Solve 41/5+[(3-4/7):(14/49+3/7:frac{7}{12})]

$$\frac { 41 } { 5 } + [ ( 3 - \frac { 4 } { 7 } ) : ( \frac { 14 } { 49 } + \frac { 3 } { 7 } : \frac { 7 } { 12 } ) ]$$

Evaluate

$$\frac{529}{50}=10.58$$

Solution Steps

Convert 3 to fraction \frac{21}{7}.

$$\frac{41}{5}+\frac{\frac{21}{7}-\frac{4}{7}}{\frac{14}{49}+\frac{\frac{3}{7}}{\frac{7}{12}}}$$

Since \frac{21}{7} and \frac{4}{7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{41}{5}+\frac{\frac{21-4}{7}}{\frac{14}{49}+\frac{\frac{3}{7}}{\frac{7}{12}}}$$

Subtract 4 from 21 to get 17.

$$\frac{41}{5}+\frac{\frac{17}{7}}{\frac{14}{49}+\frac{\frac{3}{7}}{\frac{7}{12}}}$$

Reduce the fraction \frac{14}{49} to lowest terms by extracting and canceling out 7.

$$\frac{41}{5}+\frac{\frac{17}{7}}{\frac{2}{7}+\frac{\frac{3}{7}}{\frac{7}{12}}}$$

Divide \frac{3}{7} by \frac{7}{12} by multiplying \frac{3}{7} by the reciprocal of \frac{7}{12}.

$$\frac{41}{5}+\frac{\frac{17}{7}}{\frac{2}{7}+\frac{3}{7}\times \frac{12}{7}}$$

Multiply \frac{3}{7} times \frac{12}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{41}{5}+\frac{\frac{17}{7}}{\frac{2}{7}+\frac{3\times 12}{7\times 7}}$$

Do the multiplications in the fraction \frac{3\times 12}{7\times 7}.

$$\frac{41}{5}+\frac{\frac{17}{7}}{\frac{2}{7}+\frac{36}{49}}$$

Least common multiple of 7 and 49 is 49. Convert \frac{2}{7} and \frac{36}{49} to fractions with denominator 49.

$$\frac{41}{5}+\frac{\frac{17}{7}}{\frac{14}{49}+\frac{36}{49}}$$

Since \frac{14}{49} and \frac{36}{49} have the same denominator, add them by adding their numerators.

$$\frac{41}{5}+\frac{\frac{17}{7}}{\frac{14+36}{49}}$$

Add 14 and 36 to get 50.

$$\frac{41}{5}+\frac{\frac{17}{7}}{\frac{50}{49}}$$

Divide \frac{17}{7} by \frac{50}{49} by multiplying \frac{17}{7} by the reciprocal of \frac{50}{49}.

$$\frac{41}{5}+\frac{17}{7}\times \frac{49}{50}$$

Multiply \frac{17}{7} times \frac{49}{50} by multiplying numerator times numerator and denominator times denominator.

$$\frac{41}{5}+\frac{17\times 49}{7\times 50}$$

Do the multiplications in the fraction \frac{17\times 49}{7\times 50}.

$$\frac{41}{5}+\frac{833}{350}$$

Reduce the fraction \frac{833}{350} to lowest terms by extracting and canceling out 7.

$$\frac{41}{5}+\frac{119}{50}$$

Least common multiple of 5 and 50 is 50. Convert \frac{41}{5} and \frac{119}{50} to fractions with denominator 50.

$$\frac{410}{50}+\frac{119}{50}$$

Since \frac{410}{50} and \frac{119}{50} have the same denominator, add them by adding their numerators.

$$\frac{410+119}{50}$$

Add 410 and 119 to get 529.

$$\frac{529}{50}$$

Factor

$$\frac{23 ^ {2}}{2 \cdot 5 ^ {2}} = 10\frac{29}{50} = 10.58$$