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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

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.

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.

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.

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.

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.

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.

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.

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

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