# Writing a mixed number as an improper fraction

A mixed number can also be written as an improper fraction. A mixed number is the sum of its parts, the whole number and the fraction.

Rules to convert a mixed number into an improper fraction

For example,

• Consider a mixed number $5\frac{1}{2}$. It is the sum of 5 and $\frac{1}{2}$

$5\frac{1}{2} = 5 + \frac{1}{2}$

• 5 can be written as $\frac{10}{2}$

So, $5\frac{1}{2} = 5 + \frac{1}{2} = \frac{10}{2} + \frac{1}{2} = \frac{11}{2}$ which is the improper fraction equal to the mixed number.

• The improper fraction can also be found by using an algorithm.

• Consider the same mixed number $5\frac{1}{2}$.

• We multiply 5 by 2 and add 1 to get 5 × 2 + 1 = 10 + 1 = 11.

We put 11 as numerator and 2 as the denominator of the improper fraction. So finally, $5\frac{1}{2} = \frac{11}{2}$

Write the mixed number as an improper fraction.

$3\frac{1}{4}$

### Solution

Step 1:

Using the algorithm, we multiply 3 by 4 and add 1 to get 3 × 4 + 1 = 12 + 1 = 13.

Step 2:

We put 13 as numerator and 4 as the denominator of the improper fraction.

Step 3:

So finally, $3\frac{1}{4} = \frac{13}{4}$

Write the mixed number as an improper fraction.

$5\frac{3}{7}$

### Solution

Step 1:

Using the algorithm, we multiply 5 by 7 and add 3 to get 5 × 7 + 3 = 35 + 3 = 38.

Step 2:

We put 38 as numerator and 7 as the denominator of the improper fraction.

Step 3:

So finally, $5\frac{3}{7} = \frac{38}{7}$