Solve (1/2-3/4+7/8)*(4/3)+(5)*lfloorfrac{2}{5}-(frac{2}{5}*frac{10}{3})rfloor

$$( \frac{ 1 }{ 2 } - \frac{ 3 }{ 4 } + \frac{ 7 }{ 8 } ) \times ( \frac{ 4 }{ 3 } )+(5) \times \lfloor \frac{ 2 }{ 5 } -( \frac{ 2 }{ 5 } \times \frac{ 10 }{ 3 } ) \rfloor$$

Evaluate

$$-\frac{25}{6}\approx -4.166666667$$

Solution Steps

Least common multiple of 2 and 4 is 4. Convert \frac{1}{2} and \frac{3}{4} to fractions with denominator 4.

$$\left(\frac{2}{4}-\frac{3}{4}+\frac{7}{8}\right)\times \frac{4}{3}+5\lfloor \frac{2}{5}-\frac{2}{5}\times \frac{10}{3}\rfloor$$

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

$$\left(\frac{2-3}{4}+\frac{7}{8}\right)\times \frac{4}{3}+5\lfloor \frac{2}{5}-\frac{2}{5}\times \frac{10}{3}\rfloor$$

Subtract 3 from 2 to get -1.

$$\left(-\frac{1}{4}+\frac{7}{8}\right)\times \frac{4}{3}+5\lfloor \frac{2}{5}-\frac{2}{5}\times \frac{10}{3}\rfloor$$

Least common multiple of 4 and 8 is 8. Convert -\frac{1}{4} and \frac{7}{8} to fractions with denominator 8.

$$\left(-\frac{2}{8}+\frac{7}{8}\right)\times \frac{4}{3}+5\lfloor \frac{2}{5}-\frac{2}{5}\times \frac{10}{3}\rfloor$$

Since -\frac{2}{8} and \frac{7}{8} have the same denominator, add them by adding their numerators.

$$\frac{-2+7}{8}\times \frac{4}{3}+5\lfloor \frac{2}{5}-\frac{2}{5}\times \frac{10}{3}\rfloor$$

Add -2 and 7 to get 5.

$$\frac{5}{8}\times \frac{4}{3}+5\lfloor \frac{2}{5}-\frac{2}{5}\times \frac{10}{3}\rfloor$$

Multiply \frac{5}{8} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 4}{8\times 3}+5\lfloor \frac{2}{5}-\frac{2}{5}\times \frac{10}{3}\rfloor$$

Do the multiplications in the fraction \frac{5\times 4}{8\times 3}.

$$\frac{20}{24}+5\lfloor \frac{2}{5}-\frac{2}{5}\times \frac{10}{3}\rfloor$$

Reduce the fraction \frac{20}{24} to lowest terms by extracting and canceling out 4.

$$\frac{5}{6}+5\lfloor \frac{2}{5}-\frac{2}{5}\times \frac{10}{3}\rfloor$$

Multiply \frac{2}{5} times \frac{10}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5}{6}+5\lfloor \frac{2}{5}-\frac{2\times 10}{5\times 3}\rfloor$$

Do the multiplications in the fraction \frac{2\times 10}{5\times 3}.

$$\frac{5}{6}+5\lfloor \frac{2}{5}-\frac{20}{15}\rfloor$$

Reduce the fraction \frac{20}{15} to lowest terms by extracting and canceling out 5.

$$\frac{5}{6}+5\lfloor \frac{2}{5}-\frac{4}{3}\rfloor$$

Least common multiple of 5 and 3 is 15. Convert \frac{2}{5} and \frac{4}{3} to fractions with denominator 15.

$$\frac{5}{6}+5\lfloor \frac{6}{15}-\frac{20}{15}\rfloor$$

Since \frac{6}{15} and \frac{20}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{6}+5\lfloor \frac{6-20}{15}\rfloor$$

Subtract 20 from 6 to get -14.

$$\frac{5}{6}+5\lfloor -\frac{14}{15}\rfloor$$

Dividing -14 by 15 gives -1 and remainder 1. Rewrite -\frac{14}{15} as -1+\frac{1}{15}.

$$\frac{5}{6}+5\lfloor -1+\frac{1}{15}\rfloor$$

The floor of a real number a is the largest integer number less than or equal to a. The floor of -1+\frac{1}{15} is -1.

$$\frac{5}{6}+5\left(-1\right)$$

Multiply 5 and -1 to get -5.

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

Convert 5 to fraction \frac{30}{6}.

$$\frac{5}{6}-\frac{30}{6}$$

Since \frac{5}{6} and \frac{30}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5-30}{6}$$

Subtract 30 from 5 to get -25.

$$-\frac{25}{6}$$

Factor

$$-\frac{25}{6} = -4\frac{1}{6} = -4.166666666666667$$