Solve (83/8+12/5*10/9-35/12)

$$( \frac { 83 } { 8 } + \frac { 12 } { 5 } \cdot \frac { 10 } { 9 } - \frac { 35 } { 12 } )$$

Evaluate

$$\frac{81}{8}=10.125$$

Solution Steps

Multiply \frac{12}{5} times \frac{10}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{83}{8}+\frac{12\times 10}{5\times 9}-\frac{35}{12}$$

Do the multiplications in the fraction \frac{12\times 10}{5\times 9}.

$$\frac{83}{8}+\frac{120}{45}-\frac{35}{12}$$

Reduce the fraction \frac{120}{45} to lowest terms by extracting and canceling out 15.

$$\frac{83}{8}+\frac{8}{3}-\frac{35}{12}$$

Least common multiple of 8 and 3 is 24. Convert \frac{83}{8} and \frac{8}{3} to fractions with denominator 24.

$$\frac{249}{24}+\frac{64}{24}-\frac{35}{12}$$

Since \frac{249}{24} and \frac{64}{24} have the same denominator, add them by adding their numerators.

$$\frac{249+64}{24}-\frac{35}{12}$$

Add 249 and 64 to get 313.

$$\frac{313}{24}-\frac{35}{12}$$

Least common multiple of 24 and 12 is 24. Convert \frac{313}{24} and \frac{35}{12} to fractions with denominator 24.

$$\frac{313}{24}-\frac{70}{24}$$

Since \frac{313}{24} and \frac{70}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{313-70}{24}$$

Subtract 70 from 313 to get 243.

$$\frac{243}{24}$$

Reduce the fraction \frac{243}{24} to lowest terms by extracting and canceling out 3.

$$\frac{81}{8}$$

Factor

$$\frac{3 ^ {4}}{2 ^ {3}} = 10\frac{1}{8} = 10.125$$