# Fractions

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Education

Published on March 1, 2014

Author: hjkirankumar

Source: slideshare.net

## Description

All you have to know about basics of fractions

Fractions 1 March 2014 01/03/14 1

Contents  Fractions – the Language of  Equivalent Fractions and Cancelling Fractions  Top Heavy Fractions and Mixed Numbers  Ordering Fractions  Finding a Fraction  Writing as a Fraction  +, -, x and ÷ Fractions 01/03/14 2

What are Fractions ?  Parts 1 2  Eg. 2 3 1 2 01/03/14 of a whole 3 4 2 3 6 7 Numerator Denominator 1 1 1 1 3 4 5 50 Unit Fractions 3

Fractions  What 1 2 do they mean … We have 1 of those parts The whole is split into 2 parts 3 4 We have 3 of those parts The whole is split into 4 parts 01/03/14 4

Equivalent Fractions 1 2 = 2 4 3 4 = 12 16 x2 1 2 01/03/14 = x2 2 4 x4 3 4 12 = 16 x4 5

Equivalent Fractions 5 8 x4 x3 = 32 20 x4 7 12 21 = 36 x3 6

Cancelling Fractions  Reducing fractions to their simplest form  Equivalent fractions using the smallest numbers 5  Reduce 10 to simplest form  Find HCF of 5 and 10 5  So divide both numerator & denominator by 5 5 10 01/03/14 ÷5 = ÷5 1 2 7

Cancelling Fractions  Cancel  HCF =3  So, 12 15 ÷3 = ÷3 01/03/14 16 36 12 15 HCF = 4 4 5 16 36 ÷4 = ÷4 4 9

Top Heavy Fractions & Mixed Numbers 2 7 3 1 3  Convert 12 5 into a mixed number 1 1 +  12 01/03/14 + 2 5 = 2 2 5 2 ÷ 5 = 2 with 5 left over 9

Top Heavy Fractions & Mixed Numbers  Convert  26 26 into a mixed number 3 ÷ 3 = 8, with 2 left over, so 3 8 2 3 3 3 into a top heavy fraction 5 18 5  How many fifths  Convert 01/03/14 10

Top Heavy Fractions & Mixed Numbers  Convert  So  Try  01/03/14 3 3 3 5 into a top heavy fraction 3 = ( 3 x 5 )+ 3 5 5 3 1 3 (3x 3 )+ 1 10 = 3 3 18 = 5 5 3 7 (5x7) + 3 38 = 7 7 11

Ordering Fractions 1 5  But 3 5 4 5 2 5 3 5 Easy !! what about ….. 5 8 11 20  Convert to equivalent fractions with same denominator first 40  Find LCM of 5, 8 and 20 (denominators) 01/03/14 12

Ordering Fractions 3 5 =  Now 24 40 11 20 = 22 40 24 40 25 40 then answer the question 11 20 01/03/14 = 25 40 put them in order … 22 40  So, 5 8 3 5 5 8 13

Finding a Fraction  What is 1  What about 1 of £100 ? 2 1  To find 5  To find 1 25 of £50 ? 4 ÷5 ÷ 25 1  How would we find 157 01/03/14 2 50 4 100 yes, ÷ 157 14

Finding a Fraction  What about 2 of £125 ? 5 1  Find 5 first – 25 5 125  Then, x by 2  So, 2 25 x2 50 of £125 is £50 5 01/03/14 15

Writing as a Fraction  Write the fraction in the following form: Number of Values that Meet Your Requirement Total Number of Values  and then cancel down to simplest form.  Eg. Out of 200 road accidents, 40 involved pedestrians, what fraction is this ? 40 200 01/03/14 = 1 5 16

Adding Fractions  Denominators  Eg. 1 5 + must be the same 3 5 = 4 5  Convert to equivalent fractions with same denominator, if necessary 01/03/14 17

Adding Fractions  Different 1 5 + denominators ? Convert … 3 4 = Remember LCM ?  Find LCM of 5 and 4 (denominators) 20  Convert fractions - 20 as denominator 1 4 5 20 19 15 4 + 20 = 3 15 20 20 4 20 = = 01/03/14 18

Subtracting Fractions  Subtraction  Eg. 3 5 works the same − 1 5 = 2 5  Convert to equivalent fractions with same denominator, if necessary 01/03/14 19

Subtracting Fractions  Different 1 2 − denominators – convert … 2 5 = LCM of 2 and 5 (denominators) 10  Convert fractions - 10 as denominator 5 1 2 10 1 5 4 − 10 = 2 4 10 10 5 10  Find = = 01/03/14 20

Adding & Subtracting Fractions  Use the following steps, where relevant  Convert to top heavy fractions  Convert to equivalent fractions with same denominator  Add or subtract the numerators  Cancel down to simplest terms  Convert back to mixed number

Multiplying Fractions  Easy, convert to top heavy fraction first  Multiply across top and multiply across bottom  Eg. 2 1 2 3 × 1 2 = 6 = 3  Remember to cancel to lowest terms or convert back to a mixed number 01/03/14 22

Dividing Fractions  Just as easy ! Again, convert to top heavy fractions first, if necessary.  Rule:- Turn the 2nd fraction upside down and then multiply 2 5 ÷ 3 8 = 2 5 × 8 3 = 16 15 = 1 1 15  Answers must be in their simplest form and as mixed numbers if appropriate 01/03/14 23

+, -, x and ÷ Fractions  Always …  Give your answer in its simplest form  Use mixed numbers where relevant 01/03/14 24

Session Summary  Fractions – the Language of  Equivalent Fractions and Cancelling Fractions  Top Heavy Fractions and Mixed Numbers  Ordering Fractions  Finding a Fraction  Writing as a Fraction  +, -, x and ÷ Fractions 01/03/14 25

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