Table of Contents

 

 Unit 1 | Algebra

Page 1 | Expressions and Formulae

Page 2 | Index notation

Page 3| Solving Linear Equations

Page 4| Expanding and Factorising

Page 5| Factorising Quadratics and expanding double brackets

Page 6| Patterns and Sequences

Page 7| Simultaneous Equations

Page 8| Changing the subject of a Formula

Page 9| Adding , subtracting algebraic formulas

 Unit 2 |Graphs

Page 1 | Straight line graphs

Page 2 | Graphs of Quadratic functions

Unit 3 |Geometry and Measure

Page 1 | Transformations

Page 2 | Symmetry

Page 3 | Coordinates

Page 4 | Perimeter, Area, Volume

Page 5 | Circle geometry

Page 6 | Measurement

Page 7 | Trigonometry

Page 8 | Pythagoras

Page 9 | Angles

Page 10 | Shapes

Page 11| Time

Page 12 | Locus

Unit 4 | Numbers

Page 1 | Speed, Distance and time

Page 2 | Rounding and estimating

Page 3 | Ratio and proportion

Page 4 | Factors, Multiples and primes

Page 5 | Powers and roots

Page 6 | Decimals

Page 7 | Positive and negative numbers

Page 8 | Basic operations

Page 9 | Fractions

Page 10 | Percentages

Unit 5 | Statistics and Probability

Page 1 | Sampling data (MA)

Page 2 | Recording and representing data

Page 3 | Mean median range and mode

Page 4 | Standard deviation

Unit 4 | Calculus

Equivalent Fractions


  1. Fractions represent a portion of the whole. Different fractions which represent an equal amount of the whole are called equivalent fractions.
  1. In order to find different equivalent fractions, we can multiply or divide both the numerator and denominator of the fractions we already have.
  1. For example, if we wanted to find an equivalent fraction of    , we could do this multiplying both numbers by two, which would give us   .

Example 1 :

Take a look at this cake. We can cut it into different numbers of slices and still represent one half.

In the first circle, we can show a half by taking one piece out of a possible two, so this is 

In the second circle, one half is shown by highlighting 2 pieces out of a possible four, so this is 

The third circle is    and the fourth circle is    .

As all of these fractions represent the same amount of space, we would say that they are equivalent fractions. We can see that the numerator and denominator of the first fraction    have been multiplied by 2, 3 and 4 to get the other fractions.

 

4. Equivalent fractions can come in very useful when we need to compare fractions that have different denominators.

5.If we can use equivalent fractions to make both fractions have the same denominator, all we have to do is compare the numerator.

Example 2 :

Let’s say that we need to find out whether   or  is larger .

  1. First, we need to find a number that both of the denominators are factors of (they fit into it a specific number of times). 8 and 12 both fit into 24 so we’ll choose that as our new denominator. 7
  1. Secondly, we need to find out what we need to multiply each fraction by so that it has a denominator of 24whatever we’ve done to each of our denominators has to also be done to the numerator.

  1. If we compare the two fractions, we can now clearly see that 6/8 must be bigger than 8/12, as the numerator is bigger when it is converted.

 

6. If you can see that the numerator and the denominator both have the same factor, you can divide them both by this factor, which is called cancelling.

7. Once a fraction cannot be cancelled anymore, it is said to be in its simplest form.

Example 3 :

The fraction we can use for our example is 

Both 36 and 42 are in the 6 times table, so we can cancel by a factor of six.

 

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“End  
procrastination.”

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