Solve 5/7div1/2div5/6quad(7/8+frac{13}{16})divfrac{13}{16}

$$\frac { 5 } { 7 } \div \frac { 1 } { 2 } \div \frac { 5 } { 6 } \quad ( \frac { 7 } { 8 } + \frac { 13 } { 16 } ) \div \frac { 13 } { 16 }$$

Evaluate

$$\frac{324}{91}\approx 3.56043956$$

Solution Steps

Divide \frac{\frac{5}{7}}{\frac{1}{2}} by \frac{5}{6} by multiplying \frac{\frac{5}{7}}{\frac{1}{2}} by the reciprocal of \frac{5}{6}.

$$\frac{\frac{\frac{5}{7}\times 6}{\frac{1}{2}\times 5}\left(\frac{7}{8}+\frac{13}{16}\right)}{\frac{13}{16}}$$

Express \frac{5}{7}\times 6 as a single fraction.

$$\frac{\frac{\frac{5\times 6}{7}}{\frac{1}{2}\times 5}\left(\frac{7}{8}+\frac{13}{16}\right)}{\frac{13}{16}}$$

Multiply 5 and 6 to get 30.

$$\frac{\frac{\frac{30}{7}}{\frac{1}{2}\times 5}\left(\frac{7}{8}+\frac{13}{16}\right)}{\frac{13}{16}}$$

Multiply \frac{1}{2} and 5 to get \frac{5}{2}.

$$\frac{\frac{\frac{30}{7}}{\frac{5}{2}}\left(\frac{7}{8}+\frac{13}{16}\right)}{\frac{13}{16}}$$

Divide \frac{30}{7} by \frac{5}{2} by multiplying \frac{30}{7} by the reciprocal of \frac{5}{2}.

$$\frac{\frac{30}{7}\times \frac{2}{5}\left(\frac{7}{8}+\frac{13}{16}\right)}{\frac{13}{16}}$$

Multiply \frac{30}{7} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{30\times 2}{7\times 5}\left(\frac{7}{8}+\frac{13}{16}\right)}{\frac{13}{16}}$$

Do the multiplications in the fraction \frac{30\times 2}{7\times 5}.

$$\frac{\frac{60}{35}\left(\frac{7}{8}+\frac{13}{16}\right)}{\frac{13}{16}}$$

Reduce the fraction \frac{60}{35} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{12}{7}\left(\frac{7}{8}+\frac{13}{16}\right)}{\frac{13}{16}}$$

Least common multiple of 8 and 16 is 16. Convert \frac{7}{8} and \frac{13}{16} to fractions with denominator 16.

$$\frac{\frac{12}{7}\left(\frac{14}{16}+\frac{13}{16}\right)}{\frac{13}{16}}$$

Since \frac{14}{16} and \frac{13}{16} have the same denominator, add them by adding their numerators.

$$\frac{\frac{12}{7}\times \frac{14+13}{16}}{\frac{13}{16}}$$

Add 14 and 13 to get 27.

$$\frac{\frac{12}{7}\times \frac{27}{16}}{\frac{13}{16}}$$

Multiply \frac{12}{7} times \frac{27}{16} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{12\times 27}{7\times 16}}{\frac{13}{16}}$$

Do the multiplications in the fraction \frac{12\times 27}{7\times 16}.

$$\frac{\frac{324}{112}}{\frac{13}{16}}$$

Reduce the fraction \frac{324}{112} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{81}{28}}{\frac{13}{16}}$$

Divide \frac{81}{28} by \frac{13}{16} by multiplying \frac{81}{28} by the reciprocal of \frac{13}{16}.

$$\frac{81}{28}\times \frac{16}{13}$$

Multiply \frac{81}{28} times \frac{16}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{81\times 16}{28\times 13}$$

Do the multiplications in the fraction \frac{81\times 16}{28\times 13}.

$$\frac{1296}{364}$$

Reduce the fraction \frac{1296}{364} to lowest terms by extracting and canceling out 4.

$$\frac{324}{91}$$

Factor

$$\frac{2 ^ {2} \cdot 3 ^ {4}}{7 \cdot 13} = 3\frac{51}{91} = 3.5604395604395602$$