Solve 4/7+1/2*(3-2/5)div5/8*(frac{1}{4}-3)

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

Evaluate

$$-\frac{901}{175}\approx -5.148571429$$

Solution Steps

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

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

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

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

Subtract 2 from 15 to get 13.

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

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

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

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

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

Divide \frac{13}{10} by \frac{5}{8} by multiplying \frac{13}{10} by the reciprocal of \frac{5}{8}.

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

Multiply \frac{13}{10} times \frac{8}{5} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{13\times 8}{10\times 5}.

$$\frac{4}{7}+\frac{104}{50}\left(\frac{1}{4}-3\right)$$

Reduce the fraction \frac{104}{50} to lowest terms by extracting and canceling out 2.

$$\frac{4}{7}+\frac{52}{25}\left(\frac{1}{4}-3\right)$$

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

$$\frac{4}{7}+\frac{52}{25}\left(\frac{1}{4}-\frac{12}{4}\right)$$

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

$$\frac{4}{7}+\frac{52}{25}\times \frac{1-12}{4}$$

Subtract 12 from 1 to get -11.

$$\frac{4}{7}+\frac{52}{25}\left(-\frac{11}{4}\right)$$

Multiply \frac{52}{25} times -\frac{11}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4}{7}+\frac{52\left(-11\right)}{25\times 4}$$

Do the multiplications in the fraction \frac{52\left(-11\right)}{25\times 4}.

$$\frac{4}{7}+\frac{-572}{100}$$

Reduce the fraction \frac{-572}{100} to lowest terms by extracting and canceling out 4.

$$\frac{4}{7}-\frac{143}{25}$$

Least common multiple of 7 and 25 is 175. Convert \frac{4}{7} and \frac{143}{25} to fractions with denominator 175.

$$\frac{100}{175}-\frac{1001}{175}$$

Since \frac{100}{175} and \frac{1001}{175} have the same denominator, subtract them by subtracting their numerators.

$$\frac{100-1001}{175}$$

Subtract 1001 from 100 to get -901.

$$-\frac{901}{175}$$

Factor

$$-\frac{901}{175} = -5\frac{26}{175} = -5.148571428571429$$