Solve (-213/25):(-27/10)-1725/47:(-1725/47)-4frac{3}{5}

$$( - 2 \frac { 13 } { 25 } ) : ( - 2 \frac { 7 } { 10 } ) - 17 \frac { 25 } { 47 } : ( - 17 \frac { 25 } { 47 } ) - 4 \frac { 3 } { 5 }$$

Evaluate

$$-\frac{8}{3}\approx -2.666666667$$

Solution Steps

Multiply 2 and 25 to get 50.

$$\frac{-\frac{50+13}{25}}{-\frac{2\times 10+7}{10}}-\frac{\frac{17\times 47+25}{47}}{-\frac{17\times 47+25}{47}}-\frac{4\times 5+3}{5}$$

Add 50 and 13 to get 63.

$$\frac{-\frac{63}{25}}{-\frac{2\times 10+7}{10}}-\frac{\frac{17\times 47+25}{47}}{-\frac{17\times 47+25}{47}}-\frac{4\times 5+3}{5}$$

Multiply 2 and 10 to get 20.

$$\frac{-\frac{63}{25}}{-\frac{20+7}{10}}-\frac{\frac{17\times 47+25}{47}}{-\frac{17\times 47+25}{47}}-\frac{4\times 5+3}{5}$$

Add 20 and 7 to get 27.

$$\frac{-\frac{63}{25}}{-\frac{27}{10}}-\frac{\frac{17\times 47+25}{47}}{-\frac{17\times 47+25}{47}}-\frac{4\times 5+3}{5}$$

Divide -\frac{63}{25} by -\frac{27}{10} by multiplying -\frac{63}{25} by the reciprocal of -\frac{27}{10}.

$$-\frac{63}{25}\left(-\frac{10}{27}\right)-\frac{\frac{17\times 47+25}{47}}{-\frac{17\times 47+25}{47}}-\frac{4\times 5+3}{5}$$

Multiply -\frac{63}{25} times -\frac{10}{27} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-63\left(-10\right)}{25\times 27}-\frac{\frac{17\times 47+25}{47}}{-\frac{17\times 47+25}{47}}-\frac{4\times 5+3}{5}$$

Do the multiplications in the fraction \frac{-63\left(-10\right)}{25\times 27}.

$$\frac{630}{675}-\frac{\frac{17\times 47+25}{47}}{-\frac{17\times 47+25}{47}}-\frac{4\times 5+3}{5}$$

Reduce the fraction \frac{630}{675} to lowest terms by extracting and canceling out 45.

$$\frac{14}{15}-\frac{\frac{17\times 47+25}{47}}{-\frac{17\times 47+25}{47}}-\frac{4\times 5+3}{5}$$

Multiply 17 and 47 to get 799.

$$\frac{14}{15}-\frac{\frac{799+25}{47}}{-\frac{17\times 47+25}{47}}-\frac{4\times 5+3}{5}$$

Add 799 and 25 to get 824.

$$\frac{14}{15}-\frac{\frac{824}{47}}{-\frac{17\times 47+25}{47}}-\frac{4\times 5+3}{5}$$

Multiply 17 and 47 to get 799.

$$\frac{14}{15}-\frac{\frac{824}{47}}{-\frac{799+25}{47}}-\frac{4\times 5+3}{5}$$

Add 799 and 25 to get 824.

$$\frac{14}{15}-\frac{\frac{824}{47}}{-\frac{824}{47}}-\frac{4\times 5+3}{5}$$

Divide \frac{824}{47} by -\frac{824}{47} to get -1.

$$\frac{14}{15}-\left(-1\right)-\frac{4\times 5+3}{5}$$

The opposite of -1 is 1.

$$\frac{14}{15}+1-\frac{4\times 5+3}{5}$$

Convert 1 to fraction \frac{15}{15}.

$$\frac{14}{15}+\frac{15}{15}-\frac{4\times 5+3}{5}$$

Since \frac{14}{15} and \frac{15}{15} have the same denominator, add them by adding their numerators.

$$\frac{14+15}{15}-\frac{4\times 5+3}{5}$$

Add 14 and 15 to get 29.

$$\frac{29}{15}-\frac{4\times 5+3}{5}$$

Multiply 4 and 5 to get 20.

$$\frac{29}{15}-\frac{20+3}{5}$$

Add 20 and 3 to get 23.

$$\frac{29}{15}-\frac{23}{5}$$

Least common multiple of 15 and 5 is 15. Convert \frac{29}{15} and \frac{23}{5} to fractions with denominator 15.

$$\frac{29}{15}-\frac{69}{15}$$

Since \frac{29}{15} and \frac{69}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{29-69}{15}$$

Subtract 69 from 29 to get -40.

$$\frac{-40}{15}$$

Reduce the fraction \frac{-40}{15} to lowest terms by extracting and canceling out 5.

$$-\frac{8}{3}$$

Factor

$$-\frac{8}{3} = -2\frac{2}{3} = -2.6666666666666665$$