Solve 3/5*5/21+15/28:frac{5/84}{5:0,5-9,36}

$$\frac { \frac { 3 } { 5 } \cdot \frac { 5 } { 21 } + \frac { 15 } { 28 } : \frac { 5 } { 84 } } { 5 : 0,5 - 9,36 }$$

Evaluate

$$\frac{100}{7}\approx 14,285714286$$

Solution Steps

Multiply \frac{3}{5} times \frac{5}{21} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{3\times 5}{5\times 21}+\frac{\frac{15}{28}}{\frac{5}{84}}}{\frac{5}{0,5}-9,36}$$

Cancel out 5 in both numerator and denominator.

$$\frac{\frac{3}{21}+\frac{\frac{15}{28}}{\frac{5}{84}}}{\frac{5}{0,5}-9,36}$$

Reduce the fraction \frac{3}{21} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{1}{7}+\frac{\frac{15}{28}}{\frac{5}{84}}}{\frac{5}{0,5}-9,36}$$

Divide \frac{15}{28} by \frac{5}{84} by multiplying \frac{15}{28} by the reciprocal of \frac{5}{84}.

$$\frac{\frac{1}{7}+\frac{15}{28}\times \frac{84}{5}}{\frac{5}{0,5}-9,36}$$

Multiply \frac{15}{28} times \frac{84}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1}{7}+\frac{15\times 84}{28\times 5}}{\frac{5}{0,5}-9,36}$$

Do the multiplications in the fraction \frac{15\times 84}{28\times 5}.

$$\frac{\frac{1}{7}+\frac{1260}{140}}{\frac{5}{0,5}-9,36}$$

Divide 1260 by 140 to get 9.

$$\frac{\frac{1}{7}+9}{\frac{5}{0,5}-9,36}$$

Convert 9 to fraction \frac{63}{7}.

$$\frac{\frac{1}{7}+\frac{63}{7}}{\frac{5}{0,5}-9,36}$$

Since \frac{1}{7} and \frac{63}{7} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1+63}{7}}{\frac{5}{0,5}-9,36}$$

Add 1 and 63 to get 64.

$$\frac{\frac{64}{7}}{\frac{5}{0,5}-9,36}$$

Expand \frac{5}{0,5} by multiplying both numerator and the denominator by 10.

$$\frac{\frac{64}{7}}{\frac{50}{5}-9,36}$$

Divide 50 by 5 to get 10.

$$\frac{\frac{64}{7}}{10-9,36}$$

Subtract 9,36 from 10 to get 0,64.

$$\frac{\frac{64}{7}}{0,64}$$

Express \frac{\frac{64}{7}}{0,64} as a single fraction.

$$\frac{64}{7\times 0,64}$$

Multiply 7 and 0,64 to get 4,48.

$$\frac{64}{4,48}$$

Expand \frac{64}{4,48} by multiplying both numerator and the denominator by 100.

$$\frac{6400}{448}$$

Reduce the fraction \frac{6400}{448} to lowest terms by extracting and canceling out 64.

$$\frac{100}{7}$$

Factor

$$\frac{2 ^ {2} \cdot 5 ^ {2}}{7} = 14\frac{2}{7} = 14.285714285714286$$