Solve [13/8-(5/5+5/7)]*3/4

$$[ \frac { 13 } { 8 } - ( \frac { 5 } { 5 } + \frac { 5 } { 7 } ) ] \times \frac { 3 } { 4 }$$

Evaluate

$$-\frac{15}{224}\approx -0.066964286$$

Solution Steps

Divide 5 by 5 to get 1.

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

Convert 1 to fraction \frac{7}{7}.

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

Since \frac{7}{7} and \frac{5}{7} have the same denominator, add them by adding their numerators.

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

Add 7 and 5 to get 12.

$$\left(\frac{13}{8}-\frac{12}{7}\right)\times \frac{3}{4}$$

Least common multiple of 8 and 7 is 56. Convert \frac{13}{8} and \frac{12}{7} to fractions with denominator 56.

$$\left(\frac{91}{56}-\frac{96}{56}\right)\times \frac{3}{4}$$

Since \frac{91}{56} and \frac{96}{56} have the same denominator, subtract them by subtracting their numerators.

$$\frac{91-96}{56}\times \frac{3}{4}$$

Subtract 96 from 91 to get -5.

$$-\frac{5}{56}\times \frac{3}{4}$$

Multiply -\frac{5}{56} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-5\times 3}{56\times 4}$$

Do the multiplications in the fraction \frac{-5\times 3}{56\times 4}.

$$\frac{-15}{224}$$

Fraction \frac{-15}{224} can be rewritten as -\frac{15}{224} by extracting the negative sign.

$$-\frac{15}{224}$$

Factor

$$-\frac{15}{224} = -0.06696428571428571$$