Solve -3/4+(-7/8)*51/7-9/14

$$- \frac { 3 } { 4 } + ( - \frac { 7 } { 8 } ) \times 5 \frac { 1 } { 7 } - \frac { 9 } { 14 }$$

Evaluate

$$-\frac{165}{28}\approx -5.892857143$$

Solution Steps

Multiply 5 and 7 to get 35.

$$-\frac{3}{4}-\frac{7}{8}\times \frac{35+1}{7}-\frac{9}{14}$$

Add 35 and 1 to get 36.

$$-\frac{3}{4}-\frac{7}{8}\times \frac{36}{7}-\frac{9}{14}$$

Multiply -\frac{7}{8} times \frac{36}{7} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{3}{4}+\frac{-7\times 36}{8\times 7}-\frac{9}{14}$$

Do the multiplications in the fraction \frac{-7\times 36}{8\times 7}.

$$-\frac{3}{4}+\frac{-252}{56}-\frac{9}{14}$$

Reduce the fraction \frac{-252}{56} to lowest terms by extracting and canceling out 28.

$$-\frac{3}{4}-\frac{9}{2}-\frac{9}{14}$$

Least common multiple of 4 and 2 is 4. Convert -\frac{3}{4} and \frac{9}{2} to fractions with denominator 4.

$$-\frac{3}{4}-\frac{18}{4}-\frac{9}{14}$$

Since -\frac{3}{4} and \frac{18}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-3-18}{4}-\frac{9}{14}$$

Subtract 18 from -3 to get -21.

$$-\frac{21}{4}-\frac{9}{14}$$

Least common multiple of 4 and 14 is 28. Convert -\frac{21}{4} and \frac{9}{14} to fractions with denominator 28.

$$-\frac{147}{28}-\frac{18}{28}$$

Since -\frac{147}{28} and \frac{18}{28} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-147-18}{28}$$

Subtract 18 from -147 to get -165.

$$-\frac{165}{28}$$

Factor

$$-\frac{165}{28} = -5\frac{25}{28} = -5.892857142857143$$