Solve ((2,7-0,8)*21/3/(5,2-1,4)*frac{3{70}}+0,125):21/2+0,43

$$( \frac { ( 2,7 - 0,8 ) \cdot 2 \frac { 1 } { 3 } } { ( 5,2 - 1,4 ) \cdot \frac { 3 } { 70 } } + 0,125 ) : 2 \frac { 1 } { 2 } + 0,43$$

Evaluate

$$\frac{2558}{225}\approx 11,368888889$$

Solution Steps

Subtract 0,8 from 2,7 to get 1,9.

$$\frac{\frac{1,9\times \frac{2\times 3+1}{3}}{\left(5,2-1,4\right)\times \frac{3}{70}}+0,125}{\frac{2\times 2+1}{2}}+0,43$$

Multiply 2 and 3 to get 6.

$$\frac{\frac{1,9\times \frac{6+1}{3}}{\left(5,2-1,4\right)\times \frac{3}{70}}+0,125}{\frac{2\times 2+1}{2}}+0,43$$

Add 6 and 1 to get 7.

$$\frac{\frac{1,9\times \frac{7}{3}}{\left(5,2-1,4\right)\times \frac{3}{70}}+0,125}{\frac{2\times 2+1}{2}}+0,43$$

Convert decimal number 1,9 to fraction \frac{19}{10}.

$$\frac{\frac{\frac{19}{10}\times \frac{7}{3}}{\left(5,2-1,4\right)\times \frac{3}{70}}+0,125}{\frac{2\times 2+1}{2}}+0,43$$

Multiply \frac{19}{10} times \frac{7}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{\frac{19\times 7}{10\times 3}}{\left(5,2-1,4\right)\times \frac{3}{70}}+0,125}{\frac{2\times 2+1}{2}}+0,43$$

Do the multiplications in the fraction \frac{19\times 7}{10\times 3}.

$$\frac{\frac{\frac{133}{30}}{\left(5,2-1,4\right)\times \frac{3}{70}}+0,125}{\frac{2\times 2+1}{2}}+0,43$$

Subtract 1,4 from 5,2 to get 3,8.

$$\frac{\frac{\frac{133}{30}}{3,8\times \frac{3}{70}}+0,125}{\frac{2\times 2+1}{2}}+0,43$$

Convert decimal number 3,8 to fraction \frac{38}{10}. Reduce the fraction \frac{38}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{\frac{133}{30}}{\frac{19}{5}\times \frac{3}{70}}+0,125}{\frac{2\times 2+1}{2}}+0,43$$

Multiply \frac{19}{5} times \frac{3}{70} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{\frac{133}{30}}{\frac{19\times 3}{5\times 70}}+0,125}{\frac{2\times 2+1}{2}}+0,43$$

Do the multiplications in the fraction \frac{19\times 3}{5\times 70}.

$$\frac{\frac{\frac{133}{30}}{\frac{57}{350}}+0,125}{\frac{2\times 2+1}{2}}+0,43$$

Divide \frac{133}{30} by \frac{57}{350} by multiplying \frac{133}{30} by the reciprocal of \frac{57}{350}.

$$\frac{\frac{133}{30}\times \frac{350}{57}+0,125}{\frac{2\times 2+1}{2}}+0,43$$

Multiply \frac{133}{30} times \frac{350}{57} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{133\times 350}{30\times 57}+0,125}{\frac{2\times 2+1}{2}}+0,43$$

Do the multiplications in the fraction \frac{133\times 350}{30\times 57}.

$$\frac{\frac{46550}{1710}+0,125}{\frac{2\times 2+1}{2}}+0,43$$

Reduce the fraction \frac{46550}{1710} to lowest terms by extracting and canceling out 190.

$$\frac{\frac{245}{9}+0,125}{\frac{2\times 2+1}{2}}+0,43$$

Convert decimal number 0,125 to fraction \frac{125}{1000}. Reduce the fraction \frac{125}{1000} to lowest terms by extracting and canceling out 125.

$$\frac{\frac{245}{9}+\frac{1}{8}}{\frac{2\times 2+1}{2}}+0,43$$

Least common multiple of 9 and 8 is 72. Convert \frac{245}{9} and \frac{1}{8} to fractions with denominator 72.

$$\frac{\frac{1960}{72}+\frac{9}{72}}{\frac{2\times 2+1}{2}}+0,43$$

Since \frac{1960}{72} and \frac{9}{72} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1960+9}{72}}{\frac{2\times 2+1}{2}}+0,43$$

Add 1960 and 9 to get 1969.

$$\frac{\frac{1969}{72}}{\frac{2\times 2+1}{2}}+0,43$$

Multiply 2 and 2 to get 4.

$$\frac{\frac{1969}{72}}{\frac{4+1}{2}}+0,43$$

Add 4 and 1 to get 5.

$$\frac{\frac{1969}{72}}{\frac{5}{2}}+0,43$$

Divide \frac{1969}{72} by \frac{5}{2} by multiplying \frac{1969}{72} by the reciprocal of \frac{5}{2}.

$$\frac{1969}{72}\times \frac{2}{5}+0,43$$

Multiply \frac{1969}{72} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1969\times 2}{72\times 5}+0,43$$

Do the multiplications in the fraction \frac{1969\times 2}{72\times 5}.

$$\frac{3938}{360}+0,43$$

Reduce the fraction \frac{3938}{360} to lowest terms by extracting and canceling out 2.

$$\frac{1969}{180}+0,43$$

Convert decimal number 0,43 to fraction \frac{43}{100}.

$$\frac{1969}{180}+\frac{43}{100}$$

Least common multiple of 180 and 100 is 900. Convert \frac{1969}{180} and \frac{43}{100} to fractions with denominator 900.

$$\frac{9845}{900}+\frac{387}{900}$$

Since \frac{9845}{900} and \frac{387}{900} have the same denominator, add them by adding their numerators.

$$\frac{9845+387}{900}$$

Add 9845 and 387 to get 10232.

$$\frac{10232}{900}$$

Reduce the fraction \frac{10232}{900} to lowest terms by extracting and canceling out 4.

$$\frac{2558}{225}$$

Factor

$$\frac{2 \cdot 1279}{3 ^ {2} \cdot 5 ^ {2}} = 11\frac{83}{225} = 11.36888888888889$$