Solve [(2+3/4*9/8)*9/2-7/2):frac{17}{4}-frac{6}{5}

$$[ ( 2 + \frac { 3 } { 4 } \cdot \frac { 9 } { 8 } ) \times \frac { 9 } { 2 } - \frac { 7 } { 2 } ) : \frac { 17 } { 4 } - \frac { 6 } { 5 }$$

Evaluate

$$\frac{79}{80}=0.9875$$

Solution Steps

Multiply \frac{3}{4} times \frac{9}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(2+\frac{3\times 9}{4\times 8}\right)\times \frac{9}{2}-\frac{7}{2}}{\frac{17}{4}}-\frac{6}{5}$$

Do the multiplications in the fraction \frac{3\times 9}{4\times 8}.

$$\frac{\left(2+\frac{27}{32}\right)\times \frac{9}{2}-\frac{7}{2}}{\frac{17}{4}}-\frac{6}{5}$$

Convert 2 to fraction \frac{64}{32}.

$$\frac{\left(\frac{64}{32}+\frac{27}{32}\right)\times \frac{9}{2}-\frac{7}{2}}{\frac{17}{4}}-\frac{6}{5}$$

Since \frac{64}{32} and \frac{27}{32} have the same denominator, add them by adding their numerators.

$$\frac{\frac{64+27}{32}\times \frac{9}{2}-\frac{7}{2}}{\frac{17}{4}}-\frac{6}{5}$$

Add 64 and 27 to get 91.

$$\frac{\frac{91}{32}\times \frac{9}{2}-\frac{7}{2}}{\frac{17}{4}}-\frac{6}{5}$$

Multiply \frac{91}{32} times \frac{9}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{91\times 9}{32\times 2}-\frac{7}{2}}{\frac{17}{4}}-\frac{6}{5}$$

Do the multiplications in the fraction \frac{91\times 9}{32\times 2}.

$$\frac{\frac{819}{64}-\frac{7}{2}}{\frac{17}{4}}-\frac{6}{5}$$

Least common multiple of 64 and 2 is 64. Convert \frac{819}{64} and \frac{7}{2} to fractions with denominator 64.

$$\frac{\frac{819}{64}-\frac{224}{64}}{\frac{17}{4}}-\frac{6}{5}$$

Since \frac{819}{64} and \frac{224}{64} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{819-224}{64}}{\frac{17}{4}}-\frac{6}{5}$$

Subtract 224 from 819 to get 595.

$$\frac{\frac{595}{64}}{\frac{17}{4}}-\frac{6}{5}$$

Divide \frac{595}{64} by \frac{17}{4} by multiplying \frac{595}{64} by the reciprocal of \frac{17}{4}.

$$\frac{595}{64}\times \frac{4}{17}-\frac{6}{5}$$

Multiply \frac{595}{64} times \frac{4}{17} by multiplying numerator times numerator and denominator times denominator.

$$\frac{595\times 4}{64\times 17}-\frac{6}{5}$$

Do the multiplications in the fraction \frac{595\times 4}{64\times 17}.

$$\frac{2380}{1088}-\frac{6}{5}$$

Reduce the fraction \frac{2380}{1088} to lowest terms by extracting and canceling out 68.

$$\frac{35}{16}-\frac{6}{5}$$

Least common multiple of 16 and 5 is 80. Convert \frac{35}{16} and \frac{6}{5} to fractions with denominator 80.

$$\frac{175}{80}-\frac{96}{80}$$

Since \frac{175}{80} and \frac{96}{80} have the same denominator, subtract them by subtracting their numerators.

$$\frac{175-96}{80}$$

Subtract 96 from 175 to get 79.

$$\frac{79}{80}$$

Factor

$$\frac{79}{2 ^ {4} \cdot 5} = 0.9875$$