Solve (311/27-217/18):123/27-3frac{3/5:3}{(43-42frac{2}{3}):frac{2}{3}}+2,5

$$\frac { ( 3 \frac { 11 } { 27 } - 2 \frac { 17 } { 18 } ) : 1 \frac { 23 } { 27 } - 3 \frac { 3 } { 5 } : 3 } { ( 43 - 42 \frac { 2 } { 3 } ) : \frac { 2 } { 3 } } + 2,5$$

Evaluate

$$0,6$$

Solution Steps

Multiply 3 and 27 to get 81.

$$\frac{\frac{\frac{81+11}{27}-\frac{2\times 18+17}{18}}{\frac{1\times 27+23}{27}}-\frac{\frac{3\times 5+3}{5}}{3}}{\frac{43-\frac{42\times 3+2}{3}}{\frac{2}{3}}}+2,5$$

Add 81 and 11 to get 92.

$$\frac{\frac{\frac{92}{27}-\frac{2\times 18+17}{18}}{\frac{1\times 27+23}{27}}-\frac{\frac{3\times 5+3}{5}}{3}}{\frac{43-\frac{42\times 3+2}{3}}{\frac{2}{3}}}+2,5$$

Multiply 2 and 18 to get 36.

$$\frac{\frac{\frac{92}{27}-\frac{36+17}{18}}{\frac{1\times 27+23}{27}}-\frac{\frac{3\times 5+3}{5}}{3}}{\frac{43-\frac{42\times 3+2}{3}}{\frac{2}{3}}}+2,5$$

Add 36 and 17 to get 53.

$$\frac{\frac{\frac{92}{27}-\frac{53}{18}}{\frac{1\times 27+23}{27}}-\frac{\frac{3\times 5+3}{5}}{3}}{\frac{43-\frac{42\times 3+2}{3}}{\frac{2}{3}}}+2,5$$

Least common multiple of 27 and 18 is 54. Convert \frac{92}{27} and \frac{53}{18} to fractions with denominator 54.

$$\frac{\frac{\frac{184}{54}-\frac{159}{54}}{\frac{1\times 27+23}{27}}-\frac{\frac{3\times 5+3}{5}}{3}}{\frac{43-\frac{42\times 3+2}{3}}{\frac{2}{3}}}+2,5$$

Since \frac{184}{54} and \frac{159}{54} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{\frac{184-159}{54}}{\frac{1\times 27+23}{27}}-\frac{\frac{3\times 5+3}{5}}{3}}{\frac{43-\frac{42\times 3+2}{3}}{\frac{2}{3}}}+2,5$$

Subtract 159 from 184 to get 25.

$$\frac{\frac{\frac{25}{54}}{\frac{1\times 27+23}{27}}-\frac{\frac{3\times 5+3}{5}}{3}}{\frac{43-\frac{42\times 3+2}{3}}{\frac{2}{3}}}+2,5$$

Multiply 1 and 27 to get 27.

$$\frac{\frac{\frac{25}{54}}{\frac{27+23}{27}}-\frac{\frac{3\times 5+3}{5}}{3}}{\frac{43-\frac{42\times 3+2}{3}}{\frac{2}{3}}}+2,5$$

Add 27 and 23 to get 50.

$$\frac{\frac{\frac{25}{54}}{\frac{50}{27}}-\frac{\frac{3\times 5+3}{5}}{3}}{\frac{43-\frac{42\times 3+2}{3}}{\frac{2}{3}}}+2,5$$

Divide \frac{25}{54} by \frac{50}{27} by multiplying \frac{25}{54} by the reciprocal of \frac{50}{27}.

$$\frac{\frac{25}{54}\times \frac{27}{50}-\frac{\frac{3\times 5+3}{5}}{3}}{\frac{43-\frac{42\times 3+2}{3}}{\frac{2}{3}}}+2,5$$

Multiply \frac{25}{54} times \frac{27}{50} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{25\times 27}{54\times 50}-\frac{\frac{3\times 5+3}{5}}{3}}{\frac{43-\frac{42\times 3+2}{3}}{\frac{2}{3}}}+2,5$$

Do the multiplications in the fraction \frac{25\times 27}{54\times 50}.

$$\frac{\frac{675}{2700}-\frac{\frac{3\times 5+3}{5}}{3}}{\frac{43-\frac{42\times 3+2}{3}}{\frac{2}{3}}}+2,5$$

Reduce the fraction \frac{675}{2700} to lowest terms by extracting and canceling out 675.

$$\frac{\frac{1}{4}-\frac{\frac{3\times 5+3}{5}}{3}}{\frac{43-\frac{42\times 3+2}{3}}{\frac{2}{3}}}+2,5$$

Express \frac{\frac{3\times 5+3}{5}}{3} as a single fraction.

$$\frac{\frac{1}{4}-\frac{3\times 5+3}{5\times 3}}{\frac{43-\frac{42\times 3+2}{3}}{\frac{2}{3}}}+2,5$$

Multiply 3 and 5 to get 15.

$$\frac{\frac{1}{4}-\frac{15+3}{5\times 3}}{\frac{43-\frac{42\times 3+2}{3}}{\frac{2}{3}}}+2,5$$

Add 15 and 3 to get 18.

$$\frac{\frac{1}{4}-\frac{18}{5\times 3}}{\frac{43-\frac{42\times 3+2}{3}}{\frac{2}{3}}}+2,5$$

Multiply 5 and 3 to get 15.

$$\frac{\frac{1}{4}-\frac{18}{15}}{\frac{43-\frac{42\times 3+2}{3}}{\frac{2}{3}}}+2,5$$

Reduce the fraction \frac{18}{15} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{1}{4}-\frac{6}{5}}{\frac{43-\frac{42\times 3+2}{3}}{\frac{2}{3}}}+2,5$$

Least common multiple of 4 and 5 is 20. Convert \frac{1}{4} and \frac{6}{5} to fractions with denominator 20.

$$\frac{\frac{5}{20}-\frac{24}{20}}{\frac{43-\frac{42\times 3+2}{3}}{\frac{2}{3}}}+2,5$$

Since \frac{5}{20} and \frac{24}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5-24}{20}}{\frac{43-\frac{42\times 3+2}{3}}{\frac{2}{3}}}+2,5$$

Subtract 24 from 5 to get -19.

$$\frac{-\frac{19}{20}}{\frac{43-\frac{42\times 3+2}{3}}{\frac{2}{3}}}+2,5$$

Multiply 42 and 3 to get 126.

$$\frac{-\frac{19}{20}}{\frac{43-\frac{126+2}{3}}{\frac{2}{3}}}+2,5$$

Add 126 and 2 to get 128.

$$\frac{-\frac{19}{20}}{\frac{43-\frac{128}{3}}{\frac{2}{3}}}+2,5$$

Convert 43 to fraction \frac{129}{3}.

$$\frac{-\frac{19}{20}}{\frac{\frac{129}{3}-\frac{128}{3}}{\frac{2}{3}}}+2,5$$

Since \frac{129}{3} and \frac{128}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{19}{20}}{\frac{\frac{129-128}{3}}{\frac{2}{3}}}+2,5$$

Subtract 128 from 129 to get 1.

$$\frac{-\frac{19}{20}}{\frac{\frac{1}{3}}{\frac{2}{3}}}+2,5$$

Divide \frac{1}{3} by \frac{2}{3} by multiplying \frac{1}{3} by the reciprocal of \frac{2}{3}.

$$\frac{-\frac{19}{20}}{\frac{1}{3}\times \frac{3}{2}}+2,5$$

Multiply \frac{1}{3} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\frac{19}{20}}{\frac{1\times 3}{3\times 2}}+2,5$$

Cancel out 3 in both numerator and denominator.

$$\frac{-\frac{19}{20}}{\frac{1}{2}}+2,5$$

Divide -\frac{19}{20} by \frac{1}{2} by multiplying -\frac{19}{20} by the reciprocal of \frac{1}{2}.

$$-\frac{19}{20}\times 2+2,5$$

Express -\frac{19}{20}\times 2 as a single fraction.

$$\frac{-19\times 2}{20}+2,5$$

Multiply -19 and 2 to get -38.

$$\frac{-38}{20}+2,5$$

Reduce the fraction \frac{-38}{20} to lowest terms by extracting and canceling out 2.

$$-\frac{19}{10}+2,5$$

Convert decimal number 2,5 to fraction \frac{25}{10}. Reduce the fraction \frac{25}{10} to lowest terms by extracting and canceling out 5.

$$-\frac{19}{10}+\frac{5}{2}$$

Least common multiple of 10 and 2 is 10. Convert -\frac{19}{10} and \frac{5}{2} to fractions with denominator 10.

$$-\frac{19}{10}+\frac{25}{10}$$

Since -\frac{19}{10} and \frac{25}{10} have the same denominator, add them by adding their numerators.

$$\frac{-19+25}{10}$$

Add -19 and 25 to get 6.

$$\frac{6}{10}$$

Reduce the fraction \frac{6}{10} to lowest terms by extracting and canceling out 2.

$$\frac{3}{5}$$

Factor

$$\frac{3}{5} = 0.6$$