Solve 4/7+1/2*(3-2/5)/25+frac{1{4}*(1-3)}divfrac{5}{8}*(frac{1}{4}-3)

$$\frac { \frac { 4 } { 7 } + \frac { 1 } { 2 } \cdot ( 3 - \frac { 2 } { 5 } ) } { 25 + \frac { 1 } { 4 } \cdot ( 1 - 3 ) } \div \frac { 5 } { 8 } \cdot ( \frac { 1 } { 4 } - 3 )$$

Evaluate

$$-\frac{2882}{8575}\approx -0.336093294$$

Solution Steps

Divide \frac{\frac{4}{7}+\frac{1}{2}\left(3-\frac{2}{5}\right)}{25+\frac{1}{4}\left(1-3\right)} by \frac{5}{8} by multiplying \frac{\frac{4}{7}+\frac{1}{2}\left(3-\frac{2}{5}\right)}{25+\frac{1}{4}\left(1-3\right)} by the reciprocal of \frac{5}{8}.

$$\frac{\left(\frac{4}{7}+\frac{1}{2}\left(3-\frac{2}{5}\right)\right)\times 8}{\left(25+\frac{1}{4}\left(1-3\right)\right)\times 5}\left(\frac{1}{4}-3\right)$$

Convert 3 to fraction \frac{15}{5}.

$$\frac{\left(\frac{4}{7}+\frac{1}{2}\left(\frac{15}{5}-\frac{2}{5}\right)\right)\times 8}{\left(25+\frac{1}{4}\left(1-3\right)\right)\times 5}\left(\frac{1}{4}-3\right)$$

Since \frac{15}{5} and \frac{2}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(\frac{4}{7}+\frac{1}{2}\times \frac{15-2}{5}\right)\times 8}{\left(25+\frac{1}{4}\left(1-3\right)\right)\times 5}\left(\frac{1}{4}-3\right)$$

Subtract 2 from 15 to get 13.

$$\frac{\left(\frac{4}{7}+\frac{1}{2}\times \frac{13}{5}\right)\times 8}{\left(25+\frac{1}{4}\left(1-3\right)\right)\times 5}\left(\frac{1}{4}-3\right)$$

Multiply \frac{1}{2} times \frac{13}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(\frac{4}{7}+\frac{1\times 13}{2\times 5}\right)\times 8}{\left(25+\frac{1}{4}\left(1-3\right)\right)\times 5}\left(\frac{1}{4}-3\right)$$

Do the multiplications in the fraction \frac{1\times 13}{2\times 5}.

$$\frac{\left(\frac{4}{7}+\frac{13}{10}\right)\times 8}{\left(25+\frac{1}{4}\left(1-3\right)\right)\times 5}\left(\frac{1}{4}-3\right)$$

Least common multiple of 7 and 10 is 70. Convert \frac{4}{7} and \frac{13}{10} to fractions with denominator 70.

$$\frac{\left(\frac{40}{70}+\frac{91}{70}\right)\times 8}{\left(25+\frac{1}{4}\left(1-3\right)\right)\times 5}\left(\frac{1}{4}-3\right)$$

Since \frac{40}{70} and \frac{91}{70} have the same denominator, add them by adding their numerators.

$$\frac{\frac{40+91}{70}\times 8}{\left(25+\frac{1}{4}\left(1-3\right)\right)\times 5}\left(\frac{1}{4}-3\right)$$

Add 40 and 91 to get 131.

$$\frac{\frac{131}{70}\times 8}{\left(25+\frac{1}{4}\left(1-3\right)\right)\times 5}\left(\frac{1}{4}-3\right)$$

Express \frac{131}{70}\times 8 as a single fraction.

$$\frac{\frac{131\times 8}{70}}{\left(25+\frac{1}{4}\left(1-3\right)\right)\times 5}\left(\frac{1}{4}-3\right)$$

Multiply 131 and 8 to get 1048.

$$\frac{\frac{1048}{70}}{\left(25+\frac{1}{4}\left(1-3\right)\right)\times 5}\left(\frac{1}{4}-3\right)$$

Reduce the fraction \frac{1048}{70} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{524}{35}}{\left(25+\frac{1}{4}\left(1-3\right)\right)\times 5}\left(\frac{1}{4}-3\right)$$

Subtract 3 from 1 to get -2.

$$\frac{\frac{524}{35}}{\left(25+\frac{1}{4}\left(-2\right)\right)\times 5}\left(\frac{1}{4}-3\right)$$

Multiply \frac{1}{4} and -2 to get \frac{-2}{4}.

$$\frac{\frac{524}{35}}{\left(25+\frac{-2}{4}\right)\times 5}\left(\frac{1}{4}-3\right)$$

Reduce the fraction \frac{-2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{524}{35}}{\left(25-\frac{1}{2}\right)\times 5}\left(\frac{1}{4}-3\right)$$

Convert 25 to fraction \frac{50}{2}.

$$\frac{\frac{524}{35}}{\left(\frac{50}{2}-\frac{1}{2}\right)\times 5}\left(\frac{1}{4}-3\right)$$

Since \frac{50}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{524}{35}}{\frac{50-1}{2}\times 5}\left(\frac{1}{4}-3\right)$$

Subtract 1 from 50 to get 49.

$$\frac{\frac{524}{35}}{\frac{49}{2}\times 5}\left(\frac{1}{4}-3\right)$$

Express \frac{49}{2}\times 5 as a single fraction.

$$\frac{\frac{524}{35}}{\frac{49\times 5}{2}}\left(\frac{1}{4}-3\right)$$

Multiply 49 and 5 to get 245.

$$\frac{\frac{524}{35}}{\frac{245}{2}}\left(\frac{1}{4}-3\right)$$

Divide \frac{524}{35} by \frac{245}{2} by multiplying \frac{524}{35} by the reciprocal of \frac{245}{2}.

$$\frac{524}{35}\times \frac{2}{245}\left(\frac{1}{4}-3\right)$$

Multiply \frac{524}{35} times \frac{2}{245} by multiplying numerator times numerator and denominator times denominator.

$$\frac{524\times 2}{35\times 245}\left(\frac{1}{4}-3\right)$$

Do the multiplications in the fraction \frac{524\times 2}{35\times 245}.

$$\frac{1048}{8575}\left(\frac{1}{4}-3\right)$$

Convert 3 to fraction \frac{12}{4}.

$$\frac{1048}{8575}\left(\frac{1}{4}-\frac{12}{4}\right)$$

Since \frac{1}{4} and \frac{12}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1048}{8575}\times \frac{1-12}{4}$$

Subtract 12 from 1 to get -11.

$$\frac{1048}{8575}\left(-\frac{11}{4}\right)$$

Multiply \frac{1048}{8575} times -\frac{11}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1048\left(-11\right)}{8575\times 4}$$

Do the multiplications in the fraction \frac{1048\left(-11\right)}{8575\times 4}.

$$\frac{-11528}{34300}$$

Reduce the fraction \frac{-11528}{34300} to lowest terms by extracting and canceling out 4.

$$-\frac{2882}{8575}$$

Factor

$$-\frac{2882}{8575} = -0.3360932944606414$$