Solve 1/4-5/6-frac{2{7}}

$$\frac { 1 } { 4 } - \frac { 5 } { 6 - \frac { 2 } { 7 } }$$

Evaluate

$$-\frac{5}{8}=-0.625$$

Solution Steps

Convert 6 to fraction \frac{42}{7}.

$$\frac{1}{4}-\frac{5}{\frac{42}{7}-\frac{2}{7}}$$

Since \frac{42}{7} and \frac{2}{7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{4}-\frac{5}{\frac{42-2}{7}}$$

Subtract 2 from 42 to get 40.

$$\frac{1}{4}-\frac{5}{\frac{40}{7}}$$

Divide 5 by \frac{40}{7} by multiplying 5 by the reciprocal of \frac{40}{7}.

$$\frac{1}{4}-5\times \frac{7}{40}$$

Express 5\times \frac{7}{40} as a single fraction.

$$\frac{1}{4}-\frac{5\times 7}{40}$$

Multiply 5 and 7 to get 35.

$$\frac{1}{4}-\frac{35}{40}$$

Reduce the fraction \frac{35}{40} to lowest terms by extracting and canceling out 5.

$$\frac{1}{4}-\frac{7}{8}$$

Least common multiple of 4 and 8 is 8. Convert \frac{1}{4} and \frac{7}{8} to fractions with denominator 8.

$$\frac{2}{8}-\frac{7}{8}$$

Since \frac{2}{8} and \frac{7}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2-7}{8}$$

Subtract 7 from 2 to get -5.

$$-\frac{5}{8}$$

Factor

$$-\frac{5}{8} = -0.625$$