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

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

Evaluate

$$\frac{35}{24}\approx 1.458333333$$

Solution Steps

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

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

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

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

Add 2 and 3 to get 5.

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

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

$$\frac{5}{4}\left(\frac{4}{6}+\frac{3}{6}\right)$$

Since \frac{4}{6} and \frac{3}{6} have the same denominator, add them by adding their numerators.

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

Add 4 and 3 to get 7.

$$\frac{5}{4}\times \frac{7}{6}$$

Multiply \frac{5}{4} times \frac{7}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 7}{4\times 6}$$

Do the multiplications in the fraction \frac{5\times 7}{4\times 6}.

$$\frac{35}{24}$$

Factor

$$\frac{5 \cdot 7}{2 ^ {3} \cdot 3} = 1\frac{11}{24} = 1.4583333333333333$$