Solve 4,7/frac{2,7{200}+2/40}=

$$\frac { 4,7 } { \frac { 2,7 } { 200 } + \frac { 2 } { 40 } } =$$

Evaluate

$$\frac{9400}{127}\approx 74,015748031$$

Solution Steps

Expand \frac{2,7}{200} by multiplying both numerator and the denominator by 10.

$$\frac{4,7}{\frac{27}{2000}+\frac{2}{40}}$$

Reduce the fraction \frac{2}{40} to lowest terms by extracting and canceling out 2.

$$\frac{4,7}{\frac{27}{2000}+\frac{1}{20}}$$

Least common multiple of 2000 and 20 is 2000. Convert \frac{27}{2000} and \frac{1}{20} to fractions with denominator 2000.

$$\frac{4,7}{\frac{27}{2000}+\frac{100}{2000}}$$

Since \frac{27}{2000} and \frac{100}{2000} have the same denominator, add them by adding their numerators.

$$\frac{4,7}{\frac{27+100}{2000}}$$

Add 27 and 100 to get 127.

$$\frac{4,7}{\frac{127}{2000}}$$

Divide 4,7 by \frac{127}{2000} by multiplying 4,7 by the reciprocal of \frac{127}{2000}.

$$4,7\times \frac{2000}{127}$$

Convert decimal number 4,7 to fraction \frac{47}{10}.

$$\frac{47}{10}\times \frac{2000}{127}$$

Multiply \frac{47}{10} times \frac{2000}{127} by multiplying numerator times numerator and denominator times denominator.

$$\frac{47\times 2000}{10\times 127}$$

Do the multiplications in the fraction \frac{47\times 2000}{10\times 127}.

$$\frac{94000}{1270}$$

Reduce the fraction \frac{94000}{1270} to lowest terms by extracting and canceling out 10.

$$\frac{9400}{127}$$

Factor

$$\frac{47 \cdot 2 ^ {3} \cdot 5 ^ {2}}{127} = 74\frac{2}{127} = 74.01574803149606$$