Respuesta :
A mixed number of the form [tex]a\frac{b}{c}[/tex] 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
[tex]a\frac{b}{c} = {\displaystyle a + \frac{b}{c}=\frac{a}{1}+\frac{b}{c}}[/tex]
Then do the usual procedure for adding fractions via common denominator.
For example, to convert the mixed number [tex]5 \frac{1}{4}[/tex] into an improper fraction, we have
[tex]5\frac{1}{4}={\displaystyle 5 +\frac{1}{4}=\frac{5}{1}+\frac{1}{4}}[/tex]
To add [tex]\frac{5}{1}+\frac{1}{4}[/tex], we need [tex]\frac{5}{1}[/tex] to have a denominator of 4, so we multiply the numerator and denominator by 4 to get
[tex]=\frac{5\cdot 4}{1 \cdot 4}+\frac{1}{4}=\frac{20}{4}+\frac{1}{4} = \frac{21}{4}[/tex]
Therefore,
[tex]5\frac{1}{4} = \frac{21}{4}[/tex]
