Solve -1/2+{3/7-(1/4-5/2)-(frac{3}{2}-frac{5}{4}*frac{1}{7})}

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

Evaluate

$$\frac{6}{7}\approx 0.857142857$$

Solution Steps

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

$$-\frac{1}{2}+\frac{3}{7}-\left(\frac{1}{4}-\frac{10}{4}\right)-\left(\frac{3}{2}-\frac{5}{4}\times \frac{1}{7}\right)$$

Since \frac{1}{4} and \frac{10}{4} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{2}+\frac{3}{7}-\frac{1-10}{4}-\left(\frac{3}{2}-\frac{5}{4}\times \frac{1}{7}\right)$$

Subtract 10 from 1 to get -9.

$$-\frac{1}{2}+\frac{3}{7}-\left(-\frac{9}{4}\right)-\left(\frac{3}{2}-\frac{5}{4}\times \frac{1}{7}\right)$$

The opposite of -\frac{9}{4} is \frac{9}{4}.

$$-\frac{1}{2}+\frac{3}{7}+\frac{9}{4}-\left(\frac{3}{2}-\frac{5}{4}\times \frac{1}{7}\right)$$

Least common multiple of 7 and 4 is 28. Convert \frac{3}{7} and \frac{9}{4} to fractions with denominator 28.

$$-\frac{1}{2}+\frac{12}{28}+\frac{63}{28}-\left(\frac{3}{2}-\frac{5}{4}\times \frac{1}{7}\right)$$

Since \frac{12}{28} and \frac{63}{28} have the same denominator, add them by adding their numerators.

$$-\frac{1}{2}+\frac{12+63}{28}-\left(\frac{3}{2}-\frac{5}{4}\times \frac{1}{7}\right)$$

Add 12 and 63 to get 75.

$$-\frac{1}{2}+\frac{75}{28}-\left(\frac{3}{2}-\frac{5}{4}\times \frac{1}{7}\right)$$

Multiply \frac{5}{4} times \frac{1}{7} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{1}{2}+\frac{75}{28}-\left(\frac{3}{2}-\frac{5\times 1}{4\times 7}\right)$$

Do the multiplications in the fraction \frac{5\times 1}{4\times 7}.

$$-\frac{1}{2}+\frac{75}{28}-\left(\frac{3}{2}-\frac{5}{28}\right)$$

Least common multiple of 2 and 28 is 28. Convert \frac{3}{2} and \frac{5}{28} to fractions with denominator 28.

$$-\frac{1}{2}+\frac{75}{28}-\left(\frac{42}{28}-\frac{5}{28}\right)$$

Since \frac{42}{28} and \frac{5}{28} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{2}+\frac{75}{28}-\frac{42-5}{28}$$

Subtract 5 from 42 to get 37.

$$-\frac{1}{2}+\frac{75}{28}-\frac{37}{28}$$

Since \frac{75}{28} and \frac{37}{28} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{2}+\frac{75-37}{28}$$

Subtract 37 from 75 to get 38.

$$-\frac{1}{2}+\frac{38}{28}$$

Reduce the fraction \frac{38}{28} to lowest terms by extracting and canceling out 2.

$$-\frac{1}{2}+\frac{19}{14}$$

Least common multiple of 2 and 14 is 14. Convert -\frac{1}{2} and \frac{19}{14} to fractions with denominator 14.

$$-\frac{7}{14}+\frac{19}{14}$$

Since -\frac{7}{14} and \frac{19}{14} have the same denominator, add them by adding their numerators.

$$\frac{-7+19}{14}$$

Add -7 and 19 to get 12.

$$\frac{12}{14}$$

Reduce the fraction \frac{12}{14} to lowest terms by extracting and canceling out 2.

$$\frac{6}{7}$$

Factor

$$\frac{2 \cdot 3}{7} = 0.8571428571428571$$