Solve 1/5*3/6+3/4:10/10-frac{1}{3}

$$\frac { 1 } { 5 } \cdot \frac { 3 } { 6 } + \frac { 3 } { 4 } : \frac { 10 } { 10 } - \frac { 1 } { 3 }$$

Evaluate

$$\frac{31}{60}\approx 0.516666667$$

Solution Steps

Divide 10 by 10 to get 1.

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

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

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

Multiply \frac{1}{5} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{1\times 1}{5\times 2}.

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

Anything divided by one gives itself.

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

Least common multiple of 10 and 4 is 20. Convert \frac{1}{10} and \frac{3}{4} to fractions with denominator 20.

$$\frac{2}{20}+\frac{15}{20}-\frac{1}{3}$$

Since \frac{2}{20} and \frac{15}{20} have the same denominator, add them by adding their numerators.

$$\frac{2+15}{20}-\frac{1}{3}$$

Add 2 and 15 to get 17.

$$\frac{17}{20}-\frac{1}{3}$$

Least common multiple of 20 and 3 is 60. Convert \frac{17}{20} and \frac{1}{3} to fractions with denominator 60.

$$\frac{51}{60}-\frac{20}{60}$$

Since \frac{51}{60} and \frac{20}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{51-20}{60}$$

Subtract 20 from 51 to get 31.

$$\frac{31}{60}$$

Factor

$$\frac{31}{2 ^ {2} \cdot 3 \cdot 5} = 0.5166666666666667$$