Solve (21/7)(5)/frac{3{7}+2/6+1/11}=

$$\frac { ( 2 \frac { 1 } { 7 } ) ( 5 ) } { \frac { 3 } { 7 } + \frac { 2 } { 6 } + \frac { 1 } { 11 } } =$$

Evaluate

$$\frac{2475}{197}\approx 12.563451777$$

Solution Steps

Multiply 2 and 7 to get 14.

$$\frac{\frac{14+1}{7}\times 5}{\frac{3}{7}+\frac{2}{6}+\frac{1}{11}}$$

Add 14 and 1 to get 15.

$$\frac{\frac{15}{7}\times 5}{\frac{3}{7}+\frac{2}{6}+\frac{1}{11}}$$

Express \frac{15}{7}\times 5 as a single fraction.

$$\frac{\frac{15\times 5}{7}}{\frac{3}{7}+\frac{2}{6}+\frac{1}{11}}$$

Multiply 15 and 5 to get 75.

$$\frac{\frac{75}{7}}{\frac{3}{7}+\frac{2}{6}+\frac{1}{11}}$$

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

$$\frac{\frac{75}{7}}{\frac{3}{7}+\frac{1}{3}+\frac{1}{11}}$$

Least common multiple of 7 and 3 is 21. Convert \frac{3}{7} and \frac{1}{3} to fractions with denominator 21.

$$\frac{\frac{75}{7}}{\frac{9}{21}+\frac{7}{21}+\frac{1}{11}}$$

Since \frac{9}{21} and \frac{7}{21} have the same denominator, add them by adding their numerators.

$$\frac{\frac{75}{7}}{\frac{9+7}{21}+\frac{1}{11}}$$

Add 9 and 7 to get 16.

$$\frac{\frac{75}{7}}{\frac{16}{21}+\frac{1}{11}}$$

Least common multiple of 21 and 11 is 231. Convert \frac{16}{21} and \frac{1}{11} to fractions with denominator 231.

$$\frac{\frac{75}{7}}{\frac{176}{231}+\frac{21}{231}}$$

Since \frac{176}{231} and \frac{21}{231} have the same denominator, add them by adding their numerators.

$$\frac{\frac{75}{7}}{\frac{176+21}{231}}$$

Add 176 and 21 to get 197.

$$\frac{\frac{75}{7}}{\frac{197}{231}}$$

Divide \frac{75}{7} by \frac{197}{231} by multiplying \frac{75}{7} by the reciprocal of \frac{197}{231}.

$$\frac{75}{7}\times \frac{231}{197}$$

Multiply \frac{75}{7} times \frac{231}{197} by multiplying numerator times numerator and denominator times denominator.

$$\frac{75\times 231}{7\times 197}$$

Do the multiplications in the fraction \frac{75\times 231}{7\times 197}.

$$\frac{17325}{1379}$$

Reduce the fraction \frac{17325}{1379} to lowest terms by extracting and canceling out 7.

$$\frac{2475}{197}$$

Factor

$$\frac{3 ^ {2} \cdot 5 ^ {2} \cdot 11}{197} = 12\frac{111}{197} = 12.563451776649746$$