Solve 1/2+1/3+1/4-1/5:frac{1}{3}*frac{1}{6}-frac{1}{5}

$$\frac { 1 } { 2 } + \frac { 1 } { 3 } + \frac { 1 } { 4 } - \frac { 1 } { 5 } : \frac { 1 } { 3 } \cdot \frac { 1 } { 6 } - \frac { 1 } { 5 }$$

Evaluate

$$\frac{47}{60}\approx 0.783333333$$

Solution Steps

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{1}{3} to fractions with denominator 6.

$$\frac{3}{6}+\frac{2}{6}+\frac{1}{4}-\frac{\frac{1}{5}}{\frac{1}{3}}\times \frac{1}{6}-\frac{1}{5}$$

Since \frac{3}{6} and \frac{2}{6} have the same denominator, add them by adding their numerators.

$$\frac{3+2}{6}+\frac{1}{4}-\frac{\frac{1}{5}}{\frac{1}{3}}\times \frac{1}{6}-\frac{1}{5}$$

Add 3 and 2 to get 5.

$$\frac{5}{6}+\frac{1}{4}-\frac{\frac{1}{5}}{\frac{1}{3}}\times \frac{1}{6}-\frac{1}{5}$$

Least common multiple of 6 and 4 is 12. Convert \frac{5}{6} and \frac{1}{4} to fractions with denominator 12.

$$\frac{10}{12}+\frac{3}{12}-\frac{\frac{1}{5}}{\frac{1}{3}}\times \frac{1}{6}-\frac{1}{5}$$

Since \frac{10}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.

$$\frac{10+3}{12}-\frac{\frac{1}{5}}{\frac{1}{3}}\times \frac{1}{6}-\frac{1}{5}$$

Add 10 and 3 to get 13.

$$\frac{13}{12}-\frac{\frac{1}{5}}{\frac{1}{3}}\times \frac{1}{6}-\frac{1}{5}$$

Divide \frac{1}{5} by \frac{1}{3} by multiplying \frac{1}{5} by the reciprocal of \frac{1}{3}.

$$\frac{13}{12}-\frac{1}{5}\times 3\times \frac{1}{6}-\frac{1}{5}$$

Multiply \frac{1}{5} and 3 to get \frac{3}{5}.

$$\frac{13}{12}-\frac{3}{5}\times \frac{1}{6}-\frac{1}{5}$$

Multiply \frac{3}{5} times \frac{1}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13}{12}-\frac{3\times 1}{5\times 6}-\frac{1}{5}$$

Do the multiplications in the fraction \frac{3\times 1}{5\times 6}.

$$\frac{13}{12}-\frac{3}{30}-\frac{1}{5}$$

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

$$\frac{13}{12}-\frac{1}{10}-\frac{1}{5}$$

Least common multiple of 12 and 10 is 60. Convert \frac{13}{12} and \frac{1}{10} to fractions with denominator 60.

$$\frac{65}{60}-\frac{6}{60}-\frac{1}{5}$$

Since \frac{65}{60} and \frac{6}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{65-6}{60}-\frac{1}{5}$$

Subtract 6 from 65 to get 59.

$$\frac{59}{60}-\frac{1}{5}$$

Least common multiple of 60 and 5 is 60. Convert \frac{59}{60} and \frac{1}{5} to fractions with denominator 60.

$$\frac{59}{60}-\frac{12}{60}$$

Since \frac{59}{60} and \frac{12}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{59-12}{60}$$

Subtract 12 from 59 to get 47.

$$\frac{47}{60}$$

Factor

$$\frac{47}{2 ^ {2} \cdot 3 \cdot 5} = 0.7833333333333333$$