Solve -7/8+23/4div31/2

$$- \frac { 7 } { 8 } + 2 \frac { 3 } { 4 } \div 3 \frac { 1 } { 2 }$$

Evaluate

$$-\frac{5}{56}\approx -0.089285714$$

Solution Steps

Divide \frac{2\times 4+3}{4} by \frac{3\times 2+1}{2} by multiplying \frac{2\times 4+3}{4} by the reciprocal of \frac{3\times 2+1}{2}.

$$-\frac{7}{8}+\frac{\left(2\times 4+3\right)\times 2}{4\left(3\times 2+1\right)}$$

Cancel out 2 in both numerator and denominator.

$$-\frac{7}{8}+\frac{3+2\times 4}{2\left(1+2\times 3\right)}$$

Multiply 2 and 4 to get 8.

$$-\frac{7}{8}+\frac{3+8}{2\left(1+2\times 3\right)}$$

Add 3 and 8 to get 11.

$$-\frac{7}{8}+\frac{11}{2\left(1+2\times 3\right)}$$

Multiply 2 and 3 to get 6.

$$-\frac{7}{8}+\frac{11}{2\left(1+6\right)}$$

Add 1 and 6 to get 7.

$$-\frac{7}{8}+\frac{11}{2\times 7}$$

Multiply 2 and 7 to get 14.

$$-\frac{7}{8}+\frac{11}{14}$$

Least common multiple of 8 and 14 is 56. Convert -\frac{7}{8} and \frac{11}{14} to fractions with denominator 56.

$$-\frac{49}{56}+\frac{44}{56}$$

Since -\frac{49}{56} and \frac{44}{56} have the same denominator, add them by adding their numerators.

$$\frac{-49+44}{56}$$

Add -49 and 44 to get -5.

$$-\frac{5}{56}$$

Factor

$$-\frac{5}{56} = -0.08928571428571429$$