Solve 3/2-4/frac{7{4}+1}

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

Evaluate

$$-\frac{10}{11}\approx -0.909090909$$

Solution Steps

Convert 4 to fraction \frac{8}{2}.

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

Since \frac{3}{2} and \frac{8}{2} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 8 from 3 to get -5.

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

Convert 1 to fraction \frac{4}{4}.

$$\frac{-\frac{5}{2}}{\frac{7}{4}+\frac{4}{4}}$$

Since \frac{7}{4} and \frac{4}{4} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{5}{2}}{\frac{7+4}{4}}$$

Add 7 and 4 to get 11.

$$\frac{-\frac{5}{2}}{\frac{11}{4}}$$

Divide -\frac{5}{2} by \frac{11}{4} by multiplying -\frac{5}{2} by the reciprocal of \frac{11}{4}.

$$-\frac{5}{2}\times \frac{4}{11}$$

Multiply -\frac{5}{2} times \frac{4}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-5\times 4}{2\times 11}$$

Do the multiplications in the fraction \frac{-5\times 4}{2\times 11}.

$$\frac{-20}{22}$$

Reduce the fraction \frac{-20}{22} to lowest terms by extracting and canceling out 2.

$$-\frac{10}{11}$$

Factor

$$-\frac{10}{11} = -0.9090909090909091$$