Solve 31/5div(17/5(7/50+3/12))

$$\frac { 31 } { 5 } \div ( \frac { 17 } { 5 } ( \frac { 7 } { 50 } + \frac { 3 } { 12 } ) )$$

Evaluate

$$\frac{3100}{663}\approx 4.67571644$$

Solution Steps

Reduce the fraction \frac{3}{12} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{31}{5}}{\frac{17}{5}\left(\frac{7}{50}+\frac{1}{4}\right)}$$

Least common multiple of 50 and 4 is 100. Convert \frac{7}{50} and \frac{1}{4} to fractions with denominator 100.

$$\frac{\frac{31}{5}}{\frac{17}{5}\left(\frac{14}{100}+\frac{25}{100}\right)}$$

Since \frac{14}{100} and \frac{25}{100} have the same denominator, add them by adding their numerators.

$$\frac{\frac{31}{5}}{\frac{17}{5}\times \frac{14+25}{100}}$$

Add 14 and 25 to get 39.

$$\frac{\frac{31}{5}}{\frac{17}{5}\times \frac{39}{100}}$$

Multiply \frac{17}{5} times \frac{39}{100} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{31}{5}}{\frac{17\times 39}{5\times 100}}$$

Do the multiplications in the fraction \frac{17\times 39}{5\times 100}.

$$\frac{\frac{31}{5}}{\frac{663}{500}}$$

Divide \frac{31}{5} by \frac{663}{500} by multiplying \frac{31}{5} by the reciprocal of \frac{663}{500}.

$$\frac{31}{5}\times \frac{500}{663}$$

Multiply \frac{31}{5} times \frac{500}{663} by multiplying numerator times numerator and denominator times denominator.

$$\frac{31\times 500}{5\times 663}$$

Do the multiplications in the fraction \frac{31\times 500}{5\times 663}.

$$\frac{15500}{3315}$$

Reduce the fraction \frac{15500}{3315} to lowest terms by extracting and canceling out 5.

$$\frac{3100}{663}$$

Factor

$$\frac{2 ^ {2} \cdot 5 ^ {2} \cdot 31}{3 \cdot 13 \cdot 17} = 4\frac{448}{663} = 4.675716440422323$$