Solve 4/3+(-51/2+5/4*31/5):frac{9}{10}

$$\frac { 4 } { 3 } + ( - 5 \frac { 1 } { 2 } + \frac { 5 } { 4 } \cdot 3 \frac { 1 } { 5 } ) : \frac { 9 } { 10 }$$

Evaluate

$$-\frac{1}{3}\approx -0.333333333$$

Solution Steps

Multiply 5 and 2 to get 10.

$$\frac{4}{3}+\frac{-\frac{10+1}{2}+\frac{5}{4}\times \frac{3\times 5+1}{5}}{\frac{9}{10}}$$

Add 10 and 1 to get 11.

$$\frac{4}{3}+\frac{-\frac{11}{2}+\frac{5}{4}\times \frac{3\times 5+1}{5}}{\frac{9}{10}}$$

Multiply 3 and 5 to get 15.

$$\frac{4}{3}+\frac{-\frac{11}{2}+\frac{5}{4}\times \frac{15+1}{5}}{\frac{9}{10}}$$

Add 15 and 1 to get 16.

$$\frac{4}{3}+\frac{-\frac{11}{2}+\frac{5}{4}\times \frac{16}{5}}{\frac{9}{10}}$$

Multiply \frac{5}{4} times \frac{16}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4}{3}+\frac{-\frac{11}{2}+\frac{5\times 16}{4\times 5}}{\frac{9}{10}}$$

Cancel out 5 in both numerator and denominator.

$$\frac{4}{3}+\frac{-\frac{11}{2}+\frac{16}{4}}{\frac{9}{10}}$$

Divide 16 by 4 to get 4.

$$\frac{4}{3}+\frac{-\frac{11}{2}+4}{\frac{9}{10}}$$

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

$$\frac{4}{3}+\frac{-\frac{11}{2}+\frac{8}{2}}{\frac{9}{10}}$$

Since -\frac{11}{2} and \frac{8}{2} have the same denominator, add them by adding their numerators.

$$\frac{4}{3}+\frac{\frac{-11+8}{2}}{\frac{9}{10}}$$

Add -11 and 8 to get -3.

$$\frac{4}{3}+\frac{-\frac{3}{2}}{\frac{9}{10}}$$

Divide -\frac{3}{2} by \frac{9}{10} by multiplying -\frac{3}{2} by the reciprocal of \frac{9}{10}.

$$\frac{4}{3}-\frac{3}{2}\times \frac{10}{9}$$

Multiply -\frac{3}{2} times \frac{10}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4}{3}+\frac{-3\times 10}{2\times 9}$$

Do the multiplications in the fraction \frac{-3\times 10}{2\times 9}.

$$\frac{4}{3}+\frac{-30}{18}$$

Reduce the fraction \frac{-30}{18} to lowest terms by extracting and canceling out 6.

$$\frac{4}{3}-\frac{5}{3}$$

Since \frac{4}{3} and \frac{5}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4-5}{3}$$

Subtract 5 from 4 to get -1.

$$-\frac{1}{3}$$

Factor

$$-\frac{1}{3} = -0.3333333333333333$$