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

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

Evaluate

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

Solution Steps

Multiply \frac{3}{4} times \frac{1}{5} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{3\times 1}{4\times 5}.

$$\frac{2}{3}+\frac{3}{20}\times \frac{2}{3}-\frac{1}{4}$$

Multiply \frac{3}{20} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{3}+\frac{3\times 2}{20\times 3}-\frac{1}{4}$$

Cancel out 3 in both numerator and denominator.

$$\frac{2}{3}+\frac{2}{20}-\frac{1}{4}$$

Reduce the fraction \frac{2}{20} to lowest terms by extracting and canceling out 2.

$$\frac{2}{3}+\frac{1}{10}-\frac{1}{4}$$

Least common multiple of 3 and 10 is 30. Convert \frac{2}{3} and \frac{1}{10} to fractions with denominator 30.

$$\frac{20}{30}+\frac{3}{30}-\frac{1}{4}$$

Since \frac{20}{30} and \frac{3}{30} have the same denominator, add them by adding their numerators.

$$\frac{20+3}{30}-\frac{1}{4}$$

Add 20 and 3 to get 23.

$$\frac{23}{30}-\frac{1}{4}$$

Least common multiple of 30 and 4 is 60. Convert \frac{23}{30} and \frac{1}{4} to fractions with denominator 60.

$$\frac{46}{60}-\frac{15}{60}$$

Since \frac{46}{60} and \frac{15}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{46-15}{60}$$

Subtract 15 from 46 to get 31.

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

Factor

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