Solve [(1,5+0,25-1/2)*1,3]+0,5/(0,83+frac{3{4}-0,5)*1,083}

$$\frac { [ ( 1,5 + 0,25 - \frac { 1 } { 2 } ) \times 1,3 ] + 0,5 } { ( 0,83 + \frac { 3 } { 4 } - 0,5 ) \times 1,083 }$$

Evaluate

$$\frac{53125}{29241}\approx 1,816798331$$

Solution Steps

Add 1,5 and 0,25 to get 1,75.

$$\frac{\left(1,75-\frac{1}{2}\right)\times 1,3+0,5}{\left(0,83+\frac{3}{4}-0,5\right)\times 1,083}$$

Convert decimal number 1,75 to fraction \frac{175}{100}. Reduce the fraction \frac{175}{100} to lowest terms by extracting and canceling out 25.

$$\frac{\left(\frac{7}{4}-\frac{1}{2}\right)\times 1,3+0,5}{\left(0,83+\frac{3}{4}-0,5\right)\times 1,083}$$

Least common multiple of 4 and 2 is 4. Convert \frac{7}{4} and \frac{1}{2} to fractions with denominator 4.

$$\frac{\left(\frac{7}{4}-\frac{2}{4}\right)\times 1,3+0,5}{\left(0,83+\frac{3}{4}-0,5\right)\times 1,083}$$

Since \frac{7}{4} and \frac{2}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{7-2}{4}\times 1,3+0,5}{\left(0,83+\frac{3}{4}-0,5\right)\times 1,083}$$

Subtract 2 from 7 to get 5.

$$\frac{\frac{5}{4}\times 1,3+0,5}{\left(0,83+\frac{3}{4}-0,5\right)\times 1,083}$$

Convert decimal number 1,3 to fraction \frac{13}{10}.

$$\frac{\frac{5}{4}\times \frac{13}{10}+0,5}{\left(0,83+\frac{3}{4}-0,5\right)\times 1,083}$$

Multiply \frac{5}{4} times \frac{13}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{5\times 13}{4\times 10}+0,5}{\left(0,83+\frac{3}{4}-0,5\right)\times 1,083}$$

Do the multiplications in the fraction \frac{5\times 13}{4\times 10}.

$$\frac{\frac{65}{40}+0,5}{\left(0,83+\frac{3}{4}-0,5\right)\times 1,083}$$

Reduce the fraction \frac{65}{40} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{13}{8}+0,5}{\left(0,83+\frac{3}{4}-0,5\right)\times 1,083}$$

Convert decimal number 0,5 to fraction \frac{5}{10}. Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{13}{8}+\frac{1}{2}}{\left(0,83+\frac{3}{4}-0,5\right)\times 1,083}$$

Least common multiple of 8 and 2 is 8. Convert \frac{13}{8} and \frac{1}{2} to fractions with denominator 8.

$$\frac{\frac{13}{8}+\frac{4}{8}}{\left(0,83+\frac{3}{4}-0,5\right)\times 1,083}$$

Since \frac{13}{8} and \frac{4}{8} have the same denominator, add them by adding their numerators.

$$\frac{\frac{13+4}{8}}{\left(0,83+\frac{3}{4}-0,5\right)\times 1,083}$$

Add 13 and 4 to get 17.

$$\frac{\frac{17}{8}}{\left(0,83+\frac{3}{4}-0,5\right)\times 1,083}$$

Convert decimal number 0,83 to fraction \frac{83}{100}.

$$\frac{\frac{17}{8}}{\left(\frac{83}{100}+\frac{3}{4}-0,5\right)\times 1,083}$$

Least common multiple of 100 and 4 is 100. Convert \frac{83}{100} and \frac{3}{4} to fractions with denominator 100.

$$\frac{\frac{17}{8}}{\left(\frac{83}{100}+\frac{75}{100}-0,5\right)\times 1,083}$$

Since \frac{83}{100} and \frac{75}{100} have the same denominator, add them by adding their numerators.

$$\frac{\frac{17}{8}}{\left(\frac{83+75}{100}-0,5\right)\times 1,083}$$

Add 83 and 75 to get 158.

$$\frac{\frac{17}{8}}{\left(\frac{158}{100}-0,5\right)\times 1,083}$$

Reduce the fraction \frac{158}{100} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{17}{8}}{\left(\frac{79}{50}-0,5\right)\times 1,083}$$

Convert decimal number 0,5 to fraction \frac{5}{10}. Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{17}{8}}{\left(\frac{79}{50}-\frac{1}{2}\right)\times 1,083}$$

Least common multiple of 50 and 2 is 50. Convert \frac{79}{50} and \frac{1}{2} to fractions with denominator 50.

$$\frac{\frac{17}{8}}{\left(\frac{79}{50}-\frac{25}{50}\right)\times 1,083}$$

Since \frac{79}{50} and \frac{25}{50} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{17}{8}}{\frac{79-25}{50}\times 1,083}$$

Subtract 25 from 79 to get 54.

$$\frac{\frac{17}{8}}{\frac{54}{50}\times 1,083}$$

Reduce the fraction \frac{54}{50} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{17}{8}}{\frac{27}{25}\times 1,083}$$

Convert decimal number 1,083 to fraction \frac{1083}{1000}.

$$\frac{\frac{17}{8}}{\frac{27}{25}\times \frac{1083}{1000}}$$

Multiply \frac{27}{25} times \frac{1083}{1000} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{17}{8}}{\frac{27\times 1083}{25\times 1000}}$$

Do the multiplications in the fraction \frac{27\times 1083}{25\times 1000}.

$$\frac{\frac{17}{8}}{\frac{29241}{25000}}$$

Divide \frac{17}{8} by \frac{29241}{25000} by multiplying \frac{17}{8} by the reciprocal of \frac{29241}{25000}.

$$\frac{17}{8}\times \frac{25000}{29241}$$

Multiply \frac{17}{8} times \frac{25000}{29241} by multiplying numerator times numerator and denominator times denominator.

$$\frac{17\times 25000}{8\times 29241}$$

Do the multiplications in the fraction \frac{17\times 25000}{8\times 29241}.

$$\frac{425000}{233928}$$

Reduce the fraction \frac{425000}{233928} to lowest terms by extracting and canceling out 8.

$$\frac{53125}{29241}$$

Factor

$$\frac{17 \cdot 5 ^ {5}}{3 ^ {4} \cdot 19 ^ {2}} = 1\frac{23884}{29241} = 1.8167983311104272$$