Solve 55/4+22/3*15/16/frac{2{5}+frac{4}{15}}

$$\frac { 5 \frac { 5 } { 4 } + 2 \frac { 2 } { 3 } \times 1 \frac { 5 } { 16 } } { \frac { 2 } { 5 } + \frac { 4 } { 15 } }$$

Evaluate

$$\frac{117}{8}=14.625$$

Solution Steps

Multiply 5 and 4 to get 20.

$$\frac{\frac{20+5}{4}+\frac{2\times 3+2}{3}\times \frac{1\times 16+5}{16}}{\frac{2}{5}+\frac{4}{15}}$$

Add 20 and 5 to get 25.

$$\frac{\frac{25}{4}+\frac{2\times 3+2}{3}\times \frac{1\times 16+5}{16}}{\frac{2}{5}+\frac{4}{15}}$$

Multiply 2 and 3 to get 6.

$$\frac{\frac{25}{4}+\frac{6+2}{3}\times \frac{1\times 16+5}{16}}{\frac{2}{5}+\frac{4}{15}}$$

Add 6 and 2 to get 8.

$$\frac{\frac{25}{4}+\frac{8}{3}\times \frac{1\times 16+5}{16}}{\frac{2}{5}+\frac{4}{15}}$$

Multiply 1 and 16 to get 16.

$$\frac{\frac{25}{4}+\frac{8}{3}\times \frac{16+5}{16}}{\frac{2}{5}+\frac{4}{15}}$$

Add 16 and 5 to get 21.

$$\frac{\frac{25}{4}+\frac{8}{3}\times \frac{21}{16}}{\frac{2}{5}+\frac{4}{15}}$$

Multiply \frac{8}{3} times \frac{21}{16} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{25}{4}+\frac{8\times 21}{3\times 16}}{\frac{2}{5}+\frac{4}{15}}$$

Do the multiplications in the fraction \frac{8\times 21}{3\times 16}.

$$\frac{\frac{25}{4}+\frac{168}{48}}{\frac{2}{5}+\frac{4}{15}}$$

Reduce the fraction \frac{168}{48} to lowest terms by extracting and canceling out 24.

$$\frac{\frac{25}{4}+\frac{7}{2}}{\frac{2}{5}+\frac{4}{15}}$$

Least common multiple of 4 and 2 is 4. Convert \frac{25}{4} and \frac{7}{2} to fractions with denominator 4.

$$\frac{\frac{25}{4}+\frac{14}{4}}{\frac{2}{5}+\frac{4}{15}}$$

Since \frac{25}{4} and \frac{14}{4} have the same denominator, add them by adding their numerators.

$$\frac{\frac{25+14}{4}}{\frac{2}{5}+\frac{4}{15}}$$

Add 25 and 14 to get 39.

$$\frac{\frac{39}{4}}{\frac{2}{5}+\frac{4}{15}}$$

Least common multiple of 5 and 15 is 15. Convert \frac{2}{5} and \frac{4}{15} to fractions with denominator 15.

$$\frac{\frac{39}{4}}{\frac{6}{15}+\frac{4}{15}}$$

Since \frac{6}{15} and \frac{4}{15} have the same denominator, add them by adding their numerators.

$$\frac{\frac{39}{4}}{\frac{6+4}{15}}$$

Add 6 and 4 to get 10.

$$\frac{\frac{39}{4}}{\frac{10}{15}}$$

Reduce the fraction \frac{10}{15} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{39}{4}}{\frac{2}{3}}$$

Divide \frac{39}{4} by \frac{2}{3} by multiplying \frac{39}{4} by the reciprocal of \frac{2}{3}.

$$\frac{39}{4}\times \frac{3}{2}$$

Multiply \frac{39}{4} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{39\times 3}{4\times 2}$$

Do the multiplications in the fraction \frac{39\times 3}{4\times 2}.

$$\frac{117}{8}$$

Factor

$$\frac{3 ^ {2} \cdot 13}{2 ^ {3}} = 14\frac{5}{8} = 14.625$$