Solve (1/2*1/5*9/49+1/2*frac{18}{30}*frac{17}{29})divfrac{2}{5}

$$( \frac { 1 } { 2 } \times \frac { 1 } { 5 } \times \frac { 9 } { 49 } + \frac { 1 } { 2 } \times \frac { 18 } { 30 } \times \frac { 17 } { 29 } ) \div \frac { 2 } { 5 }$$

Evaluate

$$\frac{690}{1421}\approx 0.48557354$$

Solution Steps

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

$$\frac{\frac{1\times 1}{2\times 5}\times \frac{9}{49}+\frac{1}{2}\times \frac{18}{30}\times \frac{17}{29}}{\frac{2}{5}}$$

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

$$\frac{\frac{1}{10}\times \frac{9}{49}+\frac{1}{2}\times \frac{18}{30}\times \frac{17}{29}}{\frac{2}{5}}$$

Multiply \frac{1}{10} times \frac{9}{49} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1\times 9}{10\times 49}+\frac{1}{2}\times \frac{18}{30}\times \frac{17}{29}}{\frac{2}{5}}$$

Do the multiplications in the fraction \frac{1\times 9}{10\times 49}.

$$\frac{\frac{9}{490}+\frac{1}{2}\times \frac{18}{30}\times \frac{17}{29}}{\frac{2}{5}}$$

Reduce the fraction \frac{18}{30} to lowest terms by extracting and canceling out 6.

$$\frac{\frac{9}{490}+\frac{1}{2}\times \frac{3}{5}\times \frac{17}{29}}{\frac{2}{5}}$$

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

$$\frac{\frac{9}{490}+\frac{1\times 3}{2\times 5}\times \frac{17}{29}}{\frac{2}{5}}$$

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

$$\frac{\frac{9}{490}+\frac{3}{10}\times \frac{17}{29}}{\frac{2}{5}}$$

Multiply \frac{3}{10} times \frac{17}{29} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{9}{490}+\frac{3\times 17}{10\times 29}}{\frac{2}{5}}$$

Do the multiplications in the fraction \frac{3\times 17}{10\times 29}.

$$\frac{\frac{9}{490}+\frac{51}{290}}{\frac{2}{5}}$$

Least common multiple of 490 and 290 is 14210. Convert \frac{9}{490} and \frac{51}{290} to fractions with denominator 14210.

$$\frac{\frac{261}{14210}+\frac{2499}{14210}}{\frac{2}{5}}$$

Since \frac{261}{14210} and \frac{2499}{14210} have the same denominator, add them by adding their numerators.

$$\frac{\frac{261+2499}{14210}}{\frac{2}{5}}$$

Add 261 and 2499 to get 2760.

$$\frac{\frac{2760}{14210}}{\frac{2}{5}}$$

Reduce the fraction \frac{2760}{14210} to lowest terms by extracting and canceling out 10.

$$\frac{\frac{276}{1421}}{\frac{2}{5}}$$

Divide \frac{276}{1421} by \frac{2}{5} by multiplying \frac{276}{1421} by the reciprocal of \frac{2}{5}.

$$\frac{276}{1421}\times \frac{5}{2}$$

Multiply \frac{276}{1421} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{276\times 5}{1421\times 2}$$

Do the multiplications in the fraction \frac{276\times 5}{1421\times 2}.

$$\frac{1380}{2842}$$

Reduce the fraction \frac{1380}{2842} to lowest terms by extracting and canceling out 2.

$$\frac{690}{1421}$$

Factor

$$\frac{2 \cdot 3 \cdot 5 \cdot 23}{7 ^ {2} \cdot 29} = 0.48557353976073186$$