Solve 7/8-2/5-9/20:1/4+frac{2}{5}-frac{1}{8}

$$\frac { 7 } { 8 } - \frac { 2 } { 5 } - \frac { 9 } { 20 } : \frac { 1 } { 4 } + \frac { 2 } { 5 } - \frac { 1 } { 8 }$$

Evaluate

$$-\frac{21}{20}=-1.05$$

Solution Steps

Least common multiple of 8 and 5 is 40. Convert \frac{7}{8} and \frac{2}{5} to fractions with denominator 40.

$$\frac{35}{40}-\frac{16}{40}-\frac{\frac{9}{20}}{\frac{1}{4}}+\frac{2}{5}-\frac{1}{8}$$

Since \frac{35}{40} and \frac{16}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{35-16}{40}-\frac{\frac{9}{20}}{\frac{1}{4}}+\frac{2}{5}-\frac{1}{8}$$

Subtract 16 from 35 to get 19.

$$\frac{19}{40}-\frac{\frac{9}{20}}{\frac{1}{4}}+\frac{2}{5}-\frac{1}{8}$$

Divide \frac{9}{20} by \frac{1}{4} by multiplying \frac{9}{20} by the reciprocal of \frac{1}{4}.

$$\frac{19}{40}-\frac{9}{20}\times 4+\frac{2}{5}-\frac{1}{8}$$

Express \frac{9}{20}\times 4 as a single fraction.

$$\frac{19}{40}-\frac{9\times 4}{20}+\frac{2}{5}-\frac{1}{8}$$

Multiply 9 and 4 to get 36.

$$\frac{19}{40}-\frac{36}{20}+\frac{2}{5}-\frac{1}{8}$$

Reduce the fraction \frac{36}{20} to lowest terms by extracting and canceling out 4.

$$\frac{19}{40}-\frac{9}{5}+\frac{2}{5}-\frac{1}{8}$$

Least common multiple of 40 and 5 is 40. Convert \frac{19}{40} and \frac{9}{5} to fractions with denominator 40.

$$\frac{19}{40}-\frac{72}{40}+\frac{2}{5}-\frac{1}{8}$$

Since \frac{19}{40} and \frac{72}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{19-72}{40}+\frac{2}{5}-\frac{1}{8}$$

Subtract 72 from 19 to get -53.

$$-\frac{53}{40}+\frac{2}{5}-\frac{1}{8}$$

Least common multiple of 40 and 5 is 40. Convert -\frac{53}{40} and \frac{2}{5} to fractions with denominator 40.

$$-\frac{53}{40}+\frac{16}{40}-\frac{1}{8}$$

Since -\frac{53}{40} and \frac{16}{40} have the same denominator, add them by adding their numerators.

$$\frac{-53+16}{40}-\frac{1}{8}$$

Add -53 and 16 to get -37.

$$-\frac{37}{40}-\frac{1}{8}$$

Least common multiple of 40 and 8 is 40. Convert -\frac{37}{40} and \frac{1}{8} to fractions with denominator 40.

$$-\frac{37}{40}-\frac{5}{40}$$

Since -\frac{37}{40} and \frac{5}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-37-5}{40}$$

Subtract 5 from -37 to get -42.

$$\frac{-42}{40}$$

Reduce the fraction \frac{-42}{40} to lowest terms by extracting and canceling out 2.

$$-\frac{21}{20}$$

Factor

$$-\frac{21}{20} = -1\frac{1}{20} = -1.05$$