5Limits of Accuracy 2 1.8.6End of Topic Test - Rounding & Estimation

Equations, Formulae & Identities

2.1

Algebraic Manipulation

2.2

Expressions & Formulae

2.2.1Rearranging Formulae 2.2.2Simple Formulae 2.2.3End of Topic Test - Algebra Manipulation & Formula

2.3

Linear Equations

2.3.1Solving Linear Equations 2.3.2Simultaneous Linear Equations

2.4

Quadratic Equations

2.5

Proportion

2.5.1Graphs & Proportion

2.6

Inequalities

2.6.1Solving Inequalities 2.6.2Graphs of Inequalities 2.6.3Exam-Style Questions - Inequalities 2.6.4End of Topic Test - Inequalities

Sequences, Functions & Graphs

3.1

Sequences

3.1.1Sequence Rules 3.1.2Finding Terms 3.1.3Exam-Style Questions - Sequences 3.1.4End of Topic Test - Sequences

3.2

Functions

3.2.1Functions 3.2.2Composite & Inverse 3.2.3End of Topic Test - Functions

3.3

Graphs

3.3.1Plotting Graphs 3.3.2Straight Line Graphs 3.3.3Properties of Graphs 3.3.4Quadratic Graphs 3.3.5Practical Graphs 3.3.6Graphs of Polynomials 3.3.7End of Topic Test Graphs

3.4

Common Graphs

3.4.1Graphs of Common Functions 3.4.2Transformations of Graphs 3.4.3End of Topic Test - Transformations and Graph

3.5

Calculus

3.5.1Derivatives of Functions 3.5.2Maxima & Minima

Geometry

4.1

Angles, Lines & Triangles

4.1.1Angles & Lines 4.1.2Angle Rules 4.1.3Angles in Triangles 4.1.4Exam-Style Questions - Angles

4.2

Polygons

4.2.1Polygons 4.2.2Quadrilaterals 4.2.3Congruence 4.2.4Scale Factor 4.2.5Exam-Style Questions - Enlargements 4.2.6End of Topic Test - Geometry

4.3

Symmetry

4.3.1Symmetry 4.3.2Exam-Style Questions - Reflection

4.4

Measures

4.4.1Measurements 4.4.2Time 4.4.3Bearings 4.4.4Speed

4.5

Circle Properties

4.5.1Properties of a Circle 4.5.2Circle Theorems 4.5.3Circle Theorems 2 4.5.4Circle Theorems 3 4.5.5Exam-Style Questions - Circle Theorems

4.6

Trigonometry & Pythagoras’ theorem

4.6.1Pythagoras' Theorem 4.6.2Trigonometry 4.6.3Sine & Cosine for Obtuse Angles 4.6.4Triangle Formulae 4.6.5Exam-Style Questions - Trigonometry & Area

4.7

Mensuration of 2D Shapes

4.7.1Standard Units 4.7.2Perimeter of 2D Shapes 4.7.3Area of 2D Shapes 4.7.4Area & Circumference of Circle 4.7.5End of Topic Test - Trigonometry & Shapes

4.8

3D Shapes & Volume

4.8.13D Shapes 4.8.2Surface Area 4.8.3Volume 4.8.4Exam-Style Questions - Volume

Vectors & Transformation Geometry

5.1

Vectors

5.1.1Vectors 5.1.2Vectors 2 5.1.3Exam-Style Questions - Vectors

5.2

Transformation Geometry

5.2.1Transformations 5.2.2Rotations 5.2.3Translations & Reflections 5.2.4Enlargements 5.2.5Effects of Transformations

Statistics & Probability

6.1

Statistical Measures

6.1.1Basic Statistics 6.1.2Frequency Table

6.2

Graphical Representation of Data

6.2.1Pictograms, Bar Charts & Pie Charts 6.2.2Histograms 6.2.3Cumulative Frequency 6.2.4Cumulative Frequency 2 6.2.5Exam-Style Questions - Cumulative Frequency 6.2.6End of Topic - Datasets

6.3

Probability

Practice questions on Using Fractions

Can you answer these? Test yourself with free interactive practice on Seneca — used by over 10 million students.

1
What is $$\frac{7}{10} - \frac{1}{5}$$?Multiple choice
2
What is $$\frac{4}{9} + \frac{1}{6}$$?Multiple choice
3
Which of the following additions or subtractions of fractions are correct?True / false
4
What is $$\frac{5}{6} × \frac{4}{7}$$?Multiple choice
5
Which of the following multiplications are correct?True / false

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