Solve (1/7-0,5)*(3+1/2)]:3/4-2/3}*1-frac{3}{4}

$$( \frac { 1 } { 7 } - 0,5 ) \cdot ( 3 + \frac { 1 } { 2 } ) ] : \frac { 3 } { 4 } - \frac { 2 } { 3 } \} \cdot 1 - \frac { 3 } { 4 }$$

Evaluate

$$-1.25$$

Solution Steps

Convert decimal number 0.5 to fraction \frac{5}{10}. Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$\left(\frac{1}{7}-\frac{1}{2}\right)\left(3+\frac{1}{2}\right)$$

Least common multiple of 7 and 2 is 14. Convert \frac{1}{7} and \frac{1}{2} to fractions with denominator 14.

$$\left(\frac{2}{14}-\frac{7}{14}\right)\left(3+\frac{1}{2}\right)$$

Since \frac{2}{14} and \frac{7}{14} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2-7}{14}\left(3+\frac{1}{2}\right)$$

Subtract 7 from 2 to get -5.

$$-\frac{5}{14}\left(3+\frac{1}{2}\right)$$

Convert 3 to fraction \frac{6}{2}.

$$-\frac{5}{14}\left(\frac{6}{2}+\frac{1}{2}\right)$$

Since \frac{6}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$-\frac{5}{14}\times \frac{6+1}{2}$$

Add 6 and 1 to get 7.

$$-\frac{5}{14}\times \frac{7}{2}$$

Multiply -\frac{5}{14} times \frac{7}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-5\times 7}{14\times 2}$$

Do the multiplications in the fraction \frac{-5\times 7}{14\times 2}.

$$\frac{-35}{28}$$

Reduce the fraction \frac{-35}{28} to lowest terms by extracting and canceling out 7.

$$-\frac{5}{4}$$

Factor

$$-1.25$$