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FRACTIONS
WHAT IS A FRACTION?
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A fraction is part of a whole one.
2/5 means 2 parts of 5.
The top number is the numerator; the bottom one is the
denominator.
A fraction like 2/5 is called a proper fraction.
A fraction like 12/7 is called an improper fraction.
A fraction like 14/9 is called a mixed number.
(If the numerator and the denominator are the same, then it is a
whole one, ie 5/5 = 1)
Addition and Subtraction of Fractions
The example shows the basic principles of adding and subtracting
fractions.
Example - Addition
1/8
+¾
First make the denominators the same
3 (x2) = 6
4 (X2) = 8 Replace ¾ with 6/8 so that the denominators
are now the same.
1/8
+ 6/8
= 7/8
Add the numerators 1 + 6 = 7
Do not add the denominators.
The denominator stays the same.
Example – Subtraction
¾ - 3/16
First make the denominators the same
3 (x4) = 12
4 (x4) = 16
¾ is equivalent to 12/16. Replace ¾ with 12/16
12/16
– 3/16
Subtract the numerators but not the denominators
The denominator stays the same.
= 9/16
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FRACTIONS
Fractions of a Quantity
Example:
In a class of 40 students, 2/5 of them are left-handed. How many are
left-handed?
 Divide 40 by 5 to find 1/5 (one fifth) = 8
 So to find 2/5 (two fifths) multiply the answer by 2….. 8 x 2= 16
 So 16 are left handed
Example:
Out of 36 students 2/3 walk to college. How many is this?
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To find one third - divide 36 by 3 = 12
To find two thirds - multiply by 2, so 2 x 12 = 24
24 students walk to college
Equivalent Fractions:
Example:
From the diagram it can be seen that ½ = 2/4
½
2
These are fractions that have the same value
/4
Example:
7/9 = ?/27
Fractions can be changed into their equivalent
by either multiplying or dividing the
numerator and denominator by the same
number.
7 (x3) 21
9 (x3) 27
Multiply the top
and bottom by 3
35/50 = 7/?
35 (÷5) 7
50 (÷5) 10
Divide the top
and bottom by 5
Simplifying Fractions
Fractions can be simplified if the numerator and the denominator
have a common factor.
Example:
Simplify 12/18
 6 is the highest common factor of 12 and 18
 Divide both the top and bottom number by 6
12 (÷6) = 2
18 (÷6) = 3
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FRACTIONS
Multiplication and Division of Fractions
When multiplying and dividing fractions, write out whole or mixed
numbers as improper fractions before starting. (eg 21/2 as 5/2)
Example:
4 x 2 = 8 Multiply the numerators together
7 11 77 Multiply the denominators together.
For division, change it into a multiplication by turning the second
fraction upside down, (taking the reciprocal) and multiply both
fractions together.
Example:
7 ÷ 12
9 18
Turn the
7 x 18 = 126 = 1 1
9 12 108
6
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12/18
upside down and multiply with 7/9
Rewrite back as a mixed number