Solve 3/4+40/frac{42{51}+7/frac{10{7}-4/35}}=

$$\frac{ 3 }{ 4 } + \frac{ 40 }{ \frac{ 42 }{ 51 } + \frac{ 7 }{ \frac{ 10 }{ 7 } - \frac{ 4 }{ 35 } } } =$$

Evaluate

$$\frac{139547}{19236}\approx 7.254470784$$

Solution Steps

Reduce the fraction \frac{42}{51} to lowest terms by extracting and canceling out 3.

$$\frac{3}{4}+\frac{40}{\frac{14}{17}+\frac{7}{\frac{10}{7}-\frac{4}{35}}}$$

Least common multiple of 7 and 35 is 35. Convert \frac{10}{7} and \frac{4}{35} to fractions with denominator 35.

$$\frac{3}{4}+\frac{40}{\frac{14}{17}+\frac{7}{\frac{50}{35}-\frac{4}{35}}}$$

Since \frac{50}{35} and \frac{4}{35} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{4}+\frac{40}{\frac{14}{17}+\frac{7}{\frac{50-4}{35}}}$$

Subtract 4 from 50 to get 46.

$$\frac{3}{4}+\frac{40}{\frac{14}{17}+\frac{7}{\frac{46}{35}}}$$

Divide 7 by \frac{46}{35} by multiplying 7 by the reciprocal of \frac{46}{35}.

$$\frac{3}{4}+\frac{40}{\frac{14}{17}+7\times \frac{35}{46}}$$

Express 7\times \frac{35}{46} as a single fraction.

$$\frac{3}{4}+\frac{40}{\frac{14}{17}+\frac{7\times 35}{46}}$$

Multiply 7 and 35 to get 245.

$$\frac{3}{4}+\frac{40}{\frac{14}{17}+\frac{245}{46}}$$

Least common multiple of 17 and 46 is 782. Convert \frac{14}{17} and \frac{245}{46} to fractions with denominator 782.

$$\frac{3}{4}+\frac{40}{\frac{644}{782}+\frac{4165}{782}}$$

Since \frac{644}{782} and \frac{4165}{782} have the same denominator, add them by adding their numerators.

$$\frac{3}{4}+\frac{40}{\frac{644+4165}{782}}$$

Add 644 and 4165 to get 4809.

$$\frac{3}{4}+\frac{40}{\frac{4809}{782}}$$

Divide 40 by \frac{4809}{782} by multiplying 40 by the reciprocal of \frac{4809}{782}.

$$\frac{3}{4}+40\times \frac{782}{4809}$$

Express 40\times \frac{782}{4809} as a single fraction.

$$\frac{3}{4}+\frac{40\times 782}{4809}$$

Multiply 40 and 782 to get 31280.

$$\frac{3}{4}+\frac{31280}{4809}$$

Least common multiple of 4 and 4809 is 19236. Convert \frac{3}{4} and \frac{31280}{4809} to fractions with denominator 19236.

$$\frac{14427}{19236}+\frac{125120}{19236}$$

Since \frac{14427}{19236} and \frac{125120}{19236} have the same denominator, add them by adding their numerators.

$$\frac{14427+125120}{19236}$$

Add 14427 and 125120 to get 139547.

$$\frac{139547}{19236}$$

Factor

$$\frac{139547}{2 ^ {2} \cdot 3 \cdot 7 \cdot 229} = 7\frac{4895}{19236} = 7.254470783946767$$