Solve 5/3-1/4/frac{9{10}+13/15}

$$\frac { \frac { 5 } { 3 } - \frac { 1 } { 4 } } { \frac { 9 } { 10 } + \frac { 13 } { 15 } }$$

Evaluate

$$\frac{85}{106}\approx 0.801886792$$

Solution Steps

Least common multiple of 3 and 4 is 12. Convert \frac{5}{3} and \frac{1}{4} to fractions with denominator 12.

$$\frac{\frac{20}{12}-\frac{3}{12}}{\frac{9}{10}+\frac{13}{15}}$$

Since \frac{20}{12} and \frac{3}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{20-3}{12}}{\frac{9}{10}+\frac{13}{15}}$$

Subtract 3 from 20 to get 17.

$$\frac{\frac{17}{12}}{\frac{9}{10}+\frac{13}{15}}$$

Least common multiple of 10 and 15 is 30. Convert \frac{9}{10} and \frac{13}{15} to fractions with denominator 30.

$$\frac{\frac{17}{12}}{\frac{27}{30}+\frac{26}{30}}$$

Since \frac{27}{30} and \frac{26}{30} have the same denominator, add them by adding their numerators.

$$\frac{\frac{17}{12}}{\frac{27+26}{30}}$$

Add 27 and 26 to get 53.

$$\frac{\frac{17}{12}}{\frac{53}{30}}$$

Divide \frac{17}{12} by \frac{53}{30} by multiplying \frac{17}{12} by the reciprocal of \frac{53}{30}.

$$\frac{17}{12}\times \frac{30}{53}$$

Multiply \frac{17}{12} times \frac{30}{53} by multiplying numerator times numerator and denominator times denominator.

$$\frac{17\times 30}{12\times 53}$$

Do the multiplications in the fraction \frac{17\times 30}{12\times 53}.

$$\frac{510}{636}$$

Reduce the fraction \frac{510}{636} to lowest terms by extracting and canceling out 6.

$$\frac{85}{106}$$

Factor

$$\frac{5 \cdot 17}{2 \cdot 53} = 0.8018867924528302$$