Fractions

Improper fractions and mixed numbers

Example 1: Look at the following shapes.

In fraction \(7 \over 4\) , numerator is qreater than the denominator, Such fractions are called improper fractions.  \(7 \over 4\)Is an improper fraction

An proper fraction has a numerator that is smaller than it’s denominator.

An improper fraction has a numerator that is greater than it’s denominator

Example 2: Look at the shapes again

This is 1 whole circle

\({4\over 4}=1\)

We can also write it as a mixed number

There is 1 whole circle and \(3 \over 4\) of a circle

1\(3 \over 4\) is an example of a mixed number.

A mixed number is made up of a whole number and a proper fraction

Converting fractions

Example 1: Let’s convert a mixed number 2\(1 \over 2\) to an improper fraction directly.

We will convert the whole numbers into fractions with same denominators as that of proper fraction and add all fractions

We can also do it mathematically by following these steps.

Step 1: Multiply the whole number part by the denominator of the fraction

Step 2: Add the product to the numerator.

Step 3: Write the result as a numerator over the same denominator

Let’s see how we convert improper fraction to mixed number

Look at the circles below

\(13\over6\)of the circles are coloured

Example 2: Let’s convert this improper fraction to mixed number

Divide the numerator by the denominator

\(13\over 6\)= 2 with a remainder of 1.

Write down the quotient as a whole number

Write remainder as a numerator over the same denominator.

\(13\over 6\) =2 \(1\over 2\)