Solve [3/4+1/6-2/3(4/5divfrac{5}{10})]+frac{1}{3}

$$[ \frac { 3 } { 4 } + \frac { 1 } { 6 } - \frac { 2 } { 3 } ( \frac { 4 } { 5 } \div \frac { 5 } { 10 } ) ] + \frac { 1 } { 3 }$$

Evaluate

$$\frac{11}{60}\approx 0.183333333$$

Solution Steps

Least common multiple of 4 and 6 is 12. Convert \frac{3}{4} and \frac{1}{6} to fractions with denominator 12.

$$\frac{9}{12}+\frac{2}{12}-\frac{2}{3}\times \frac{\frac{4}{5}}{\frac{5}{10}}+\frac{1}{3}$$

Since \frac{9}{12} and \frac{2}{12} have the same denominator, add them by adding their numerators.

$$\frac{9+2}{12}-\frac{2}{3}\times \frac{\frac{4}{5}}{\frac{5}{10}}+\frac{1}{3}$$

Add 9 and 2 to get 11.

$$\frac{11}{12}-\frac{2}{3}\times \frac{\frac{4}{5}}{\frac{5}{10}}+\frac{1}{3}$$

Divide \frac{4}{5} by \frac{5}{10} by multiplying \frac{4}{5} by the reciprocal of \frac{5}{10}.

$$\frac{11}{12}-\frac{2}{3}\times \frac{4\times 10}{5\times 5}+\frac{1}{3}$$

Cancel out 5 in both numerator and denominator.

$$\frac{11}{12}-\frac{2}{3}\times \frac{2\times 4}{5}+\frac{1}{3}$$

Multiply 2 and 4 to get 8.

$$\frac{11}{12}-\frac{2}{3}\times \frac{8}{5}+\frac{1}{3}$$

Multiply \frac{2}{3} times \frac{8}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{11}{12}-\frac{2\times 8}{3\times 5}+\frac{1}{3}$$

Do the multiplications in the fraction \frac{2\times 8}{3\times 5}.

$$\frac{11}{12}-\frac{16}{15}+\frac{1}{3}$$

Least common multiple of 12 and 15 is 60. Convert \frac{11}{12} and \frac{16}{15} to fractions with denominator 60.

$$\frac{55}{60}-\frac{64}{60}+\frac{1}{3}$$

Since \frac{55}{60} and \frac{64}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{55-64}{60}+\frac{1}{3}$$

Subtract 64 from 55 to get -9.

$$\frac{-9}{60}+\frac{1}{3}$$

Reduce the fraction \frac{-9}{60} to lowest terms by extracting and canceling out 3.

$$-\frac{3}{20}+\frac{1}{3}$$

Least common multiple of 20 and 3 is 60. Convert -\frac{3}{20} and \frac{1}{3} to fractions with denominator 60.

$$-\frac{9}{60}+\frac{20}{60}$$

Since -\frac{9}{60} and \frac{20}{60} have the same denominator, add them by adding their numerators.

$$\frac{-9+20}{60}$$

Add -9 and 20 to get 11.

$$\frac{11}{60}$$

Factor

$$\frac{11}{2 ^ {2} \cdot 3 \cdot 5} = 0.18333333333333332$$