Solve 2/3*(23/8+5/4)

$$\frac { 2 } { 3 } \cdot ( 2 \frac { 3 } { 8 } + \frac { 5 } { 4 } )$$

Evaluate

$$\frac{29}{12}\approx 2.416666667$$

Solution Steps

Multiply 2 and 8 to get 16.

$$\frac{2}{3}\left(\frac{16+3}{8}+\frac{5}{4}\right)$$

Add 16 and 3 to get 19.

$$\frac{2}{3}\left(\frac{19}{8}+\frac{5}{4}\right)$$

Least common multiple of 8 and 4 is 8. Convert \frac{19}{8} and \frac{5}{4} to fractions with denominator 8.

$$\frac{2}{3}\left(\frac{19}{8}+\frac{10}{8}\right)$$

Since \frac{19}{8} and \frac{10}{8} have the same denominator, add them by adding their numerators.

$$\frac{2}{3}\times \frac{19+10}{8}$$

Add 19 and 10 to get 29.

$$\frac{2}{3}\times \frac{29}{8}$$

Multiply \frac{2}{3} times \frac{29}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 29}{3\times 8}$$

Do the multiplications in the fraction \frac{2\times 29}{3\times 8}.

$$\frac{58}{24}$$

Reduce the fraction \frac{58}{24} to lowest terms by extracting and canceling out 2.

$$\frac{29}{12}$$

Factor

$$\frac{29}{2 ^ {2} \cdot 3} = 2\frac{5}{12} = 2.4166666666666665$$