Question

what is 24 1/2 divided by 3 1/4

Answer 1

From the problem, we have :

$24\frac{1}{2}\div3\frac{1}{4}$

The given fractions are in mixed form. We need to convert it or rewrite as an improper fractions.

Note that in converting mixed fraction to improper fraction :

$a\frac{b}{c}=\frac{ac+b}{c}$$\begin{gathered} 24\frac{1}{2}=\frac{24(2)+1}{2}=\frac{49}{2} \\ 3\frac{1}{4}=\frac{3(4)+1}{4}=\frac{13}{4} \end{gathered}$

The expression will be :

$\frac{49}{2}\div\frac{13}{4}$

Next is to rewrite the expression as multiplication.

In rewriting division into multiplication :

$\frac{a}{b}\div\frac{c}{d}\Rightarrow\frac{a}{b}\times\frac{d}{c}$

The numerator and denominator of the 2nd term will interchange.

from c/d to d/c.

So it follows that :

$\frac{49}{2}\div\frac{13}{4}\Rightarrow\frac{49}{2}\times\frac{4}{13}$

Simplify the expression :

$\begin{gathered} \frac{49}{2}\times\frac{4}{13}=\frac{49}{\cancel{2}}\times\frac{2(\cancel{2})}{13}=\frac{49\times2}{13} \\ \Rightarrow\frac{98}{13} \end{gathered}$

Rewriting as mixed fraction :

$\frac{98}{13}=7\frac{7}{13}$

The answer is 98/13 or 7 7/13