This document provides an overview of key concepts for working with fractions including: equivalent fractions, cancelling fractions, top heavy fractions and mixed numbers, ordering fractions, finding fractions, writing quantities as fractions, and performing addition, subtraction, multiplication, and division of fractions. Examples are provided to demonstrate how to convert between fraction forms, find common denominators, and simplify fractional expressions.

1. Fractions
1 March 2014
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2. 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
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3. What are Fractions ?
 Parts
1
2
 Eg.
2
3
1
2
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of a whole
3
4
2
3
6
7
Numerator
Denominator
1 1 1 1
3 4 5 50
Unit Fractions
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4. 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
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5. Equivalent Fractions
1
2
=
2
4
3
4
=
12
16
x2
1
2
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=
x2
2
4
x4
3
4
12
= 16
x4
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6. Equivalent Fractions
5
8
x4
x3
= 32
20
x4
7
12
21
= 36
x3
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7. 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
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÷5
=
÷5
1
2
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8. Cancelling Fractions
 Cancel
 HCF
=3
 So,
12
15
÷3
=
÷3
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16
36
12
15
HCF = 4
4
5
16
36
÷4
=
÷4
4
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9. Top Heavy Fractions & Mixed Numbers
2
7
3
1
3
 Convert
12
5
into a mixed number
1
1
+
 12
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+
2
5
=
2
2
5
2
÷ 5 = 2 with 5 left over
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10. 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
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11. Top Heavy Fractions & Mixed
Numbers
 Convert
 So
 Try

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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
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12. 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)
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13. Ordering Fractions
3
5
=
 Now
24
40
11
20
=
22
40
24
40
25
40
then answer the question
11
20
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=
25
40
put them in order …
22
40
 So,
5
8
3
5
5
8
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14. 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
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2 50
4 100
yes,
÷ 157
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15. 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
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16. 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
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=
1
5
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17. Adding Fractions
 Denominators
 Eg.
1
5
+
must be the same
3
5
=
4
5
 Convert
to equivalent fractions with
same denominator, if necessary
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18. 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
=
=
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19. Subtracting Fractions
 Subtraction
 Eg.
3
5
works the same
−
1
5
=
2
5
 Convert
to equivalent fractions with
same denominator, if necessary
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20. 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
=
=
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21. 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

22. 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
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23. 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
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24. +, -, x and ÷ Fractions
 Always
…
 Give your answer in its simplest form
 Use mixed numbers where relevant
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25. 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
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