Solve [(57/12-317/36)21/2-41/3*frac{3}{26}]frac{1}{2}

$$[ ( 5 \frac { 7 } { 12 } - 3 \frac { 17 } { 36 } ) 2 \frac { 1 } { 2 } - 4 \frac { 1 } { 3 } \cdot \frac { 3 } { 26 } ] \frac { 1 } { 2 }$$

Evaluate

$$\frac{43}{18}\approx 2.388888889$$

Solution Steps

Multiply 5 and 12 to get 60.

$$\left(\left(\frac{60+7}{12}-\frac{3\times 36+17}{36}\right)\times \frac{2\times 2+1}{2}-\frac{4\times 3+1}{3}\times \frac{3}{26}\right)\times \frac{1}{2}$$

Add 60 and 7 to get 67.

$$\left(\left(\frac{67}{12}-\frac{3\times 36+17}{36}\right)\times \frac{2\times 2+1}{2}-\frac{4\times 3+1}{3}\times \frac{3}{26}\right)\times \frac{1}{2}$$

Multiply 3 and 36 to get 108.

$$\left(\left(\frac{67}{12}-\frac{108+17}{36}\right)\times \frac{2\times 2+1}{2}-\frac{4\times 3+1}{3}\times \frac{3}{26}\right)\times \frac{1}{2}$$

Add 108 and 17 to get 125.

$$\left(\left(\frac{67}{12}-\frac{125}{36}\right)\times \frac{2\times 2+1}{2}-\frac{4\times 3+1}{3}\times \frac{3}{26}\right)\times \frac{1}{2}$$

Least common multiple of 12 and 36 is 36. Convert \frac{67}{12} and \frac{125}{36} to fractions with denominator 36.

$$\left(\left(\frac{201}{36}-\frac{125}{36}\right)\times \frac{2\times 2+1}{2}-\frac{4\times 3+1}{3}\times \frac{3}{26}\right)\times \frac{1}{2}$$

Since \frac{201}{36} and \frac{125}{36} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{201-125}{36}\times \frac{2\times 2+1}{2}-\frac{4\times 3+1}{3}\times \frac{3}{26}\right)\times \frac{1}{2}$$

Subtract 125 from 201 to get 76.

$$\left(\frac{76}{36}\times \frac{2\times 2+1}{2}-\frac{4\times 3+1}{3}\times \frac{3}{26}\right)\times \frac{1}{2}$$

Reduce the fraction \frac{76}{36} to lowest terms by extracting and canceling out 4.

$$\left(\frac{19}{9}\times \frac{2\times 2+1}{2}-\frac{4\times 3+1}{3}\times \frac{3}{26}\right)\times \frac{1}{2}$$

Multiply 2 and 2 to get 4.

$$\left(\frac{19}{9}\times \frac{4+1}{2}-\frac{4\times 3+1}{3}\times \frac{3}{26}\right)\times \frac{1}{2}$$

Add 4 and 1 to get 5.

$$\left(\frac{19}{9}\times \frac{5}{2}-\frac{4\times 3+1}{3}\times \frac{3}{26}\right)\times \frac{1}{2}$$

Multiply \frac{19}{9} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$\left(\frac{19\times 5}{9\times 2}-\frac{4\times 3+1}{3}\times \frac{3}{26}\right)\times \frac{1}{2}$$

Do the multiplications in the fraction \frac{19\times 5}{9\times 2}.

$$\left(\frac{95}{18}-\frac{4\times 3+1}{3}\times \frac{3}{26}\right)\times \frac{1}{2}$$

Multiply 4 and 3 to get 12.

$$\left(\frac{95}{18}-\frac{12+1}{3}\times \frac{3}{26}\right)\times \frac{1}{2}$$

Add 12 and 1 to get 13.

$$\left(\frac{95}{18}-\frac{13}{3}\times \frac{3}{26}\right)\times \frac{1}{2}$$

Multiply \frac{13}{3} times \frac{3}{26} by multiplying numerator times numerator and denominator times denominator.

$$\left(\frac{95}{18}-\frac{13\times 3}{3\times 26}\right)\times \frac{1}{2}$$

Cancel out 3 in both numerator and denominator.

$$\left(\frac{95}{18}-\frac{13}{26}\right)\times \frac{1}{2}$$

Reduce the fraction \frac{13}{26} to lowest terms by extracting and canceling out 13.

$$\left(\frac{95}{18}-\frac{1}{2}\right)\times \frac{1}{2}$$

Least common multiple of 18 and 2 is 18. Convert \frac{95}{18} and \frac{1}{2} to fractions with denominator 18.

$$\left(\frac{95}{18}-\frac{9}{18}\right)\times \frac{1}{2}$$

Since \frac{95}{18} and \frac{9}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{95-9}{18}\times \frac{1}{2}$$

Subtract 9 from 95 to get 86.

$$\frac{86}{18}\times \frac{1}{2}$$

Reduce the fraction \frac{86}{18} to lowest terms by extracting and canceling out 2.

$$\frac{43}{9}\times \frac{1}{2}$$

Multiply \frac{43}{9} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{43\times 1}{9\times 2}$$

Do the multiplications in the fraction \frac{43\times 1}{9\times 2}.

$$\frac{43}{18}$$

Factor

$$\frac{43}{2 \cdot 3 ^ {2}} = 2\frac{7}{18} = 2.388888888888889$$