Solve (31/2+2/5text{of}1/3)

$$( 3 \frac { 1 } { 2 } + \frac { 2 } { 5 } \text { of } \frac { 1 } { 3 } )$$

Evaluate

$$\frac{109}{30}\approx 3.633333333$$

Solution Steps

Multiply 3 and 2 to get 6.

$$\frac{6+1}{2}+\frac{2}{5}\times \frac{1}{3}$$

Add 6 and 1 to get 7.

$$\frac{7}{2}+\frac{2}{5}\times \frac{1}{3}$$

Multiply \frac{2}{5} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7}{2}+\frac{2\times 1}{5\times 3}$$

Do the multiplications in the fraction \frac{2\times 1}{5\times 3}.

$$\frac{7}{2}+\frac{2}{15}$$

Least common multiple of 2 and 15 is 30. Convert \frac{7}{2} and \frac{2}{15} to fractions with denominator 30.

$$\frac{105}{30}+\frac{4}{30}$$

Since \frac{105}{30} and \frac{4}{30} have the same denominator, add them by adding their numerators.

$$\frac{105+4}{30}$$

Add 105 and 4 to get 109.

$$\frac{109}{30}$$

Factor

$$\frac{109}{2 \cdot 3 \cdot 5} = 3\frac{19}{30} = 3.6333333333333333$$