Solve 43/5+{3-2/5-1/2[-3(-2/3)-1+frac{1}{5}]+4(-frac{5}{2})}+[2(-frac{1}{5})-frac{6}{5}]

$$\frac { 43 } { 5 } + \{ 3 - \frac { 2 } { 5 } - \frac { 1 } { 2 } [ - 3 ( - \frac { 2 } { 3 } ) - 1 + \frac { 1 } { 5 } ] + 4 ( - \frac { 5 } { 2 } ) \} + [ 2 ( - \frac { 1 } { 5 } ) - \frac { 6 } { 5 } ]$$

Evaluate

$$-1$$

Solution Steps

Convert 3 to fraction \frac{15}{5}.

$$\frac{43}{5}+\frac{15}{5}-\frac{2}{5}-\frac{1}{2}\left(-3\left(-\frac{2}{3}\right)-1+\frac{1}{5}\right)+4\left(-\frac{5}{2}\right)+2\left(-\frac{1}{5}\right)-\frac{6}{5}$$

Since \frac{15}{5} and \frac{2}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{43}{5}+\frac{15-2}{5}-\frac{1}{2}\left(-3\left(-\frac{2}{3}\right)-1+\frac{1}{5}\right)+4\left(-\frac{5}{2}\right)+2\left(-\frac{1}{5}\right)-\frac{6}{5}$$

Subtract 2 from 15 to get 13.

$$\frac{43}{5}+\frac{13}{5}-\frac{1}{2}\left(-3\left(-\frac{2}{3}\right)-1+\frac{1}{5}\right)+4\left(-\frac{5}{2}\right)+2\left(-\frac{1}{5}\right)-\frac{6}{5}$$

Multiply -3 times -\frac{2}{3}.

$$\frac{43}{5}+\frac{13}{5}-\frac{1}{2}\left(2-1+\frac{1}{5}\right)+4\left(-\frac{5}{2}\right)+2\left(-\frac{1}{5}\right)-\frac{6}{5}$$

Subtract 1 from 2 to get 1.

$$\frac{43}{5}+\frac{13}{5}-\frac{1}{2}\left(1+\frac{1}{5}\right)+4\left(-\frac{5}{2}\right)+2\left(-\frac{1}{5}\right)-\frac{6}{5}$$

Convert 1 to fraction \frac{5}{5}.

$$\frac{43}{5}+\frac{13}{5}-\frac{1}{2}\left(\frac{5}{5}+\frac{1}{5}\right)+4\left(-\frac{5}{2}\right)+2\left(-\frac{1}{5}\right)-\frac{6}{5}$$

Since \frac{5}{5} and \frac{1}{5} have the same denominator, add them by adding their numerators.

$$\frac{43}{5}+\frac{13}{5}-\frac{1}{2}\times \frac{5+1}{5}+4\left(-\frac{5}{2}\right)+2\left(-\frac{1}{5}\right)-\frac{6}{5}$$

Add 5 and 1 to get 6.

$$\frac{43}{5}+\frac{13}{5}-\frac{1}{2}\times \frac{6}{5}+4\left(-\frac{5}{2}\right)+2\left(-\frac{1}{5}\right)-\frac{6}{5}$$

Multiply \frac{1}{2} times \frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{43}{5}+\frac{13}{5}-\frac{1\times 6}{2\times 5}+4\left(-\frac{5}{2}\right)+2\left(-\frac{1}{5}\right)-\frac{6}{5}$$

Do the multiplications in the fraction \frac{1\times 6}{2\times 5}.

$$\frac{43}{5}+\frac{13}{5}-\frac{6}{10}+4\left(-\frac{5}{2}\right)+2\left(-\frac{1}{5}\right)-\frac{6}{5}$$

Reduce the fraction \frac{6}{10} to lowest terms by extracting and canceling out 2.

$$\frac{43}{5}+\frac{13}{5}-\frac{3}{5}+4\left(-\frac{5}{2}\right)+2\left(-\frac{1}{5}\right)-\frac{6}{5}$$

Since \frac{13}{5} and \frac{3}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{43}{5}+\frac{13-3}{5}+4\left(-\frac{5}{2}\right)+2\left(-\frac{1}{5}\right)-\frac{6}{5}$$

Subtract 3 from 13 to get 10.

$$\frac{43}{5}+\frac{10}{5}+4\left(-\frac{5}{2}\right)+2\left(-\frac{1}{5}\right)-\frac{6}{5}$$

Since \frac{43}{5} and \frac{10}{5} have the same denominator, add them by adding their numerators.

$$\frac{43+10}{5}+4\left(-\frac{5}{2}\right)+2\left(-\frac{1}{5}\right)-\frac{6}{5}$$

Add 43 and 10 to get 53.

$$\frac{53}{5}+4\left(-\frac{5}{2}\right)+2\left(-\frac{1}{5}\right)-\frac{6}{5}$$

Express 4\left(-\frac{5}{2}\right) as a single fraction.

$$\frac{53}{5}+\frac{4\left(-5\right)}{2}+2\left(-\frac{1}{5}\right)-\frac{6}{5}$$

Multiply 4 and -5 to get -20.

$$\frac{53}{5}+\frac{-20}{2}+2\left(-\frac{1}{5}\right)-\frac{6}{5}$$

Divide -20 by 2 to get -10.

$$\frac{53}{5}-10+2\left(-\frac{1}{5}\right)-\frac{6}{5}$$

Convert 10 to fraction \frac{50}{5}.

$$\frac{53}{5}-\frac{50}{5}+2\left(-\frac{1}{5}\right)-\frac{6}{5}$$

Since \frac{53}{5} and \frac{50}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{53-50}{5}+2\left(-\frac{1}{5}\right)-\frac{6}{5}$$

Subtract 50 from 53 to get 3.

$$\frac{3}{5}+2\left(-\frac{1}{5}\right)-\frac{6}{5}$$

Express 2\left(-\frac{1}{5}\right) as a single fraction.

$$\frac{3}{5}+\frac{2\left(-1\right)}{5}-\frac{6}{5}$$

Multiply 2 and -1 to get -2.

$$\frac{3}{5}+\frac{-2}{5}-\frac{6}{5}$$

Fraction \frac{-2}{5} can be rewritten as -\frac{2}{5} by extracting the negative sign.

$$\frac{3}{5}-\frac{2}{5}-\frac{6}{5}$$

Since \frac{3}{5} and \frac{2}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-2}{5}-\frac{6}{5}$$

Subtract 2 from 3 to get 1.

$$\frac{1}{5}-\frac{6}{5}$$

Since \frac{1}{5} and \frac{6}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1-6}{5}$$

Subtract 6 from 1 to get -5.

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

Divide -5 by 5 to get -1.

$$-1$$

Factor

$$-1$$