Solve (1/2+3/4)*1/3-1/21*(frac{2}{3}+1)

$$( \frac { 1 } { 2 } + \frac { 3 } { 4 } ) \cdot \frac { 1 } { 3 } - \frac { 1 } { 21 } \cdot ( \frac { 2 } { 3 } + 1 )$$

Evaluate

$$\frac{85}{252}\approx 0.337301587$$

Solution Steps

Least common multiple of 2 and 4 is 4. Convert \frac{1}{2} and \frac{3}{4} to fractions with denominator 4.

$$\left(\frac{2}{4}+\frac{3}{4}\right)\times \frac{1}{3}-\frac{1}{21}\left(\frac{2}{3}+1\right)$$

Since \frac{2}{4} and \frac{3}{4} have the same denominator, add them by adding their numerators.

$$\frac{2+3}{4}\times \frac{1}{3}-\frac{1}{21}\left(\frac{2}{3}+1\right)$$

Add 2 and 3 to get 5.

$$\frac{5}{4}\times \frac{1}{3}-\frac{1}{21}\left(\frac{2}{3}+1\right)$$

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

$$\frac{5\times 1}{4\times 3}-\frac{1}{21}\left(\frac{2}{3}+1\right)$$

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

$$\frac{5}{12}-\frac{1}{21}\left(\frac{2}{3}+1\right)$$

Convert 1 to fraction \frac{3}{3}.

$$\frac{5}{12}-\frac{1}{21}\left(\frac{2}{3}+\frac{3}{3}\right)$$

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

$$\frac{5}{12}-\frac{1}{21}\times \frac{2+3}{3}$$

Add 2 and 3 to get 5.

$$\frac{5}{12}-\frac{1}{21}\times \frac{5}{3}$$

Multiply \frac{1}{21} times \frac{5}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5}{12}-\frac{1\times 5}{21\times 3}$$

Do the multiplications in the fraction \frac{1\times 5}{21\times 3}.

$$\frac{5}{12}-\frac{5}{63}$$

Least common multiple of 12 and 63 is 252. Convert \frac{5}{12} and \frac{5}{63} to fractions with denominator 252.

$$\frac{105}{252}-\frac{20}{252}$$

Since \frac{105}{252} and \frac{20}{252} have the same denominator, subtract them by subtracting their numerators.

$$\frac{105-20}{252}$$

Subtract 20 from 105 to get 85.

$$\frac{85}{252}$$

Factor

$$\frac{5 \cdot 17}{2 ^ {2} \cdot 3 ^ {2} \cdot 7} = 0.3373015873015873$$