Solve 17/3-10/3div8/34/5+frac{11}{5}+frac{11}{4}

$$\frac{ 17 }{ 3 } - \frac{ 10 }{ 3 } \div \frac{ 8 }{ 3 } \frac{ 4 }{ 5 } + \frac{ 11 }{ 5 } + \frac{ 11 }{ 4 }$$

Evaluate

$$\frac{577}{60}\approx 9.616666667$$

Solution Steps

Divide \frac{10}{3} by \frac{8}{3} by multiplying \frac{10}{3} by the reciprocal of \frac{8}{3}.

$$\frac{17}{3}-\frac{10}{3}\times \frac{3}{8}\times \frac{4}{5}+\frac{11}{5}+\frac{11}{4}$$

Multiply \frac{10}{3} times \frac{3}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{17}{3}-\frac{10\times 3}{3\times 8}\times \frac{4}{5}+\frac{11}{5}+\frac{11}{4}$$

Cancel out 3 in both numerator and denominator.

$$\frac{17}{3}-\frac{10}{8}\times \frac{4}{5}+\frac{11}{5}+\frac{11}{4}$$

Reduce the fraction \frac{10}{8} to lowest terms by extracting and canceling out 2.

$$\frac{17}{3}-\frac{5}{4}\times \frac{4}{5}+\frac{11}{5}+\frac{11}{4}$$

Cancel out \frac{5}{4} and its reciprocal \frac{4}{5}.

$$\frac{17}{3}-1+\frac{11}{5}+\frac{11}{4}$$

Convert 1 to fraction \frac{3}{3}.

$$\frac{17}{3}-\frac{3}{3}+\frac{11}{5}+\frac{11}{4}$$

Since \frac{17}{3} and \frac{3}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{17-3}{3}+\frac{11}{5}+\frac{11}{4}$$

Subtract 3 from 17 to get 14.

$$\frac{14}{3}+\frac{11}{5}+\frac{11}{4}$$

Least common multiple of 3 and 5 is 15. Convert \frac{14}{3} and \frac{11}{5} to fractions with denominator 15.

$$\frac{70}{15}+\frac{33}{15}+\frac{11}{4}$$

Since \frac{70}{15} and \frac{33}{15} have the same denominator, add them by adding their numerators.

$$\frac{70+33}{15}+\frac{11}{4}$$

Add 70 and 33 to get 103.

$$\frac{103}{15}+\frac{11}{4}$$

Least common multiple of 15 and 4 is 60. Convert \frac{103}{15} and \frac{11}{4} to fractions with denominator 60.

$$\frac{412}{60}+\frac{165}{60}$$

Since \frac{412}{60} and \frac{165}{60} have the same denominator, add them by adding their numerators.

$$\frac{412+165}{60}$$

Add 412 and 165 to get 577.

$$\frac{577}{60}$$

Factor

$$\frac{577}{2 ^ {2} \cdot 3 \cdot 5} = 9\frac{37}{60} = 9.616666666666667$$