Solve 1/12-5/12-6/15-19/20+1frac{11}{15}

$$\frac { 1 } { 12 } - \frac { 5 } { 12 } - \frac { 6 } { 15 } - 1 \frac { 9 } { 20 } + 1 \frac { 11 } { 15 }$$

Evaluate

$$-\frac{9}{20}=-0.45$$

Solution Steps

Since \frac{1}{12} and \frac{5}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1-5}{12}-\frac{6}{15}-\frac{1\times 20+9}{20}+\frac{1\times 15+11}{15}$$

Subtract 5 from 1 to get -4.

$$\frac{-4}{12}-\frac{6}{15}-\frac{1\times 20+9}{20}+\frac{1\times 15+11}{15}$$

Reduce the fraction \frac{-4}{12} to lowest terms by extracting and canceling out 4.

$$-\frac{1}{3}-\frac{6}{15}-\frac{1\times 20+9}{20}+\frac{1\times 15+11}{15}$$

Reduce the fraction \frac{6}{15} to lowest terms by extracting and canceling out 3.

$$-\frac{1}{3}-\frac{2}{5}-\frac{1\times 20+9}{20}+\frac{1\times 15+11}{15}$$

Least common multiple of 3 and 5 is 15. Convert -\frac{1}{3} and \frac{2}{5} to fractions with denominator 15.

$$-\frac{5}{15}-\frac{6}{15}-\frac{1\times 20+9}{20}+\frac{1\times 15+11}{15}$$

Since -\frac{5}{15} and \frac{6}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-5-6}{15}-\frac{1\times 20+9}{20}+\frac{1\times 15+11}{15}$$

Subtract 6 from -5 to get -11.

$$-\frac{11}{15}-\frac{1\times 20+9}{20}+\frac{1\times 15+11}{15}$$

Multiply 1 and 20 to get 20.

$$-\frac{11}{15}-\frac{20+9}{20}+\frac{1\times 15+11}{15}$$

Add 20 and 9 to get 29.

$$-\frac{11}{15}-\frac{29}{20}+\frac{1\times 15+11}{15}$$

Least common multiple of 15 and 20 is 60. Convert -\frac{11}{15} and \frac{29}{20} to fractions with denominator 60.

$$-\frac{44}{60}-\frac{87}{60}+\frac{1\times 15+11}{15}$$

Since -\frac{44}{60} and \frac{87}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-44-87}{60}+\frac{1\times 15+11}{15}$$

Subtract 87 from -44 to get -131.

$$-\frac{131}{60}+\frac{1\times 15+11}{15}$$

Multiply 1 and 15 to get 15.

$$-\frac{131}{60}+\frac{15+11}{15}$$

Add 15 and 11 to get 26.

$$-\frac{131}{60}+\frac{26}{15}$$

Least common multiple of 60 and 15 is 60. Convert -\frac{131}{60} and \frac{26}{15} to fractions with denominator 60.

$$-\frac{131}{60}+\frac{104}{60}$$

Since -\frac{131}{60} and \frac{104}{60} have the same denominator, add them by adding their numerators.

$$\frac{-131+104}{60}$$

Add -131 and 104 to get -27.

$$\frac{-27}{60}$$

Reduce the fraction \frac{-27}{60} to lowest terms by extracting and canceling out 3.

$$-\frac{9}{20}$$

Factor

$$-\frac{9}{20} = -0.45$$