# Fractions & Percentages 14/08/2015 1 14 August 2015.

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Fractions & Percentages 14/08/2015 1 14 August 2015

Contents Fractions – the Language of Equivalent Fractions and Cancelling Fractions Top Heavy Fractions and Mixed Numbers Ordering Fractions Finding a Fraction 14/08/2015 2

What are Fractions ? Parts of a whole Eg. Numerator Denominator Unit Fractions 14/08/2015 3

Fractions What do they mean … We have 1 of those parts The whole is split into 2 parts We have 3 of those parts The whole is split into 4 parts 14/08/2015 4

Equivalent Fractions 14/08/2015 5 12 x 2 x 4

Equivalent Fractions 6 x 4 x 3 20 36

Cancelling Fractions Reducing fractions to their simplest form Equivalent fractions using the smallest numbers Reduce to simplest form Find HCF of 5 and 10 So divide both numerator & denominator by 5 14/08/2015 7 5 ÷ 5

Cancelling Fractions Cancel HCF = 3HCF = 4 So, 14/08/2015 ÷ 3 ÷ 4

Top Heavy Fractions & Mixed Numbers Convert into a mixed number 1 + 1 + = 12 ÷ 5 = 2 with left over 14/08/2015 9

Top Heavy Fractions & Mixed Numbers Convert into a mixed number 26 ÷ 3 = 8, with left over, so Convert into a top heavy fraction How many fifths 14/08/2015 10

Top Heavy Fractions & Mixed Numbers Convert into a top heavy fraction So == Try == 14/08/2015 11

Ordering Fractions Easy !! But what about ….. Convert to equivalent fractions with same denominator first Find LCM of 5, 8 and 20 (denominators) 14/08/2015 12 40

Ordering Fractions Now put them in order … So, then answer the question 14/08/2015 13

Finding a Fraction What is of £50 ? What about of £100 ? To find ÷ 5 To find ÷ 25 How would we find 14/08/2015 14 yes, ÷ 157

Finding a Fraction What about of £125 ? Find first – Then, x by 2 So, of £125 is £50 14/08/2015 15 25 x 2 50

Contents - Percentages What are Percentages ? Converting between Fractions and Percentages Finding a Percentage 14/08/2015 16

What are Percentages ? They are just like fractions The whole is always split into 100 parts So 35% means 35 out of the 100 parts 14/08/2015 17

Converting between F, D & P Converting a percentage to a fraction 40% means 40 out of every 100 Don’t forget to cancel down, if possible

Converting between F, D & P Converting a fraction to a percentage You need to find the equivalent fraction which has 100 as the denominator ___ 100 x 20 60 So 60%

Finding a Percentage - Remember, 10% = To find we  by 10 Without a Calculator

Finding a Percentage - Use this info to find any percentage i.e. Find 30% of £240 10% = £24 So, 30% = 3 x £24 = £72 30% = £72.00 Without a Calculator

Finding a Percentage - 45% of 120 children at the theatre were boys, how many were boys ? 10% = 12 so 5% = 6 ( half of 10% ) So, 40% = 4 x 12 = 48 and 5% = 6 45% = 48 + 6 = 54 boys Without a Calculator

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