Solve =1/2*3/5/(frac{1{2}*3/5)+(frac{1}{2}*frac{4}{7})}

$$= \frac { \frac { 1 } { 2 } \times \frac { 3 } { 5 } } { ( \frac { 1 } { 2 } \times \frac { 3 } { 5 } ) + ( \frac { 1 } { 2 } \times \frac { 4 } { 7 } ) }$$

Evaluate

$$\frac{21}{41}\approx 0.512195122$$

Solution Steps

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

$$\frac{\frac{1\times 3}{2\times 5}}{\frac{1}{2}\times \frac{3}{5}+\frac{1}{2}\times \frac{4}{7}}$$

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

$$\frac{\frac{3}{10}}{\frac{1}{2}\times \frac{3}{5}+\frac{1}{2}\times \frac{4}{7}}$$

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

$$\frac{\frac{3}{10}}{\frac{1\times 3}{2\times 5}+\frac{1}{2}\times \frac{4}{7}}$$

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

$$\frac{\frac{3}{10}}{\frac{3}{10}+\frac{1}{2}\times \frac{4}{7}}$$

Multiply \frac{1}{2} times \frac{4}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{3}{10}}{\frac{3}{10}+\frac{1\times 4}{2\times 7}}$$

Do the multiplications in the fraction \frac{1\times 4}{2\times 7}.

$$\frac{\frac{3}{10}}{\frac{3}{10}+\frac{4}{14}}$$

Reduce the fraction \frac{4}{14} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{3}{10}}{\frac{3}{10}+\frac{2}{7}}$$

Least common multiple of 10 and 7 is 70. Convert \frac{3}{10} and \frac{2}{7} to fractions with denominator 70.

$$\frac{\frac{3}{10}}{\frac{21}{70}+\frac{20}{70}}$$

Since \frac{21}{70} and \frac{20}{70} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3}{10}}{\frac{21+20}{70}}$$

Add 21 and 20 to get 41.

$$\frac{\frac{3}{10}}{\frac{41}{70}}$$

Divide \frac{3}{10} by \frac{41}{70} by multiplying \frac{3}{10} by the reciprocal of \frac{41}{70}.

$$\frac{3}{10}\times \frac{70}{41}$$

Multiply \frac{3}{10} times \frac{70}{41} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 70}{10\times 41}$$

Do the multiplications in the fraction \frac{3\times 70}{10\times 41}.

$$\frac{210}{410}$$

Reduce the fraction \frac{210}{410} to lowest terms by extracting and canceling out 10.

$$\frac{21}{41}$$

Factor

$$\frac{3 \cdot 7}{41} = 0.5121951219512195$$