Solve [2-(5/3-1.5)div17/12]*51/8

$$[ 2 - ( \frac { 5 } { 3 } - 1.5 ) \div \frac { 17 } { 12 } ] \times \frac { 51 } { 8 }$$

Evaluate

$$12$$

Solution Steps

Convert decimal number 1.5 to fraction \frac{15}{10}. Reduce the fraction \frac{15}{10} to lowest terms by extracting and canceling out 5.

$$\left(2-\frac{\frac{5}{3}-\frac{3}{2}}{\frac{17}{12}}\right)\times \frac{51}{8}$$

Least common multiple of 3 and 2 is 6. Convert \frac{5}{3} and \frac{3}{2} to fractions with denominator 6.

$$\left(2-\frac{\frac{10}{6}-\frac{9}{6}}{\frac{17}{12}}\right)\times \frac{51}{8}$$

Since \frac{10}{6} and \frac{9}{6} have the same denominator, subtract them by subtracting their numerators.

$$\left(2-\frac{\frac{10-9}{6}}{\frac{17}{12}}\right)\times \frac{51}{8}$$

Subtract 9 from 10 to get 1.

$$\left(2-\frac{\frac{1}{6}}{\frac{17}{12}}\right)\times \frac{51}{8}$$

Divide \frac{1}{6} by \frac{17}{12} by multiplying \frac{1}{6} by the reciprocal of \frac{17}{12}.

$$\left(2-\frac{1}{6}\times \frac{12}{17}\right)\times \frac{51}{8}$$

Multiply \frac{1}{6} times \frac{12}{17} by multiplying numerator times numerator and denominator times denominator.

$$\left(2-\frac{1\times 12}{6\times 17}\right)\times \frac{51}{8}$$

Do the multiplications in the fraction \frac{1\times 12}{6\times 17}.

$$\left(2-\frac{12}{102}\right)\times \frac{51}{8}$$

Reduce the fraction \frac{12}{102} to lowest terms by extracting and canceling out 6.

$$\left(2-\frac{2}{17}\right)\times \frac{51}{8}$$

Convert 2 to fraction \frac{34}{17}.

$$\left(\frac{34}{17}-\frac{2}{17}\right)\times \frac{51}{8}$$

Since \frac{34}{17} and \frac{2}{17} have the same denominator, subtract them by subtracting their numerators.

$$\frac{34-2}{17}\times \frac{51}{8}$$

Subtract 2 from 34 to get 32.

$$\frac{32}{17}\times \frac{51}{8}$$

Multiply \frac{32}{17} times \frac{51}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{32\times 51}{17\times 8}$$

Do the multiplications in the fraction \frac{32\times 51}{17\times 8}.

$$\frac{1632}{136}$$

Divide 1632 by 136 to get 12.

$$12$$

Factor

$$3\times 2^{2}$$