Solve 28/19+15/50/frac{24{54}+14/21+frac{56}{12}}=

$$\frac { \frac { 28 } { 19 } + \frac { 15 } { 50 } } { \frac { 24 } { 54 } + \frac { 14 } { 21 } + \frac { 56 } { 12 } } =$$

Evaluate

$$\frac{3033}{9880}\approx 0.306983806$$

Solution Steps

Reduce the fraction \frac{15}{50} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{28}{19}+\frac{3}{10}}{\frac{24}{54}+\frac{14}{21}+\frac{56}{12}}$$

Least common multiple of 19 and 10 is 190. Convert \frac{28}{19} and \frac{3}{10} to fractions with denominator 190.

$$\frac{\frac{280}{190}+\frac{57}{190}}{\frac{24}{54}+\frac{14}{21}+\frac{56}{12}}$$

Since \frac{280}{190} and \frac{57}{190} have the same denominator, add them by adding their numerators.

$$\frac{\frac{280+57}{190}}{\frac{24}{54}+\frac{14}{21}+\frac{56}{12}}$$

Add 280 and 57 to get 337.

$$\frac{\frac{337}{190}}{\frac{24}{54}+\frac{14}{21}+\frac{56}{12}}$$

Reduce the fraction \frac{24}{54} to lowest terms by extracting and canceling out 6.

$$\frac{\frac{337}{190}}{\frac{4}{9}+\frac{14}{21}+\frac{56}{12}}$$

Reduce the fraction \frac{14}{21} to lowest terms by extracting and canceling out 7.

$$\frac{\frac{337}{190}}{\frac{4}{9}+\frac{2}{3}+\frac{56}{12}}$$

Least common multiple of 9 and 3 is 9. Convert \frac{4}{9} and \frac{2}{3} to fractions with denominator 9.

$$\frac{\frac{337}{190}}{\frac{4}{9}+\frac{6}{9}+\frac{56}{12}}$$

Since \frac{4}{9} and \frac{6}{9} have the same denominator, add them by adding their numerators.

$$\frac{\frac{337}{190}}{\frac{4+6}{9}+\frac{56}{12}}$$

Add 4 and 6 to get 10.

$$\frac{\frac{337}{190}}{\frac{10}{9}+\frac{56}{12}}$$

Reduce the fraction \frac{56}{12} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{337}{190}}{\frac{10}{9}+\frac{14}{3}}$$

Least common multiple of 9 and 3 is 9. Convert \frac{10}{9} and \frac{14}{3} to fractions with denominator 9.

$$\frac{\frac{337}{190}}{\frac{10}{9}+\frac{42}{9}}$$

Since \frac{10}{9} and \frac{42}{9} have the same denominator, add them by adding their numerators.

$$\frac{\frac{337}{190}}{\frac{10+42}{9}}$$

Add 10 and 42 to get 52.

$$\frac{\frac{337}{190}}{\frac{52}{9}}$$

Divide \frac{337}{190} by \frac{52}{9} by multiplying \frac{337}{190} by the reciprocal of \frac{52}{9}.

$$\frac{337}{190}\times \frac{9}{52}$$

Multiply \frac{337}{190} times \frac{9}{52} by multiplying numerator times numerator and denominator times denominator.

$$\frac{337\times 9}{190\times 52}$$

Do the multiplications in the fraction \frac{337\times 9}{190\times 52}.

$$\frac{3033}{9880}$$

Factor

$$\frac{3 ^ {2} \cdot 337}{2 ^ {3} \cdot 5 \cdot 13 \cdot 19} = 0.3069838056680162$$