Solve (5,3:22/5-11/12/0,702:1,3-0,415

$$( \frac { 5,3 : 2 \frac { 2 } { 5 } - 1 \frac { 1 } { 12 } } { 0,702 : 1,3 - 0,415 }$$

Evaluate

$$9$$

Solution Steps

Divide 5,3 by \frac{2\times 5+2}{5} by multiplying 5,3 by the reciprocal of \frac{2\times 5+2}{5}.

$$\frac{\frac{5,3\times 5}{2\times 5+2}-\frac{1\times 12+1}{12}}{\frac{0,702}{1,3}-0,415}$$

Multiply 5,3 and 5 to get 26,5.

$$\frac{\frac{26,5}{2\times 5+2}-\frac{1\times 12+1}{12}}{\frac{0,702}{1,3}-0,415}$$

Multiply 2 and 5 to get 10.

$$\frac{\frac{26,5}{10+2}-\frac{1\times 12+1}{12}}{\frac{0,702}{1,3}-0,415}$$

Add 10 and 2 to get 12.

$$\frac{\frac{26,5}{12}-\frac{1\times 12+1}{12}}{\frac{0,702}{1,3}-0,415}$$

Expand \frac{26,5}{12} by multiplying both numerator and the denominator by 10.

$$\frac{\frac{265}{120}-\frac{1\times 12+1}{12}}{\frac{0,702}{1,3}-0,415}$$

Reduce the fraction \frac{265}{120} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{53}{24}-\frac{1\times 12+1}{12}}{\frac{0,702}{1,3}-0,415}$$

Multiply 1 and 12 to get 12.

$$\frac{\frac{53}{24}-\frac{12+1}{12}}{\frac{0,702}{1,3}-0,415}$$

Add 12 and 1 to get 13.

$$\frac{\frac{53}{24}-\frac{13}{12}}{\frac{0,702}{1,3}-0,415}$$

Least common multiple of 24 and 12 is 24. Convert \frac{53}{24} and \frac{13}{12} to fractions with denominator 24.

$$\frac{\frac{53}{24}-\frac{26}{24}}{\frac{0,702}{1,3}-0,415}$$

Since \frac{53}{24} and \frac{26}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{53-26}{24}}{\frac{0,702}{1,3}-0,415}$$

Subtract 26 from 53 to get 27.

$$\frac{\frac{27}{24}}{\frac{0,702}{1,3}-0,415}$$

Reduce the fraction \frac{27}{24} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{9}{8}}{\frac{0,702}{1,3}-0,415}$$

Expand \frac{0,702}{1,3} by multiplying both numerator and the denominator by 1000.

$$\frac{\frac{9}{8}}{\frac{702}{1300}-0,415}$$

Reduce the fraction \frac{702}{1300} to lowest terms by extracting and canceling out 26.

$$\frac{\frac{9}{8}}{\frac{27}{50}-0,415}$$

Convert decimal number 0,415 to fraction \frac{415}{1000}. Reduce the fraction \frac{415}{1000} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{9}{8}}{\frac{27}{50}-\frac{83}{200}}$$

Least common multiple of 50 and 200 is 200. Convert \frac{27}{50} and \frac{83}{200} to fractions with denominator 200.

$$\frac{\frac{9}{8}}{\frac{108}{200}-\frac{83}{200}}$$

Since \frac{108}{200} and \frac{83}{200} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{9}{8}}{\frac{108-83}{200}}$$

Subtract 83 from 108 to get 25.

$$\frac{\frac{9}{8}}{\frac{25}{200}}$$

Reduce the fraction \frac{25}{200} to lowest terms by extracting and canceling out 25.

$$\frac{\frac{9}{8}}{\frac{1}{8}}$$

Divide \frac{9}{8} by \frac{1}{8} by multiplying \frac{9}{8} by the reciprocal of \frac{1}{8}.

$$\frac{9}{8}\times 8$$

Cancel out 8 and 8.

$$9$$

Factor

$$3^{2}$$