Solve (25/7-13/5):1,3-13/7*0,25/(frac{2{5}-frac{7}{18})*15}

$$\frac { ( 2 \frac { 5 } { 7 } - 1 \frac { 3 } { 5 } ) : 1,3 - 1 \frac { 3 } { 7 } \cdot 0,25 } { ( \frac { 2 } { 5 } - \frac { 7 } { 18 } ) \cdot 15 }$$

Evaluate

$$3$$

Solution Steps

Multiply 2 and 7 to get 14.

$$\frac{\frac{\frac{14+5}{7}-\frac{1\times 5+3}{5}}{1,3}-\frac{1\times 7+3}{7}\times 0,25}{\left(\frac{2}{5}-\frac{7}{18}\right)\times 15}$$

Add 14 and 5 to get 19.

$$\frac{\frac{\frac{19}{7}-\frac{1\times 5+3}{5}}{1,3}-\frac{1\times 7+3}{7}\times 0,25}{\left(\frac{2}{5}-\frac{7}{18}\right)\times 15}$$

Multiply 1 and 5 to get 5.

$$\frac{\frac{\frac{19}{7}-\frac{5+3}{5}}{1,3}-\frac{1\times 7+3}{7}\times 0,25}{\left(\frac{2}{5}-\frac{7}{18}\right)\times 15}$$

Add 5 and 3 to get 8.

$$\frac{\frac{\frac{19}{7}-\frac{8}{5}}{1,3}-\frac{1\times 7+3}{7}\times 0,25}{\left(\frac{2}{5}-\frac{7}{18}\right)\times 15}$$

Least common multiple of 7 and 5 is 35. Convert \frac{19}{7} and \frac{8}{5} to fractions with denominator 35.

$$\frac{\frac{\frac{95}{35}-\frac{56}{35}}{1,3}-\frac{1\times 7+3}{7}\times 0,25}{\left(\frac{2}{5}-\frac{7}{18}\right)\times 15}$$

Since \frac{95}{35} and \frac{56}{35} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{\frac{95-56}{35}}{1,3}-\frac{1\times 7+3}{7}\times 0,25}{\left(\frac{2}{5}-\frac{7}{18}\right)\times 15}$$

Subtract 56 from 95 to get 39.

$$\frac{\frac{\frac{39}{35}}{1,3}-\frac{1\times 7+3}{7}\times 0,25}{\left(\frac{2}{5}-\frac{7}{18}\right)\times 15}$$

Express \frac{\frac{39}{35}}{1,3} as a single fraction.

$$\frac{\frac{39}{35\times 1,3}-\frac{1\times 7+3}{7}\times 0,25}{\left(\frac{2}{5}-\frac{7}{18}\right)\times 15}$$

Multiply 35 and 1,3 to get 45,5.

$$\frac{\frac{39}{45,5}-\frac{1\times 7+3}{7}\times 0,25}{\left(\frac{2}{5}-\frac{7}{18}\right)\times 15}$$

Expand \frac{39}{45,5} by multiplying both numerator and the denominator by 10.

$$\frac{\frac{390}{455}-\frac{1\times 7+3}{7}\times 0,25}{\left(\frac{2}{5}-\frac{7}{18}\right)\times 15}$$

Reduce the fraction \frac{390}{455} to lowest terms by extracting and canceling out 65.

$$\frac{\frac{6}{7}-\frac{1\times 7+3}{7}\times 0,25}{\left(\frac{2}{5}-\frac{7}{18}\right)\times 15}$$

Multiply 1 and 7 to get 7.

$$\frac{\frac{6}{7}-\frac{7+3}{7}\times 0,25}{\left(\frac{2}{5}-\frac{7}{18}\right)\times 15}$$

Add 7 and 3 to get 10.

$$\frac{\frac{6}{7}-\frac{10}{7}\times 0,25}{\left(\frac{2}{5}-\frac{7}{18}\right)\times 15}$$

Convert decimal number 0,25 to fraction \frac{25}{100}. Reduce the fraction \frac{25}{100} to lowest terms by extracting and canceling out 25.

$$\frac{\frac{6}{7}-\frac{10}{7}\times \frac{1}{4}}{\left(\frac{2}{5}-\frac{7}{18}\right)\times 15}$$

Multiply \frac{10}{7} times \frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{6}{7}-\frac{10\times 1}{7\times 4}}{\left(\frac{2}{5}-\frac{7}{18}\right)\times 15}$$

Do the multiplications in the fraction \frac{10\times 1}{7\times 4}.

$$\frac{\frac{6}{7}-\frac{10}{28}}{\left(\frac{2}{5}-\frac{7}{18}\right)\times 15}$$

Reduce the fraction \frac{10}{28} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{6}{7}-\frac{5}{14}}{\left(\frac{2}{5}-\frac{7}{18}\right)\times 15}$$

Least common multiple of 7 and 14 is 14. Convert \frac{6}{7} and \frac{5}{14} to fractions with denominator 14.

$$\frac{\frac{12}{14}-\frac{5}{14}}{\left(\frac{2}{5}-\frac{7}{18}\right)\times 15}$$

Since \frac{12}{14} and \frac{5}{14} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{12-5}{14}}{\left(\frac{2}{5}-\frac{7}{18}\right)\times 15}$$

Subtract 5 from 12 to get 7.

$$\frac{\frac{7}{14}}{\left(\frac{2}{5}-\frac{7}{18}\right)\times 15}$$

Reduce the fraction \frac{7}{14} to lowest terms by extracting and canceling out 7.

$$\frac{\frac{1}{2}}{\left(\frac{2}{5}-\frac{7}{18}\right)\times 15}$$

Least common multiple of 5 and 18 is 90. Convert \frac{2}{5} and \frac{7}{18} to fractions with denominator 90.

$$\frac{\frac{1}{2}}{\left(\frac{36}{90}-\frac{35}{90}\right)\times 15}$$

Since \frac{36}{90} and \frac{35}{90} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1}{2}}{\frac{36-35}{90}\times 15}$$

Subtract 35 from 36 to get 1.

$$\frac{\frac{1}{2}}{\frac{1}{90}\times 15}$$

Multiply \frac{1}{90} and 15 to get \frac{15}{90}.

$$\frac{\frac{1}{2}}{\frac{15}{90}}$$

Reduce the fraction \frac{15}{90} to lowest terms by extracting and canceling out 15.

$$\frac{\frac{1}{2}}{\frac{1}{6}}$$

Divide \frac{1}{2} by \frac{1}{6} by multiplying \frac{1}{2} by the reciprocal of \frac{1}{6}.

$$\frac{1}{2}\times 6$$

Multiply \frac{1}{2} and 6 to get \frac{6}{2}.

$$\frac{6}{2}$$

Divide 6 by 2 to get 3.

$$3$$

Factor

$$3$$