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

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

Verify

Solution Steps

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

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

Cancel out 2 in both numerator and denominator.

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

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

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

Subtract 1 from 2 to get 1.

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

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

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

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

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

Add 5 and 1 to get 6.

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

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

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

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

$$\frac{43}{5}+3-\frac{6}{25}+4\left(-\frac{5}{2}\right)=\frac{1}{5}\times \frac{6}{5}$$

Convert 3 to fraction \frac{75}{25}.

$$\frac{43}{5}+\frac{75}{25}-\frac{6}{25}+4\left(-\frac{5}{2}\right)=\frac{1}{5}\times \frac{6}{5}$$

Since \frac{75}{25} and \frac{6}{25} have the same denominator, subtract them by subtracting their numerators.

$$\frac{43}{5}+\frac{75-6}{25}+4\left(-\frac{5}{2}\right)=\frac{1}{5}\times \frac{6}{5}$$

Subtract 6 from 75 to get 69.

$$\frac{43}{5}+\frac{69}{25}+4\left(-\frac{5}{2}\right)=\frac{1}{5}\times \frac{6}{5}$$

Least common multiple of 5 and 25 is 25. Convert \frac{43}{5} and \frac{69}{25} to fractions with denominator 25.

$$\frac{215}{25}+\frac{69}{25}+4\left(-\frac{5}{2}\right)=\frac{1}{5}\times \frac{6}{5}$$

Since \frac{215}{25} and \frac{69}{25} have the same denominator, add them by adding their numerators.

$$\frac{215+69}{25}+4\left(-\frac{5}{2}\right)=\frac{1}{5}\times \frac{6}{5}$$

Add 215 and 69 to get 284.

$$\frac{284}{25}+4\left(-\frac{5}{2}\right)=\frac{1}{5}\times \frac{6}{5}$$

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

$$\frac{284}{25}+\frac{4\left(-5\right)}{2}=\frac{1}{5}\times \frac{6}{5}$$

Multiply 4 and -5 to get -20.

$$\frac{284}{25}+\frac{-20}{2}=\frac{1}{5}\times \frac{6}{5}$$

Divide -20 by 2 to get -10.

$$\frac{284}{25}-10=\frac{1}{5}\times \frac{6}{5}$$

Convert 10 to fraction \frac{250}{25}.

$$\frac{284}{25}-\frac{250}{25}=\frac{1}{5}\times \frac{6}{5}$$

Since \frac{284}{25} and \frac{250}{25} have the same denominator, subtract them by subtracting their numerators.

$$\frac{284-250}{25}=\frac{1}{5}\times \frac{6}{5}$$

Subtract 250 from 284 to get 34.

$$\frac{34}{25}=\frac{1}{5}\times \frac{6}{5}$$

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

$$\frac{34}{25}=\frac{1\times 6}{5\times 5}$$

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

$$\frac{34}{25}=\frac{6}{25}$$

Compare \frac{34}{25} and \frac{6}{25}.

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