Solve 1/3+2/51/30/frac{23{30}}

$$\frac { \frac { 1 } { 3 } + \frac { 2 } { 5 } \frac { 1 } { 30 } } { \frac { 23 } { 30 } }$$

Evaluate

$$\frac{52}{115}\approx 0.452173913$$

Solution Steps

Multiply \frac{2}{5} times \frac{1}{30} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1}{3}+\frac{2\times 1}{5\times 30}}{\frac{23}{30}}$$

Do the multiplications in the fraction \frac{2\times 1}{5\times 30}.

$$\frac{\frac{1}{3}+\frac{2}{150}}{\frac{23}{30}}$$

Reduce the fraction \frac{2}{150} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{1}{3}+\frac{1}{75}}{\frac{23}{30}}$$

Least common multiple of 3 and 75 is 75. Convert \frac{1}{3} and \frac{1}{75} to fractions with denominator 75.

$$\frac{\frac{25}{75}+\frac{1}{75}}{\frac{23}{30}}$$

Since \frac{25}{75} and \frac{1}{75} have the same denominator, add them by adding their numerators.

$$\frac{\frac{25+1}{75}}{\frac{23}{30}}$$

Add 25 and 1 to get 26.

$$\frac{\frac{26}{75}}{\frac{23}{30}}$$

Divide \frac{26}{75} by \frac{23}{30} by multiplying \frac{26}{75} by the reciprocal of \frac{23}{30}.

$$\frac{26}{75}\times \frac{30}{23}$$

Multiply \frac{26}{75} times \frac{30}{23} by multiplying numerator times numerator and denominator times denominator.

$$\frac{26\times 30}{75\times 23}$$

Do the multiplications in the fraction \frac{26\times 30}{75\times 23}.

$$\frac{780}{1725}$$

Reduce the fraction \frac{780}{1725} to lowest terms by extracting and canceling out 15.

$$\frac{52}{115}$$

Factor

$$\frac{2 ^ {2} \cdot 13}{5 \cdot 23} = 0.45217391304347826$$