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What is a Fraction?
A fraction is a number, which
contains parts of a whole.
Fractions can be smaller than or
larger than one (one whole).
N
A fraction is a number with the form
D
where n and d are two numbers
N
The number n above the line is called the numerator
D
The number d below the line is called the denominator.
Fraction can be written in different ways
A fraction is a number with the form
N
D
Alternative ways of expressing this statement include:
"n over d", n ÷ d
Example
The fraction
5
6
could be expressed as:
five-sixths, five over six, 5 ÷ 6
Proper, Improper and Mixed Numbers
If the numerator is smaller than the denominator (if n < d), then the fraction is called
a proper fraction, and its value is less than 1.
3
7
2
10
17
26
If the numerator is greater than the denominator (if n > d), then the fraction is called
an improper fraction, and its value is greater than 1.
31 15
5 10
37
23
If the numerator is equal to the denominator, then the fraction's value is equal to 1.
A mixed number (or mixed fraction) is a number that has a whole number part to it, and a
fraction part to it.
31
5
1 2
3
12 7
10
Common Fractions
A common fraction is simply an ordinary fraction.
The numerator and denominator must be integers, or whole numbers, and the denominator
cannot equal zero.
Common Fractions
Not Common
Fractions
35
45
5
9
51
16
3.2
4.5
5
0
0.57
1.6
Decimal Fractions
A decimal fraction is a fraction where the denominator is a power of ten.
7
10
.7
3
5
5
100
.05
263
500
Are not decimal
fractions
537
1000
.537
Are all decimal
fractions
Equal to
Equivalent Fractions
Equivalent fractions are fractions, which have the same value as each other.
A quick way to tell whether or not two fractions are equivalent is to change them both into
decimals using a calculator.
If the two decimals are identical, then the fractions have the same value.
2 .66
3
2 =
3
=
4
6
.66
4
6
=
6
9
= 8 =
12
10
15
Each time the fraction is split, both the denominator and the numerator are
multiplied by the split. This gives us an equivalent fraction.
In other words, if you multiply the numerator and denominator by the same
number, you get the same (or equivalent) fraction.
And by using the same logic, if we divide the numerator and denominator by the same
number, you get an equivalent fraction.
Simplifying/ Reducing Fractions
This is also sometimes called reducing fractions to their simplest form.
This involves dividing both the numerator and denominator by a common factor to reduce
the fraction to the equivalent fraction with the smallest possible numerator and
denominator.
10 =
100
50 =
60
1
10
5
6
12 =
24
75 =
90
1
2
15 =
18
5
6
Adding and Subtracting Fractions
Adding and subtracting fractions works differently from adding and subtracting integers or
decimals.
If the two fractions have the same denominator, then it is quite easy to add or subtract the
fractions by simply adding the numerators together.
1
5
+ 3
5
= 4
5
6 + 15 = __
25
25
4
6
+ 1
6
= 5
6
6 + 17 = __
30
30
If the fractions have different denominators, then they need to be changed into equivalent
fractions with the same denominator before they can be added or subtracted.
2
+
6
Multiply by the
opposite denominator
7
12
Multiply by
the opposite
denominator
2 x12 + 7 x6
6 x12
12 x6
Now that both have a common
denominator add them together
24 + 42
72
72
66
66 6
72 reduces to
72 6
=
=
=
=
66
72
11
12
Multiplying and Dividing Fractions
To multiply two fractions together, simply multiply the two numerators together, then
multiply the 2 denominators together.
Multiply
7
12
x 5 = 35
10
120
8
32
x 8 = 64
20
640
To divide () one fraction by a second fraction, you need to invert the numerator and
denominator of the second fraction so that the 'old denominator' is on the top, and the 'old
numerator' is on the bottom half of the fraction. They can then be multiplied together to
give an answer.
Divide
Invert
Answer
Reduce
Regroup if
nd
2
needed
fraction
7  5 = 7 x 10 = 70
= 7
= 11
12
10
12
5
60
6
6
9  7 = 9 x 20 = 180
32
20
32
7
224
= 45
56