Fractions
(Did you know that one third of the letters in the word ‘Fractions’ are vowels)
Numerator
Denominator
(Number of parts you have)
(Number of parts in total)
For simple fractions you can tell how small it is by the size of the
denominator (the bigger the number the smaller the fraction)
http://www.taw.org.uk/demo/mathematics/shapes/fractionStrip.htm
If the numerator and denominator are the same you have one whole
http://www.topmarks.co.uk/Flash.aspx?f=WhatFractionv3
(choose the chocolate bar)
Find the fraction ……
1/10
1/10
1/10
1/10
1/10
1/10
1/10
1/10
¼
¼
¼
¼
1/10
1/21
1/21
1/21
1/21
1/21
1/21
1/21
1/21
1/21
1/21
1/21
1/21
1/21
1/21
1/21
1/21
1/21
1/21
1/21
1/21
1/21
1/10
1/6
1/6
1/6
1/6
1/6
1/6
1/12 1/12 1/12 1/12
1/18
1/18
1/18
1/18
1/18
1/18
1/12 1/12 1/12 1/12
1/18
1/18
1/18
1/18
1/18
1/18
1/12 1/12 1/12 1/12
1/18
1/18
1/18
1/18
1/18
1/18
Time for a game:
Fish Game, fraction and picture match:
http://www.iknowthat.com/com/L3?Area=F
ractionGame

Fraction of
E.g. 1
1
of 30 = 6
5
This means share
30 into 5 parts
6
(30
6

6
5 = 6)
6
6
E.g. 2
4
of 30 = 24
5
This means share 30
into 5 parts and find 4
of these parts
6
6

6
6
(30
5 = 6)
(4 x 6 = 24)
6
Find the answer to…
1
of 30 = 10
3
1
of 15 = 3
5
2
of 18 = 12
3
3
of 28 = 12
7
Time for a game…
Proper fraction of numbers easy (egg laying):
http://www.echalk.co.uk/tasters/taster2/taster.html
Equivalent Fractions
(Equal Fractions)
1/4
1/4
1/4
3
4
1/4
=
1/8
1/8
1/8
1/8
1/8
1/8
X2
X2
=
6
8
Multiply or divide numerator and denominator by
another number to find equivalent fractions
1/8
1/8
Find fractions equivalent to ….
½
1/3
½
1/3
1/3
1/4
1/4
1/4
1/4
1/5 1/5 1/5 1/5 1/5
Click mouse for hints
Time for a game:
Fish Game, equivalent fractions:
http://www.iknowthat.com/com/L3?Area=F
ractionGame
Simplify Fractions
(Cancel down)
1/4
1/4
1/4
2
4
1/4
1/2
=
1/2
1
2
To simplify fractions, divide numerator and denominator by the same
number. Repeat if necessary to find the simplest form.
2
4
2
=
2
1
2
Simplify the following …
1/4
½
1/4
1/8
1/8
¾
1/8
1/8
1/4
1/4
1/8
1/8
1/8
1/8
2/31/6
1/6
1/6
4/5
1/15 1/15 1/15 1/15 1/15
1/15 1/15 1/15 1/15 1/15
1/6
1/6
1/6
1/15 1/15 1/15 1/15 1/15
Time for a game:
Fish Game, simplest form:
http://www.iknowthat.com/com/L3?Area=F
ractionGame
Addition/Subtraction (easy)
(Common Denominator)
Khan: http://www.khanacademy.org/math/arithmetic/fractions/v/adding-fractions-with-like-denominators
1/7 1/7 1/7 1/7 1/7 1/7 1/7
+
2
1/7 1/7 1/7 1/7 1/7 1/7 1/7
7
=
+
3
7
=
1/7 1/7 1/7 1/7 1/7 1/7 1/7
Rule: add the numerators and leave the common denominator
2+3=5
2
7
+
3
7
=
Leave the common denominator
5
7
5
7
Add the following
1/10
1/10
1/10
1/10
1/9
1/9
1/9
1/9
1/10
1/10
1/9
1/10
1/10
1/9
1/9
1/10
1/10
1/9
1/9
+
+
2
11
5
19
1/10 1/10
1/10
1/10
1/10
1/10
1/10
1/10
1/10
1/9
+
+
1/10
1/9
1/9
1/9
1/9
1/9
1/9
1/9
1/9
7/10
8/9
4
= 6/11
11
12
19
= 17/19
Click mouse for
answers
Time for a game:
Fish Game, add with common denominator:
http://www.iknowthat.com/com/L3?Area=F
ractionGame
Addition/Subtraction (medium)
(Related Denominator)
Year 9 add Fractions (page 11 – 21):http://e-learningforkids.org/Courses/EN/M1101/index.html
1)
You cannot add or
subtract fractions that
have different
denominators.
2)
If the denominators are
different, find a
common (same)
denominator.
1
2
+
1
4
= ?
To add ½ + ¼ together find a number that both the
denominators, 2 and 4, go into (common multiple)
Using equivalent fractions
1
2
1
2
=
+
1/4
1/4
1/4
1/4
2
4
1
becomes
4
2
4
=
3
4
+
1
4
Add the following …
7/8
+
2
5
1
6
+
+
3
= 4/10 + 3/10 = 7/10
10
5
18
= 3/18 + 5/18 = 8/18 = 4/9
Addition/Subtraction (Hard)
(Unrelated Denominator)
Khan: http://www.khanacademy.org/math/arithmetic/fractions/v/adding-fractions-with-unlike-denominators
Or
Year 9 add Fractions (page 22 - 25):http://e-learningforkids.org/Courses/EN/M1101/index.html
Some addition and subtraction of factions involve converting
both fractions to a common denominator.
E.g.
2
+
3
1
5
The common multiple of 3 and 5 is 15 (common denominator)
The above sum becomes
10
15
+
3
15
=
13
15
Add the following …
3
7
+
2
5
= 15/35 + 14/35 = 29/35
1
3
3
8
+
4
9
+
3
5
= 5/15 + 9/15 = 14/15
= 27/72 + 32/72 = 59/72
Time for ….
Fish Game, add unlike denominators:
http://www.iknowthat.com/com/L3?Area=F
ractionGame
Music video:
http://www.youtube.com/watch?v=iunSAbA4
2OY&feature=related
Multiplication of Fractions
E.g.
2
3
2
3
x
1
of
4
1
4
=
Notice ‘of’ means
multiply (times)
2
(1 x 2 = 2)
12
(3 x 4 = 12)
Multiply the following …
2
5
x
3
2x3
4
5x4
2
2
2x2
3
7x3
7
4
5
x
x
1
4x1
9
5x9
=
=
6
20
4
45
=
4
21
Mixed Numbers
A mixed number has 2
parts: a whole number
and a fraction.
e.g.
3½
Improper Fractions
An improper fraction has a numerator bigger
than the denominator.
E.g.
5
3
Bigger
Smaller
Time for a game:
Fish Game, improper fractions:
http://www.iknowthat.com/com/L3?Area=FractionGame
Improper fractions (easy) Improper to Mixed egg laying
game: http://www.echalk.co.uk/tasters/taster2/taster.html
Mixed Numbers to Improper Fractions
3
5
5
+
5
5
2
5
=
+
?
5
5
5
+
Notice how the numerator is found (3 x 5 + 2 = 17)
The denominator does not change.
2
5
=
17
5
Convert to improper fractions…
4
1
2
(4 x 2 + 1 = 9) therefore = 9/2
3
5
5
8
2
7
(3 x 7 + 2 = 23) therefore = 23/7
(8 x 5 + 5 = 45) therefore = 45/8
Improper Fractions to Mixed Numbers
7
3
E.g.
=
?
?
3
7 over 3 means 7 lots of 1/3
1/3
1/3
1/3
1/3
1/3
1/3
1/3
(We can make 2 wholes and have 1/3 left over)
Therefore
Notice that 7
3
7
3
=2
1
3
= 2 with remainder 1
The denominator does not change.
Convert the following to mixed numbers
3
2
7
4
(3 divide by 2 = 1 r 1) Therefore = 1 1/2
11
3
(11 divide by 3 = 3 r 2) therefore = 3 2/3

(7 divide by 4 = 1 r 3) therefore = 1 3/4
Fractions made complicated!
(Warning: Top set only, this will blow your
mind!)
http://www.khanacademy.org/math/vihart/v/fractal-fractions
Ratio
The colon (:) is used as the ration sign.
To share something in the ratio 5 to 3 we write
5:3
E.g. If Aunty Jane has left her nephews money to
be shared so that for every $2 Albert receives, Bob
receives $3, we write this as
2:3
(Notice that as Albert’s name was mentioned first
then this amount is written first)
Write the following as ratios
Circle : Cross
3:2
Cat : Dog
4:3
Try the following
Easy ratio matching: http://www.galaxygoo.org/math/allAboutRatios.html
Sharing in a given Ratio
The long way
If Aunt Jane had $35 in her will to share between Albert and Bob
in the ratio 2:3, how much would each receive?
Take 40 counters (you could use pencil marks on scrap paper)
Share the 40 counters into 2 piles in the ratio 2:3 until you have no counters left.
2
$ $
3
$ $ $
5
$ $
$ $ $
10
$ $
$ $ $
15
$
$
$
$
$
$
$
$
20
25
30
35…………7 rows of 5
$
$
$
$
Albert receives 7 x 2
=$14
:
$
$
$
$
$
$
$
$
Bob receives 7 x 3
=$21
(Check: $14 + $21 = $35)
Sharing in a given Ratio
The quick way
If Aunt Jane had $4000 in her will to share between Albert and
Bob in the ratio 2:3, how much would each receive?
As Albert gets 2 parts and Bob gets 3 parts, we need to share
the money into 5 (2 + 3) parts i.e.
1/5 of $4000 = $800 (each part is worth $800)
$800 $800 $800 $800 $800
Albert requires 2 parts i.e. 2/5 of $4000 = $1600
Bob required 3 parts i.e. 3/5 of $4000 = $2400
(Check: $1600 + $2400 = $4000)
3 ways to explain ratio: http://www.seemath.com/?mid=52#/Menu--Decomposition-in-a-given-ratio/
Share the following in the given ratio …
Share 20 in the ratio 1:3
1/4 x 20 = 5
3/4 x 20 = 15
(Check: 5 + 15 = 20)
Share 32 in the ratio 5:3
5/8 x 32 = 20
3/8 x 32 = 12
(Check: 20 + 12 = 32)
Thanks
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