Solve 21/17*(8/3-3/4)+151/12*frac{21}{17}

$$\frac { 21 } { 17 } \times ( \frac { 8 } { 3 } - \frac { 3 } { 4 } ) + 15 \frac { 1 } { 12 } \times \frac { 21 } { 17 }$$

Evaluate

$$21$$

Solution Steps

Least common multiple of 3 and 4 is 12. Convert \frac{8}{3} and \frac{3}{4} to fractions with denominator 12.

$$\frac{21}{17}\left(\frac{32}{12}-\frac{9}{12}\right)+\frac{15\times 12+1}{12}\times \frac{21}{17}$$

Since \frac{32}{12} and \frac{9}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{21}{17}\times \frac{32-9}{12}+\frac{15\times 12+1}{12}\times \frac{21}{17}$$

Subtract 9 from 32 to get 23.

$$\frac{21}{17}\times \frac{23}{12}+\frac{15\times 12+1}{12}\times \frac{21}{17}$$

Multiply \frac{21}{17} times \frac{23}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{21\times 23}{17\times 12}+\frac{15\times 12+1}{12}\times \frac{21}{17}$$

Do the multiplications in the fraction \frac{21\times 23}{17\times 12}.

$$\frac{483}{204}+\frac{15\times 12+1}{12}\times \frac{21}{17}$$

Reduce the fraction \frac{483}{204} to lowest terms by extracting and canceling out 3.

$$\frac{161}{68}+\frac{15\times 12+1}{12}\times \frac{21}{17}$$

Multiply 15 and 12 to get 180.

$$\frac{161}{68}+\frac{180+1}{12}\times \frac{21}{17}$$

Add 180 and 1 to get 181.

$$\frac{161}{68}+\frac{181}{12}\times \frac{21}{17}$$

Multiply \frac{181}{12} times \frac{21}{17} by multiplying numerator times numerator and denominator times denominator.

$$\frac{161}{68}+\frac{181\times 21}{12\times 17}$$

Do the multiplications in the fraction \frac{181\times 21}{12\times 17}.

$$\frac{161}{68}+\frac{3801}{204}$$

Reduce the fraction \frac{3801}{204} to lowest terms by extracting and canceling out 3.

$$\frac{161}{68}+\frac{1267}{68}$$

Since \frac{161}{68} and \frac{1267}{68} have the same denominator, add them by adding their numerators.

$$\frac{161+1267}{68}$$

Add 161 and 1267 to get 1428.

$$\frac{1428}{68}$$

Divide 1428 by 68 to get 21.

$$21$$

Factor

$$3\times 7$$