Solve 2/3+3/4*(1/3+1/2)=

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

Evaluate

$$\frac{31}{24}\approx 1.291666667$$

Solution Steps

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

$$\frac{2}{3}+\frac{3}{4}\left(\frac{2}{6}+\frac{3}{6}\right)$$

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

$$\frac{2}{3}+\frac{3}{4}\times \frac{2+3}{6}$$

Add 2 and 3 to get 5.

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

Multiply \frac{3}{4} times \frac{5}{6} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{3\times 5}{4\times 6}.

$$\frac{2}{3}+\frac{15}{24}$$

Reduce the fraction \frac{15}{24} to lowest terms by extracting and canceling out 3.

$$\frac{2}{3}+\frac{5}{8}$$

Least common multiple of 3 and 8 is 24. Convert \frac{2}{3} and \frac{5}{8} to fractions with denominator 24.

$$\frac{16}{24}+\frac{15}{24}$$

Since \frac{16}{24} and \frac{15}{24} have the same denominator, add them by adding their numerators.

$$\frac{16+15}{24}$$

Add 16 and 15 to get 31.

$$\frac{31}{24}$$

Factor

$$\frac{31}{2 ^ {3} \cdot 3} = 1\frac{7}{24} = 1.2916666666666667$$