Improper Fractions

Example 1: 

Convert \(4\frac{2}{5}\) into an improper fraction.

Solution: 

Here, we will first multiply the whole number part with the denominator.

4 x 5 = 20

Then, we will add it to the numerator.

(20 + 2 = 22)

The final result will be written as a numerator and the denominator will be the required fraction.

Hence, the improper fraction is \(\frac{22}{5}\).

Example 2: 

Find the following sum: 3 + \(\frac{12}{5}\)

Solution: 

We will follow these steps:

3 + \(\frac{12}{5}\) = \(\frac{3}{1}\) + \(\frac{12}{5}\)      [3 can be written as \(\frac{3}{1}\)]

= \(\frac{3~\times~5}{1~\times~5}\) + \(\frac{12}{5}\)            [Multiply 5 to the numerator and denominator of \(\frac{3}{1}\)]

= \(\frac{15}{5}\) + \(\frac{12}{5}\)

= \(\frac{15~+~12}{5}\)                 [Add]

= \(\frac{27}{5}\)  

Hence, the sum will be \(\frac{27}{5}\).

Example 3: 

Jordan ate seven-fourths of two pizzas and left the remainder for his sister. What is the fraction of pizza that Jordan’s sister gets?

Solution: 

There were 2 pizzas, and Jordan ate \(\frac{7}{4}\) slices from both pizzas.

Hence, the number of slices left for his sister is,

2 – \(\frac{7}{4}\)

= \(\frac{2}{1}\) – \(\frac{7}{4}\)           [2 can be written as \(\frac{2}{1}\)]

= \(\frac{2~\times~4}{1~\times~4}\) – \(\frac{7}{4}\)      [Multiply 4 to the numerator and denominator of \(\frac{2}{1}\)]

= \(\frac{8}{4}~-~\frac{7}{4}\) 

= \(\frac{8~-~7}{4}\)             [Substract]

= \(\frac{1}{4}\) 

Hence, Jordan’s sister had \(\frac{1}{4}\) of the remaining pieces from both pizzas.