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

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

Evaluate

$$\frac{13}{24}\approx 0.541666667$$

Solution Steps

Least common multiple of 3 and 4 is 12. Convert \frac{2}{3} and \frac{1}{4} to fractions with denominator 12.

$$\left(\frac{8}{12}+\frac{3}{12}\right)\times \frac{1}{2}+\frac{1}{3}\left(1-\frac{3}{4}\right)$$

Since \frac{8}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.

$$\frac{8+3}{12}\times \frac{1}{2}+\frac{1}{3}\left(1-\frac{3}{4}\right)$$

Add 8 and 3 to get 11.

$$\frac{11}{12}\times \frac{1}{2}+\frac{1}{3}\left(1-\frac{3}{4}\right)$$

Multiply \frac{11}{12} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{11\times 1}{12\times 2}+\frac{1}{3}\left(1-\frac{3}{4}\right)$$

Do the multiplications in the fraction \frac{11\times 1}{12\times 2}.

$$\frac{11}{24}+\frac{1}{3}\left(1-\frac{3}{4}\right)$$

Convert 1 to fraction \frac{4}{4}.

$$\frac{11}{24}+\frac{1}{3}\left(\frac{4}{4}-\frac{3}{4}\right)$$

Since \frac{4}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{11}{24}+\frac{1}{3}\times \frac{4-3}{4}$$

Subtract 3 from 4 to get 1.

$$\frac{11}{24}+\frac{1}{3}\times \frac{1}{4}$$

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

$$\frac{11}{24}+\frac{1\times 1}{3\times 4}$$

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

$$\frac{11}{24}+\frac{1}{12}$$

Least common multiple of 24 and 12 is 24. Convert \frac{11}{24} and \frac{1}{12} to fractions with denominator 24.

$$\frac{11}{24}+\frac{2}{24}$$

Since \frac{11}{24} and \frac{2}{24} have the same denominator, add them by adding their numerators.

$$\frac{11+2}{24}$$

Add 11 and 2 to get 13.

$$\frac{13}{24}$$

Factor

$$\frac{13}{2 ^ {3} \cdot 3} = 0.5416666666666666$$