Question

How to make a mixed number a improper fraction ​

Answer 1

A mixed number of the form $a\frac{b}{c}$ can be turned into an improper fraction by using the fact that a mixed number is really het whole number plus its fraction part, so

  $a\frac{b}{c} = {\displaystyle a + \frac{b}{c}=\frac{a}{1}+\frac{b}{c}}$

Then do the usual procedure for adding fractions via common denominator.

For example, to convert the mixed number $5 \frac{1}{4}$ into an improper fraction, we have

  $5\frac{1}{4}={\displaystyle 5 +\frac{1}{4}=\frac{5}{1}+\frac{1}{4}}$

To add $\frac{5}{1}+\frac{1}{4}$, we need $\frac{5}{1}$ to have a denominator of 4, so we multiply the numerator and denominator by 4 to get

   $=\frac{5\cdot 4}{1 \cdot 4}+\frac{1}{4}=\frac{20}{4}+\frac{1}{4} = \frac{21}{4}$

Therefore,

  $5\frac{1}{4} = \frac{21}{4}$