Solve 1,15-[1.25-(1.35-13/5)]+35/5/5-frac{4{3}(2.6:13/6+0.2)}=

$$\frac { 1,15 - [ 1.25 - ( 1.35 - \frac { 13 } { 5 } ) ] + 3 \frac { 5 } { 5 } } { 5 - \frac { 4 } { 3 } ( 2.6 : \frac { 13 } { 6 } + 0.2 ) } =$$

Evaluate

$$\frac{159}{188}\approx 0.845744681$$

Solution Steps

Convert decimal number 1.35 to fraction \frac{135}{100}. Reduce the fraction \frac{135}{100} to lowest terms by extracting and canceling out 5.

$$\frac{1.15-\left(1.25-\left(\frac{27}{20}-\frac{13}{5}\right)\right)+\frac{3\times 5+5}{5}}{5-\frac{4}{3}\left(\frac{2.6}{\frac{13}{6}}+0.2\right)}$$

Least common multiple of 20 and 5 is 20. Convert \frac{27}{20} and \frac{13}{5} to fractions with denominator 20.

$$\frac{1.15-\left(1.25-\left(\frac{27}{20}-\frac{52}{20}\right)\right)+\frac{3\times 5+5}{5}}{5-\frac{4}{3}\left(\frac{2.6}{\frac{13}{6}}+0.2\right)}$$

Since \frac{27}{20} and \frac{52}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1.15-\left(1.25-\frac{27-52}{20}\right)+\frac{3\times 5+5}{5}}{5-\frac{4}{3}\left(\frac{2.6}{\frac{13}{6}}+0.2\right)}$$

Subtract 52 from 27 to get -25.

$$\frac{1.15-\left(1.25-\frac{-25}{20}\right)+\frac{3\times 5+5}{5}}{5-\frac{4}{3}\left(\frac{2.6}{\frac{13}{6}}+0.2\right)}$$

Reduce the fraction \frac{-25}{20} to lowest terms by extracting and canceling out 5.

$$\frac{1.15-\left(1.25-\left(-\frac{5}{4}\right)\right)+\frac{3\times 5+5}{5}}{5-\frac{4}{3}\left(\frac{2.6}{\frac{13}{6}}+0.2\right)}$$

The opposite of -\frac{5}{4} is \frac{5}{4}.

$$\frac{1.15-\left(1.25+\frac{5}{4}\right)+\frac{3\times 5+5}{5}}{5-\frac{4}{3}\left(\frac{2.6}{\frac{13}{6}}+0.2\right)}$$

Convert decimal number 1.25 to fraction \frac{125}{100}. Reduce the fraction \frac{125}{100} to lowest terms by extracting and canceling out 25.

$$\frac{1.15-\left(\frac{5}{4}+\frac{5}{4}\right)+\frac{3\times 5+5}{5}}{5-\frac{4}{3}\left(\frac{2.6}{\frac{13}{6}}+0.2\right)}$$

Since \frac{5}{4} and \frac{5}{4} have the same denominator, add them by adding their numerators.

$$\frac{1.15-\frac{5+5}{4}+\frac{3\times 5+5}{5}}{5-\frac{4}{3}\left(\frac{2.6}{\frac{13}{6}}+0.2\right)}$$

Add 5 and 5 to get 10.

$$\frac{1.15-\frac{10}{4}+\frac{3\times 5+5}{5}}{5-\frac{4}{3}\left(\frac{2.6}{\frac{13}{6}}+0.2\right)}$$

Reduce the fraction \frac{10}{4} to lowest terms by extracting and canceling out 2.

$$\frac{1.15-\frac{5}{2}+\frac{3\times 5+5}{5}}{5-\frac{4}{3}\left(\frac{2.6}{\frac{13}{6}}+0.2\right)}$$

Convert decimal number 1.15 to fraction \frac{115}{100}. Reduce the fraction \frac{115}{100} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{23}{20}-\frac{5}{2}+\frac{3\times 5+5}{5}}{5-\frac{4}{3}\left(\frac{2.6}{\frac{13}{6}}+0.2\right)}$$

Least common multiple of 20 and 2 is 20. Convert \frac{23}{20} and \frac{5}{2} to fractions with denominator 20.

$$\frac{\frac{23}{20}-\frac{50}{20}+\frac{3\times 5+5}{5}}{5-\frac{4}{3}\left(\frac{2.6}{\frac{13}{6}}+0.2\right)}$$

Since \frac{23}{20} and \frac{50}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{23-50}{20}+\frac{3\times 5+5}{5}}{5-\frac{4}{3}\left(\frac{2.6}{\frac{13}{6}}+0.2\right)}$$

Subtract 50 from 23 to get -27.

$$\frac{-\frac{27}{20}+\frac{3\times 5+5}{5}}{5-\frac{4}{3}\left(\frac{2.6}{\frac{13}{6}}+0.2\right)}$$

Multiply 3 and 5 to get 15.

$$\frac{-\frac{27}{20}+\frac{15+5}{5}}{5-\frac{4}{3}\left(\frac{2.6}{\frac{13}{6}}+0.2\right)}$$

Add 15 and 5 to get 20.

$$\frac{-\frac{27}{20}+\frac{20}{5}}{5-\frac{4}{3}\left(\frac{2.6}{\frac{13}{6}}+0.2\right)}$$

Divide 20 by 5 to get 4.

$$\frac{-\frac{27}{20}+4}{5-\frac{4}{3}\left(\frac{2.6}{\frac{13}{6}}+0.2\right)}$$

Convert 4 to fraction \frac{80}{20}.

$$\frac{-\frac{27}{20}+\frac{80}{20}}{5-\frac{4}{3}\left(\frac{2.6}{\frac{13}{6}}+0.2\right)}$$

Since -\frac{27}{20} and \frac{80}{20} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-27+80}{20}}{5-\frac{4}{3}\left(\frac{2.6}{\frac{13}{6}}+0.2\right)}$$

Add -27 and 80 to get 53.

$$\frac{\frac{53}{20}}{5-\frac{4}{3}\left(\frac{2.6}{\frac{13}{6}}+0.2\right)}$$

Divide 2.6 by \frac{13}{6} by multiplying 2.6 by the reciprocal of \frac{13}{6}.

$$\frac{\frac{53}{20}}{5-\frac{4}{3}\left(2.6\times \frac{6}{13}+0.2\right)}$$

Convert decimal number 2.6 to fraction \frac{26}{10}. Reduce the fraction \frac{26}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{53}{20}}{5-\frac{4}{3}\left(\frac{13}{5}\times \frac{6}{13}+0.2\right)}$$

Multiply \frac{13}{5} times \frac{6}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{53}{20}}{5-\frac{4}{3}\left(\frac{13\times 6}{5\times 13}+0.2\right)}$$

Cancel out 13 in both numerator and denominator.

$$\frac{\frac{53}{20}}{5-\frac{4}{3}\left(\frac{6}{5}+0.2\right)}$$

Convert decimal number 0.2 to fraction \frac{2}{10}. Reduce the fraction \frac{2}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{53}{20}}{5-\frac{4}{3}\left(\frac{6}{5}+\frac{1}{5}\right)}$$

Since \frac{6}{5} and \frac{1}{5} have the same denominator, add them by adding their numerators.

$$\frac{\frac{53}{20}}{5-\frac{4}{3}\times \frac{6+1}{5}}$$

Add 6 and 1 to get 7.

$$\frac{\frac{53}{20}}{5-\frac{4}{3}\times \frac{7}{5}}$$

Multiply \frac{4}{3} times \frac{7}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{53}{20}}{5-\frac{4\times 7}{3\times 5}}$$

Do the multiplications in the fraction \frac{4\times 7}{3\times 5}.

$$\frac{\frac{53}{20}}{5-\frac{28}{15}}$$

Convert 5 to fraction \frac{75}{15}.

$$\frac{\frac{53}{20}}{\frac{75}{15}-\frac{28}{15}}$$

Since \frac{75}{15} and \frac{28}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{53}{20}}{\frac{75-28}{15}}$$

Subtract 28 from 75 to get 47.

$$\frac{\frac{53}{20}}{\frac{47}{15}}$$

Divide \frac{53}{20} by \frac{47}{15} by multiplying \frac{53}{20} by the reciprocal of \frac{47}{15}.

$$\frac{53}{20}\times \frac{15}{47}$$

Multiply \frac{53}{20} times \frac{15}{47} by multiplying numerator times numerator and denominator times denominator.

$$\frac{53\times 15}{20\times 47}$$

Do the multiplications in the fraction \frac{53\times 15}{20\times 47}.

$$\frac{795}{940}$$

Reduce the fraction \frac{795}{940} to lowest terms by extracting and canceling out 5.

$$\frac{159}{188}$$

Factor

$$\frac{3 \cdot 53}{47 \cdot 2 ^ {2}} = 0.8457446808510638$$