Fractions

1
Fractions
What is a fraction? Equivalent fractions Improper
Fractions Mixed Numbers Converting mixed
numbers into improper fractions Writing a
Fraction as a Decimal Exercises
Presented by Hansi Sumedha hansis_at_hlacademy.org
2
What is a fraction? Lets think about a loaf of
bread. We cut it into four equal pieces.
I ate one part. Then there are 3 parts remaining.
So out of four parts now there are only 3 parts.
We can represent the remaining part as
So a fraction is a number that expresses part of
a group.
We call the upper part the numerator, and the
lower part the denominator.
3
Example
You can see the circle is divided into four equal
segments and three are coloured. So we can
represent coloured parts as
Exercises You can implement the following
fractions.
4
Equivalent fractions
We can represent the coloured parts of first
circle as
We can represent the coloured parts of second
circle as
Although the fractions are different, the amounts
they represent are the same.
5
How can we write an equivalent fraction for a
fraction? Example
We just multiply both the numerator and
denominator by the same number. You can multiply
by any whole value. Lets assume we multiply by
2. Then
So and are equivalent.
If both the numerator and denominator can be
divided by the same whole value, we can obtain
equivalent fractions using that method too.
6
Improper Fractions
Lets consider the following fractions.
Can you see any difference between these
fractions and the fractions discussed
earlier? Yes the numerators are larger than the
denominators of these fractions. Such fractions
are called improper fractions. Definitions
Improper fractions are fractions where the
numerator is larger than or equal to the
denominator.
7
Mixed Numbers

Here you can see a whole number fraction. So a
mixed number is a number which has a whole number
and a fraction part. We can write a mixed number
as
Try to implement the following mixed numbers
using figures as above.
8
Converting mixed numbers into improper fractions
When the fractions are simplified (
multiplication, division, addition and
subtraction) it is very important to know the way
of converting mixed numbers into improper
fractions and vise versa. Example Now we want
to convert this into an improper fraction. Just
multiply the whole number (that is 3) by the
denominator and add the numerator to the
answer. The denominator of the mixed number is
the same as the denominator of the improper
number. So the answer is
Exercises Try converting the following numbers
into improper fractions.
9
Converting improper fractions to mixed numbers
Example Consider the answer of the previous
example we discussed. Now we want to convert
improper fractions into mixed numbers.
First divide 13 by 4. The answer is 3 and the
remainder is 1. We implement the remainder as the
numerator of the mixed number and the answer as
the whole number. So the mixed number is
10
Writing a fraction as a decimal Example we need
to convert this fraction to decimal number.
How? The mean of this fraction is found by
dividing the 3 by the 4. The answer is
0.75 Example we need to convert this fraction
to decimal number. First we must convert this
into an improper number.
Now divide 7 by 4. Answer is 1.75