Solve 3/8+5/6quad7/3+5/8

$$\frac { 3 } { 8 } + \frac { 5 } { 6 } \quad \frac { 7 } { 3 } + \frac { 5 } { 8 }$$

Evaluate

$$\frac{53}{18}\approx 2.944444444$$

Solution Steps

Multiply \frac{5}{6} times \frac{7}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{8}+\frac{5\times 7}{6\times 3}+\frac{5}{8}$$

Do the multiplications in the fraction \frac{5\times 7}{6\times 3}.

$$\frac{3}{8}+\frac{35}{18}+\frac{5}{8}$$

Least common multiple of 8 and 18 is 72. Convert \frac{3}{8} and \frac{35}{18} to fractions with denominator 72.

$$\frac{27}{72}+\frac{140}{72}+\frac{5}{8}$$

Since \frac{27}{72} and \frac{140}{72} have the same denominator, add them by adding their numerators.

$$\frac{27+140}{72}+\frac{5}{8}$$

Add 27 and 140 to get 167.

$$\frac{167}{72}+\frac{5}{8}$$

Least common multiple of 72 and 8 is 72. Convert \frac{167}{72} and \frac{5}{8} to fractions with denominator 72.

$$\frac{167}{72}+\frac{45}{72}$$

Since \frac{167}{72} and \frac{45}{72} have the same denominator, add them by adding their numerators.

$$\frac{167+45}{72}$$

Add 167 and 45 to get 212.

$$\frac{212}{72}$$

Reduce the fraction \frac{212}{72} to lowest terms by extracting and canceling out 4.

$$\frac{53}{18}$$

Factor

$$\frac{53}{2 \cdot 3 ^ {2}} = 2\frac{17}{18} = 2.9444444444444446$$