Solve 23/5-57/8+13/4+(-31/8)-4frac{3}{4}-1frac{1}{5}

$$2 \frac { 3 } { 5 } -5 \frac { 7 } { 8 } + 1 \frac { 3 } { 4 } +(- 3 \frac { 1 } { 8 } )- 4 \frac { 3 } { 4 } - 1 \frac { 1 } { 5 }$$

Evaluate

$$-\frac{53}{5}=-10.6$$

Solution Steps

Multiply 2 and 5 to get 10.

$$\frac{10+3}{5}-\frac{5\times 8+7}{8}+\frac{1\times 4+3}{4}-\frac{3\times 8+1}{8}-\frac{4\times 4+3}{4}-\frac{1\times 5+1}{5}$$

Add 10 and 3 to get 13.

$$\frac{13}{5}-\frac{5\times 8+7}{8}+\frac{1\times 4+3}{4}-\frac{3\times 8+1}{8}-\frac{4\times 4+3}{4}-\frac{1\times 5+1}{5}$$

Multiply 5 and 8 to get 40.

$$\frac{13}{5}-\frac{40+7}{8}+\frac{1\times 4+3}{4}-\frac{3\times 8+1}{8}-\frac{4\times 4+3}{4}-\frac{1\times 5+1}{5}$$

Add 40 and 7 to get 47.

$$\frac{13}{5}-\frac{47}{8}+\frac{1\times 4+3}{4}-\frac{3\times 8+1}{8}-\frac{4\times 4+3}{4}-\frac{1\times 5+1}{5}$$

Least common multiple of 5 and 8 is 40. Convert \frac{13}{5} and \frac{47}{8} to fractions with denominator 40.

$$\frac{104}{40}-\frac{235}{40}+\frac{1\times 4+3}{4}-\frac{3\times 8+1}{8}-\frac{4\times 4+3}{4}-\frac{1\times 5+1}{5}$$

Since \frac{104}{40} and \frac{235}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{104-235}{40}+\frac{1\times 4+3}{4}-\frac{3\times 8+1}{8}-\frac{4\times 4+3}{4}-\frac{1\times 5+1}{5}$$

Subtract 235 from 104 to get -131.

$$-\frac{131}{40}+\frac{1\times 4+3}{4}-\frac{3\times 8+1}{8}-\frac{4\times 4+3}{4}-\frac{1\times 5+1}{5}$$

Multiply 1 and 4 to get 4.

$$-\frac{131}{40}+\frac{4+3}{4}-\frac{3\times 8+1}{8}-\frac{4\times 4+3}{4}-\frac{1\times 5+1}{5}$$

Add 4 and 3 to get 7.

$$-\frac{131}{40}+\frac{7}{4}-\frac{3\times 8+1}{8}-\frac{4\times 4+3}{4}-\frac{1\times 5+1}{5}$$

Least common multiple of 40 and 4 is 40. Convert -\frac{131}{40} and \frac{7}{4} to fractions with denominator 40.

$$-\frac{131}{40}+\frac{70}{40}-\frac{3\times 8+1}{8}-\frac{4\times 4+3}{4}-\frac{1\times 5+1}{5}$$

Since -\frac{131}{40} and \frac{70}{40} have the same denominator, add them by adding their numerators.

$$\frac{-131+70}{40}-\frac{3\times 8+1}{8}-\frac{4\times 4+3}{4}-\frac{1\times 5+1}{5}$$

Add -131 and 70 to get -61.

$$-\frac{61}{40}-\frac{3\times 8+1}{8}-\frac{4\times 4+3}{4}-\frac{1\times 5+1}{5}$$

Multiply 3 and 8 to get 24.

$$-\frac{61}{40}-\frac{24+1}{8}-\frac{4\times 4+3}{4}-\frac{1\times 5+1}{5}$$

Add 24 and 1 to get 25.

$$-\frac{61}{40}-\frac{25}{8}-\frac{4\times 4+3}{4}-\frac{1\times 5+1}{5}$$

Least common multiple of 40 and 8 is 40. Convert -\frac{61}{40} and \frac{25}{8} to fractions with denominator 40.

$$-\frac{61}{40}-\frac{125}{40}-\frac{4\times 4+3}{4}-\frac{1\times 5+1}{5}$$

Since -\frac{61}{40} and \frac{125}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-61-125}{40}-\frac{4\times 4+3}{4}-\frac{1\times 5+1}{5}$$

Subtract 125 from -61 to get -186.

$$\frac{-186}{40}-\frac{4\times 4+3}{4}-\frac{1\times 5+1}{5}$$

Reduce the fraction \frac{-186}{40} to lowest terms by extracting and canceling out 2.

$$-\frac{93}{20}-\frac{4\times 4+3}{4}-\frac{1\times 5+1}{5}$$

Multiply 4 and 4 to get 16.

$$-\frac{93}{20}-\frac{16+3}{4}-\frac{1\times 5+1}{5}$$

Add 16 and 3 to get 19.

$$-\frac{93}{20}-\frac{19}{4}-\frac{1\times 5+1}{5}$$

Least common multiple of 20 and 4 is 20. Convert -\frac{93}{20} and \frac{19}{4} to fractions with denominator 20.

$$-\frac{93}{20}-\frac{95}{20}-\frac{1\times 5+1}{5}$$

Since -\frac{93}{20} and \frac{95}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-93-95}{20}-\frac{1\times 5+1}{5}$$

Subtract 95 from -93 to get -188.

$$\frac{-188}{20}-\frac{1\times 5+1}{5}$$

Reduce the fraction \frac{-188}{20} to lowest terms by extracting and canceling out 4.

$$-\frac{47}{5}-\frac{1\times 5+1}{5}$$

Multiply 1 and 5 to get 5.

$$-\frac{47}{5}-\frac{5+1}{5}$$

Add 5 and 1 to get 6.

$$-\frac{47}{5}-\frac{6}{5}$$

Since -\frac{47}{5} and \frac{6}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-47-6}{5}$$

Subtract 6 from -47 to get -53.

$$-\frac{53}{5}$$

Factor

$$-\frac{53}{5} = -10\frac{3}{5} = -10.6$$