Solve [1/3+1/2(1/2-1/4)+5]-3[4div(frac{3}{5}+1)]

$$[ \frac { 1 } { 3 } + \frac { 1 } { 2 } ( \frac { 1 } { 2 } - \frac { 1 } { 4 } ) + 5 ] - 3 [ 4 \div ( \frac { 3 } { 5 } + 1 ) ]$$

Evaluate

$$-\frac{49}{24}\approx -2.041666667$$

Solution Steps

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

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

Since \frac{2}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{3}+\frac{1}{2}\times \frac{2-1}{4}+5-3\times \frac{4}{\frac{3}{5}+1}$$

Subtract 1 from 2 to get 1.

$$\frac{1}{3}+\frac{1}{2}\times \frac{1}{4}+5-3\times \frac{4}{\frac{3}{5}+1}$$

Multiply \frac{1}{2} times \frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{3}+\frac{1\times 1}{2\times 4}+5-3\times \frac{4}{\frac{3}{5}+1}$$

Do the multiplications in the fraction \frac{1\times 1}{2\times 4}.

$$\frac{1}{3}+\frac{1}{8}+5-3\times \frac{4}{\frac{3}{5}+1}$$

Least common multiple of 3 and 8 is 24. Convert \frac{1}{3} and \frac{1}{8} to fractions with denominator 24.

$$\frac{8}{24}+\frac{3}{24}+5-3\times \frac{4}{\frac{3}{5}+1}$$

Since \frac{8}{24} and \frac{3}{24} have the same denominator, add them by adding their numerators.

$$\frac{8+3}{24}+5-3\times \frac{4}{\frac{3}{5}+1}$$

Add 8 and 3 to get 11.

$$\frac{11}{24}+5-3\times \frac{4}{\frac{3}{5}+1}$$

Convert 5 to fraction \frac{120}{24}.

$$\frac{11}{24}+\frac{120}{24}-3\times \frac{4}{\frac{3}{5}+1}$$

Since \frac{11}{24} and \frac{120}{24} have the same denominator, add them by adding their numerators.

$$\frac{11+120}{24}-3\times \frac{4}{\frac{3}{5}+1}$$

Add 11 and 120 to get 131.

$$\frac{131}{24}-3\times \frac{4}{\frac{3}{5}+1}$$

Convert 1 to fraction \frac{5}{5}.

$$\frac{131}{24}-3\times \frac{4}{\frac{3}{5}+\frac{5}{5}}$$

Since \frac{3}{5} and \frac{5}{5} have the same denominator, add them by adding their numerators.

$$\frac{131}{24}-3\times \frac{4}{\frac{3+5}{5}}$$

Add 3 and 5 to get 8.

$$\frac{131}{24}-3\times \frac{4}{\frac{8}{5}}$$

Divide 4 by \frac{8}{5} by multiplying 4 by the reciprocal of \frac{8}{5}.

$$\frac{131}{24}-3\times 4\times \frac{5}{8}$$

Express 4\times \frac{5}{8} as a single fraction.

$$\frac{131}{24}-3\times \frac{4\times 5}{8}$$

Multiply 4 and 5 to get 20.

$$\frac{131}{24}-3\times \frac{20}{8}$$

Reduce the fraction \frac{20}{8} to lowest terms by extracting and canceling out 4.

$$\frac{131}{24}-3\times \frac{5}{2}$$

Express 3\times \frac{5}{2} as a single fraction.

$$\frac{131}{24}-\frac{3\times 5}{2}$$

Multiply 3 and 5 to get 15.

$$\frac{131}{24}-\frac{15}{2}$$

Least common multiple of 24 and 2 is 24. Convert \frac{131}{24} and \frac{15}{2} to fractions with denominator 24.

$$\frac{131}{24}-\frac{180}{24}$$

Since \frac{131}{24} and \frac{180}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{131-180}{24}$$

Subtract 180 from 131 to get -49.

$$-\frac{49}{24}$$

Factor

$$-\frac{49}{24} = -2\frac{1}{24} = -2.0416666666666665$$