Solve 11/5-(0.9+1/3)*3.5+(6.95+1/20)

$$1 \frac { 1 } { 5 } - ( 0.9 + \frac { 1 } { 3 } ) \times 3.5 + ( 6.95 + \frac { 1 } { 20 } )$$

Evaluate

$$\frac{233}{60}\approx 3.883333333$$

Solution Steps

Multiply 1 and 5 to get 5.

$$\frac{5+1}{5}-\left(0.9+\frac{1}{3}\right)\times 3.5+6.95+\frac{1}{20}$$

Add 5 and 1 to get 6.

$$\frac{6}{5}-\left(0.9+\frac{1}{3}\right)\times 3.5+6.95+\frac{1}{20}$$

Convert decimal number 0.9 to fraction \frac{9}{10}.

$$\frac{6}{5}-\left(\frac{9}{10}+\frac{1}{3}\right)\times 3.5+6.95+\frac{1}{20}$$

Least common multiple of 10 and 3 is 30. Convert \frac{9}{10} and \frac{1}{3} to fractions with denominator 30.

$$\frac{6}{5}-\left(\frac{27}{30}+\frac{10}{30}\right)\times 3.5+6.95+\frac{1}{20}$$

Since \frac{27}{30} and \frac{10}{30} have the same denominator, add them by adding their numerators.

$$\frac{6}{5}-\frac{27+10}{30}\times 3.5+6.95+\frac{1}{20}$$

Add 27 and 10 to get 37.

$$\frac{6}{5}-\frac{37}{30}\times 3.5+6.95+\frac{1}{20}$$

Convert decimal number 3.5 to fraction \frac{35}{10}. Reduce the fraction \frac{35}{10} to lowest terms by extracting and canceling out 5.

$$\frac{6}{5}-\frac{37}{30}\times \frac{7}{2}+6.95+\frac{1}{20}$$

Multiply \frac{37}{30} times \frac{7}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{6}{5}-\frac{37\times 7}{30\times 2}+6.95+\frac{1}{20}$$

Do the multiplications in the fraction \frac{37\times 7}{30\times 2}.

$$\frac{6}{5}-\frac{259}{60}+6.95+\frac{1}{20}$$

Least common multiple of 5 and 60 is 60. Convert \frac{6}{5} and \frac{259}{60} to fractions with denominator 60.

$$\frac{72}{60}-\frac{259}{60}+6.95+\frac{1}{20}$$

Since \frac{72}{60} and \frac{259}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{72-259}{60}+6.95+\frac{1}{20}$$

Subtract 259 from 72 to get -187.

$$-\frac{187}{60}+6.95+\frac{1}{20}$$

Convert decimal number 6.95 to fraction \frac{695}{100}. Reduce the fraction \frac{695}{100} to lowest terms by extracting and canceling out 5.

$$-\frac{187}{60}+\frac{139}{20}+\frac{1}{20}$$

Least common multiple of 60 and 20 is 60. Convert -\frac{187}{60} and \frac{139}{20} to fractions with denominator 60.

$$-\frac{187}{60}+\frac{417}{60}+\frac{1}{20}$$

Since -\frac{187}{60} and \frac{417}{60} have the same denominator, add them by adding their numerators.

$$\frac{-187+417}{60}+\frac{1}{20}$$

Add -187 and 417 to get 230.

$$\frac{230}{60}+\frac{1}{20}$$

Reduce the fraction \frac{230}{60} to lowest terms by extracting and canceling out 10.

$$\frac{23}{6}+\frac{1}{20}$$

Least common multiple of 6 and 20 is 60. Convert \frac{23}{6} and \frac{1}{20} to fractions with denominator 60.

$$\frac{230}{60}+\frac{3}{60}$$

Since \frac{230}{60} and \frac{3}{60} have the same denominator, add them by adding their numerators.

$$\frac{230+3}{60}$$

Add 230 and 3 to get 233.

$$\frac{233}{60}$$

Factor

$$\frac{233}{3 \cdot 5 \cdot 2 ^ {2}} = 3\frac{53}{60} = 3.8833333333333333$$