Solve 92/6+502/6+601/6+8L/6+frac{52}{6}+frac{81}{6}]8

$$\frac { 92 } { 6 } + \frac { 502 } { 6 } + \frac { 601 } { 6 } + \frac { 8 L } { 6 } + \frac { 52 } { 6 } + \frac { 81 } { 6 } ] 8$$

Evaluate

$$\frac{4\left(L+166\right)}{3}$$

Solution Steps

Reduce the fraction \frac{92}{6} to lowest terms by extracting and canceling out 2.

$$\frac{46}{3}+\frac{502}{6}+\frac{601}{6}+\frac{8L}{6}+\frac{52}{6}+\frac{81}{6}$$

Reduce the fraction \frac{502}{6} to lowest terms by extracting and canceling out 2.

$$\frac{46}{3}+\frac{251}{3}+\frac{601}{6}+\frac{8L}{6}+\frac{52}{6}+\frac{81}{6}$$

Since \frac{46}{3} and \frac{251}{3} have the same denominator, add them by adding their numerators.

$$\frac{46+251}{3}+\frac{601}{6}+\frac{8L}{6}+\frac{52}{6}+\frac{81}{6}$$

Add 46 and 251 to get 297.

$$\frac{297}{3}+\frac{601}{6}+\frac{8L}{6}+\frac{52}{6}+\frac{81}{6}$$

Divide 297 by 3 to get 99.

$$99+\frac{601}{6}+\frac{8L}{6}+\frac{52}{6}+\frac{81}{6}$$

Convert 99 to fraction \frac{594}{6}.

$$\frac{594}{6}+\frac{601}{6}+\frac{8L}{6}+\frac{52}{6}+\frac{81}{6}$$

Since \frac{594}{6} and \frac{601}{6} have the same denominator, add them by adding their numerators.

$$\frac{594+601}{6}+\frac{8L}{6}+\frac{52}{6}+\frac{81}{6}$$

Add 594 and 601 to get 1195.

$$\frac{1195}{6}+\frac{8L}{6}+\frac{52}{6}+\frac{81}{6}$$

Divide 8L by 6 to get \frac{4}{3}L.

$$\frac{1195}{6}+\frac{4}{3}L+\frac{52}{6}+\frac{81}{6}$$

Since \frac{1195}{6} and \frac{52}{6} have the same denominator, add them by adding their numerators.

$$\frac{1195+52}{6}+\frac{4}{3}L+\frac{81}{6}$$

Add 1195 and 52 to get 1247.

$$\frac{1247}{6}+\frac{4}{3}L+\frac{81}{6}$$

Since \frac{1247}{6} and \frac{81}{6} have the same denominator, add them by adding their numerators.

$$\frac{1247+81}{6}+\frac{4}{3}L$$

Add 1247 and 81 to get 1328.

$$\frac{1328}{6}+\frac{4}{3}L$$

Reduce the fraction \frac{1328}{6} to lowest terms by extracting and canceling out 2.

$$\frac{664}{3}+\frac{4}{3}L$$

Factor

$$\frac{4\left(L+166\right)}{3}$$

Solution Steps

Factor out \frac{1}{6}.

$$\frac{1328+8L}{6}$$

Consider 92+502+601+8L+52+81. Multiply and combine like terms.

$$8L+1328$$

Consider 8L+1328. Factor out 8.

$$8\left(L+166\right)$$

Rewrite the complete factored expression.

$$\frac{4\left(L+166\right)}{3}$$