Solve (5/6-1/5):(-15)-(-5/8):(1+1-3/2)-(frac{16}{5}+30):(-frac{7}{4})

$$( \frac { 5 } { 6 } - \frac { 1 } { 5 } ) : ( - 15 ) - ( - \frac { 5 } { 8 } ) : ( 1 + 1 - \frac { 3 } { 2 } ) - ( \frac { 16 } { 5 } + 30 ) : ( - \frac { 7 } { 4 } )$$

Evaluate

$$\frac{127129}{6300}\approx 20.179206349$$

Solution Steps

Least common multiple of 6 and 5 is 30. Convert \frac{5}{6} and \frac{1}{5} to fractions with denominator 30.

$$\frac{\frac{25}{30}-\frac{6}{30}}{-15}-\frac{-\frac{5}{8}}{1+1-\frac{3}{2}}-\frac{\frac{16}{5}+30}{-\frac{7}{4}}$$

Since \frac{25}{30} and \frac{6}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{25-6}{30}}{-15}-\frac{-\frac{5}{8}}{1+1-\frac{3}{2}}-\frac{\frac{16}{5}+30}{-\frac{7}{4}}$$

Subtract 6 from 25 to get 19.

$$\frac{\frac{19}{30}}{-15}-\frac{-\frac{5}{8}}{1+1-\frac{3}{2}}-\frac{\frac{16}{5}+30}{-\frac{7}{4}}$$

Express \frac{\frac{19}{30}}{-15} as a single fraction.

$$\frac{19}{30\left(-15\right)}-\frac{-\frac{5}{8}}{1+1-\frac{3}{2}}-\frac{\frac{16}{5}+30}{-\frac{7}{4}}$$

Multiply 30 and -15 to get -450.

$$\frac{19}{-450}-\frac{-\frac{5}{8}}{1+1-\frac{3}{2}}-\frac{\frac{16}{5}+30}{-\frac{7}{4}}$$

Fraction \frac{19}{-450} can be rewritten as -\frac{19}{450} by extracting the negative sign.

$$-\frac{19}{450}-\frac{-\frac{5}{8}}{1+1-\frac{3}{2}}-\frac{\frac{16}{5}+30}{-\frac{7}{4}}$$

Add 1 and 1 to get 2.

$$-\frac{19}{450}-\frac{-\frac{5}{8}}{2-\frac{3}{2}}-\frac{\frac{16}{5}+30}{-\frac{7}{4}}$$

Convert 2 to fraction \frac{4}{2}.

$$-\frac{19}{450}-\frac{-\frac{5}{8}}{\frac{4}{2}-\frac{3}{2}}-\frac{\frac{16}{5}+30}{-\frac{7}{4}}$$

Since \frac{4}{2} and \frac{3}{2} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{19}{450}-\frac{-\frac{5}{8}}{\frac{4-3}{2}}-\frac{\frac{16}{5}+30}{-\frac{7}{4}}$$

Subtract 3 from 4 to get 1.

$$-\frac{19}{450}-\frac{-\frac{5}{8}}{\frac{1}{2}}-\frac{\frac{16}{5}+30}{-\frac{7}{4}}$$

Divide -\frac{5}{8} by \frac{1}{2} by multiplying -\frac{5}{8} by the reciprocal of \frac{1}{2}.

$$-\frac{19}{450}-\left(-\frac{5}{8}\times 2\right)-\frac{\frac{16}{5}+30}{-\frac{7}{4}}$$

Express -\frac{5}{8}\times 2 as a single fraction.

$$-\frac{19}{450}-\frac{-5\times 2}{8}-\frac{\frac{16}{5}+30}{-\frac{7}{4}}$$

Multiply -5 and 2 to get -10.

$$-\frac{19}{450}-\frac{-10}{8}-\frac{\frac{16}{5}+30}{-\frac{7}{4}}$$

Reduce the fraction \frac{-10}{8} to lowest terms by extracting and canceling out 2.

$$-\frac{19}{450}-\left(-\frac{5}{4}\right)-\frac{\frac{16}{5}+30}{-\frac{7}{4}}$$

The opposite of -\frac{5}{4} is \frac{5}{4}.

$$-\frac{19}{450}+\frac{5}{4}-\frac{\frac{16}{5}+30}{-\frac{7}{4}}$$

Least common multiple of 450 and 4 is 900. Convert -\frac{19}{450} and \frac{5}{4} to fractions with denominator 900.

$$-\frac{38}{900}+\frac{1125}{900}-\frac{\frac{16}{5}+30}{-\frac{7}{4}}$$

Since -\frac{38}{900} and \frac{1125}{900} have the same denominator, add them by adding their numerators.

$$\frac{-38+1125}{900}-\frac{\frac{16}{5}+30}{-\frac{7}{4}}$$

Add -38 and 1125 to get 1087.

$$\frac{1087}{900}-\frac{\frac{16}{5}+30}{-\frac{7}{4}}$$

Convert 30 to fraction \frac{150}{5}.

$$\frac{1087}{900}-\frac{\frac{16}{5}+\frac{150}{5}}{-\frac{7}{4}}$$

Since \frac{16}{5} and \frac{150}{5} have the same denominator, add them by adding their numerators.

$$\frac{1087}{900}-\frac{\frac{16+150}{5}}{-\frac{7}{4}}$$

Add 16 and 150 to get 166.

$$\frac{1087}{900}-\frac{\frac{166}{5}}{-\frac{7}{4}}$$

Divide \frac{166}{5} by -\frac{7}{4} by multiplying \frac{166}{5} by the reciprocal of -\frac{7}{4}.

$$\frac{1087}{900}-\frac{166}{5}\left(-\frac{4}{7}\right)$$

Multiply \frac{166}{5} times -\frac{4}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1087}{900}-\frac{166\left(-4\right)}{5\times 7}$$

Do the multiplications in the fraction \frac{166\left(-4\right)}{5\times 7}.

$$\frac{1087}{900}-\frac{-664}{35}$$

Fraction \frac{-664}{35} can be rewritten as -\frac{664}{35} by extracting the negative sign.

$$\frac{1087}{900}-\left(-\frac{664}{35}\right)$$

The opposite of -\frac{664}{35} is \frac{664}{35}.

$$\frac{1087}{900}+\frac{664}{35}$$

Least common multiple of 900 and 35 is 6300. Convert \frac{1087}{900} and \frac{664}{35} to fractions with denominator 6300.

$$\frac{7609}{6300}+\frac{119520}{6300}$$

Since \frac{7609}{6300} and \frac{119520}{6300} have the same denominator, add them by adding their numerators.

$$\frac{7609+119520}{6300}$$

Add 7609 and 119520 to get 127129.

$$\frac{127129}{6300}$$

Factor

$$\frac{19 \cdot 6691}{2 ^ {2} \cdot 3 ^ {2} \cdot 5 ^ {2} \cdot 7} = 20\frac{1129}{6300} = 20.17920634920635$$