Solve -1/3*(0.5+2/5)-3/4=

$$- \frac { 1 } { 3 } \cdot ( 0.5 + \frac { 2 } { 5 } ) - \frac { 3 } { 4 } =$$

Evaluate

$$-1.05$$

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.

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

Least common multiple of 2 and 5 is 10. Convert \frac{1}{2} and \frac{2}{5} to fractions with denominator 10.

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

Since \frac{5}{10} and \frac{4}{10} have the same denominator, add them by adding their numerators.

$$-\frac{1}{3}\times \frac{5+4}{10}-\frac{3}{4}$$

Add 5 and 4 to get 9.

$$-\frac{1}{3}\times \frac{9}{10}-\frac{3}{4}$$

Multiply -\frac{1}{3} times \frac{9}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-9}{3\times 10}-\frac{3}{4}$$

Do the multiplications in the fraction \frac{-9}{3\times 10}.

$$\frac{-9}{30}-\frac{3}{4}$$

Reduce the fraction \frac{-9}{30} to lowest terms by extracting and canceling out 3.

$$-\frac{3}{10}-\frac{3}{4}$$

Least common multiple of 10 and 4 is 20. Convert -\frac{3}{10} and \frac{3}{4} to fractions with denominator 20.

$$-\frac{6}{20}-\frac{15}{20}$$

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

$$\frac{-6-15}{20}$$

Subtract 15 from -6 to get -21.

$$-\frac{21}{20}$$

Factor

$$-1.05$$