Simplify

$\frac{38}{29}$

Explanation

In the numerator, write 7 as \(\frac71\).  The LCD for the numerator is 3.  Build \(\frac71\) so that it has a denominator of 3.  In the denominator, write \(4\frac56\) as the improper fraction \(\frac{29}{6}\)

$\large{\frac{7 - \frac23}{4\frac56} = \frac{\frac71 \cdot \color{red}{\frac33} - \frac23}{\frac{29}{6}}}$

Multiply the numerator.

$\large{= \frac{\frac{21}{3} - \frac23}{\frac{29}{6}}}$

In the numerator of the complex fraction, subtract the numerators: 21 -2 = 19.  Then write the difference over the common denominator 3.

$\large{= \frac{\frac{19}{3}}{\frac{29}{6}}}$

Write the division indicated by the main fraction bar using a ÷ symbol

$ = \frac{19}{3} ÷ \frac{29}{6}$

Multiply the first fraction by the reciprocal of \(\frac{29}{6}\), which is \(\frac{6}{29}\).

$= \frac{19}{3} \cdot \frac{6}{29}$

Multiply the numerators.  Multiply the denominators.

$= \frac{19 \cdot 6}{3 \cdot 29}$

To simplify, factor 6 as 2 • 3.  Then remove the common factor of 3 from the numerator and denominator.

$\require{cancel} = \frac{19 \cdot 2 \cdot \cancel{3}^1}{\cancel{3}_1 \cdot 29}$

Multiply the remaining factors in the numerator.  Multiply the remaining factors in the denominator.

$= \frac{38}{29}$