Solve -11/4+0.5-1.5-0.3+31/4-21/3-22/5

$$- 1 \frac { 1 } { 4 } + 0.5 - 1.5 - 0.3 + 3 \frac { 1 } { 4 } - 2 \frac { 1 } { 3 } - 2 \frac { 2 } { 5 }$$

Evaluate

$$-\frac{121}{30}\approx -4.033333333$$

Solution Steps

Multiply 1 and 4 to get 4.

$$-\frac{4+1}{4}+0.5-1.5-0.3+\frac{3\times 4+1}{4}-\frac{2\times 3+1}{3}-\frac{2\times 5+2}{5}$$

Add 4 and 1 to get 5.

$$-\frac{5}{4}+0.5-1.5-0.3+\frac{3\times 4+1}{4}-\frac{2\times 3+1}{3}-\frac{2\times 5+2}{5}$$

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.

$$-\frac{5}{4}+\frac{1}{2}-1.5-0.3+\frac{3\times 4+1}{4}-\frac{2\times 3+1}{3}-\frac{2\times 5+2}{5}$$

Least common multiple of 4 and 2 is 4. Convert -\frac{5}{4} and \frac{1}{2} to fractions with denominator 4.

$$-\frac{5}{4}+\frac{2}{4}-1.5-0.3+\frac{3\times 4+1}{4}-\frac{2\times 3+1}{3}-\frac{2\times 5+2}{5}$$

Since -\frac{5}{4} and \frac{2}{4} have the same denominator, add them by adding their numerators.

$$\frac{-5+2}{4}-1.5-0.3+\frac{3\times 4+1}{4}-\frac{2\times 3+1}{3}-\frac{2\times 5+2}{5}$$

Add -5 and 2 to get -3.

$$-\frac{3}{4}-1.5-0.3+\frac{3\times 4+1}{4}-\frac{2\times 3+1}{3}-\frac{2\times 5+2}{5}$$

Convert decimal number 1.5 to fraction \frac{15}{10}. Reduce the fraction \frac{15}{10} to lowest terms by extracting and canceling out 5.

$$-\frac{3}{4}-\frac{3}{2}-0.3+\frac{3\times 4+1}{4}-\frac{2\times 3+1}{3}-\frac{2\times 5+2}{5}$$

Least common multiple of 4 and 2 is 4. Convert -\frac{3}{4} and \frac{3}{2} to fractions with denominator 4.

$$-\frac{3}{4}-\frac{6}{4}-0.3+\frac{3\times 4+1}{4}-\frac{2\times 3+1}{3}-\frac{2\times 5+2}{5}$$

Since -\frac{3}{4} and \frac{6}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-3-6}{4}-0.3+\frac{3\times 4+1}{4}-\frac{2\times 3+1}{3}-\frac{2\times 5+2}{5}$$

Subtract 6 from -3 to get -9.

$$-\frac{9}{4}-0.3+\frac{3\times 4+1}{4}-\frac{2\times 3+1}{3}-\frac{2\times 5+2}{5}$$

Convert decimal number 0.3 to fraction \frac{3}{10}.

$$-\frac{9}{4}-\frac{3}{10}+\frac{3\times 4+1}{4}-\frac{2\times 3+1}{3}-\frac{2\times 5+2}{5}$$

Least common multiple of 4 and 10 is 20. Convert -\frac{9}{4} and \frac{3}{10} to fractions with denominator 20.

$$-\frac{45}{20}-\frac{6}{20}+\frac{3\times 4+1}{4}-\frac{2\times 3+1}{3}-\frac{2\times 5+2}{5}$$

Since -\frac{45}{20} and \frac{6}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-45-6}{20}+\frac{3\times 4+1}{4}-\frac{2\times 3+1}{3}-\frac{2\times 5+2}{5}$$

Subtract 6 from -45 to get -51.

$$-\frac{51}{20}+\frac{3\times 4+1}{4}-\frac{2\times 3+1}{3}-\frac{2\times 5+2}{5}$$

Multiply 3 and 4 to get 12.

$$-\frac{51}{20}+\frac{12+1}{4}-\frac{2\times 3+1}{3}-\frac{2\times 5+2}{5}$$

Add 12 and 1 to get 13.

$$-\frac{51}{20}+\frac{13}{4}-\frac{2\times 3+1}{3}-\frac{2\times 5+2}{5}$$

Least common multiple of 20 and 4 is 20. Convert -\frac{51}{20} and \frac{13}{4} to fractions with denominator 20.

$$-\frac{51}{20}+\frac{65}{20}-\frac{2\times 3+1}{3}-\frac{2\times 5+2}{5}$$

Since -\frac{51}{20} and \frac{65}{20} have the same denominator, add them by adding their numerators.

$$\frac{-51+65}{20}-\frac{2\times 3+1}{3}-\frac{2\times 5+2}{5}$$

Add -51 and 65 to get 14.

$$\frac{14}{20}-\frac{2\times 3+1}{3}-\frac{2\times 5+2}{5}$$

Reduce the fraction \frac{14}{20} to lowest terms by extracting and canceling out 2.

$$\frac{7}{10}-\frac{2\times 3+1}{3}-\frac{2\times 5+2}{5}$$

Multiply 2 and 3 to get 6.

$$\frac{7}{10}-\frac{6+1}{3}-\frac{2\times 5+2}{5}$$

Add 6 and 1 to get 7.

$$\frac{7}{10}-\frac{7}{3}-\frac{2\times 5+2}{5}$$

Least common multiple of 10 and 3 is 30. Convert \frac{7}{10} and \frac{7}{3} to fractions with denominator 30.

$$\frac{21}{30}-\frac{70}{30}-\frac{2\times 5+2}{5}$$

Since \frac{21}{30} and \frac{70}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{21-70}{30}-\frac{2\times 5+2}{5}$$

Subtract 70 from 21 to get -49.

$$-\frac{49}{30}-\frac{2\times 5+2}{5}$$

Multiply 2 and 5 to get 10.

$$-\frac{49}{30}-\frac{10+2}{5}$$

Add 10 and 2 to get 12.

$$-\frac{49}{30}-\frac{12}{5}$$

Least common multiple of 30 and 5 is 30. Convert -\frac{49}{30} and \frac{12}{5} to fractions with denominator 30.

$$-\frac{49}{30}-\frac{72}{30}$$

Since -\frac{49}{30} and \frac{72}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-49-72}{30}$$

Subtract 72 from -49 to get -121.

$$-\frac{121}{30}$$

Factor

$$-\frac{121}{30} = -4\frac{1}{30} = -4.033333333333333$$