Solve (text{ii})2/5*(-1/9)+2/5*(-3/7)

$$( \text { ii } ) \frac { 2 } { 5 } \times ( \frac { - 1 } { 9 } ) + \frac { 2 } { 5 } \times ( \frac { - 3 } { 7 } )$$

Evaluate

$$-\frac{8}{63}\approx -0.126984127$$

Solution Steps

Multiply i and \frac{2}{5}i to get -\frac{2}{5}.

$$-\frac{2}{5}\times \frac{-1}{9}+\frac{2}{5}\times \frac{-3}{7}$$

Fraction \frac{-1}{9} can be rewritten as -\frac{1}{9} by extracting the negative sign.

$$-\frac{2}{5}\left(-\frac{1}{9}\right)+\frac{2}{5}\times \frac{-3}{7}$$

Multiply -\frac{2}{5} times -\frac{1}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-2\left(-1\right)}{5\times 9}+\frac{2}{5}\times \frac{-3}{7}$$

Do the multiplications in the fraction \frac{-2\left(-1\right)}{5\times 9}.

$$\frac{2}{45}+\frac{2}{5}\times \frac{-3}{7}$$

Fraction \frac{-3}{7} can be rewritten as -\frac{3}{7} by extracting the negative sign.

$$\frac{2}{45}+\frac{2}{5}\left(-\frac{3}{7}\right)$$

Multiply \frac{2}{5} times -\frac{3}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{45}+\frac{2\left(-3\right)}{5\times 7}$$

Do the multiplications in the fraction \frac{2\left(-3\right)}{5\times 7}.

$$\frac{2}{45}+\frac{-6}{35}$$

Fraction \frac{-6}{35} can be rewritten as -\frac{6}{35} by extracting the negative sign.

$$\frac{2}{45}-\frac{6}{35}$$

Least common multiple of 45 and 35 is 315. Convert \frac{2}{45} and \frac{6}{35} to fractions with denominator 315.

$$\frac{14}{315}-\frac{54}{315}$$

Since \frac{14}{315} and \frac{54}{315} have the same denominator, subtract them by subtracting their numerators.

$$\frac{14-54}{315}$$

Subtract 54 from 14 to get -40.

$$\frac{-40}{315}$$

Reduce the fraction \frac{-40}{315} to lowest terms by extracting and canceling out 5.

$$-\frac{8}{63}$$

Real Part

$$-\frac{8}{63} = -0.12698412698412698$$

Solution Steps

Multiply i and \frac{2}{5}i to get -\frac{2}{5}.

$$Re(-\frac{2}{5}\times \frac{-1}{9}+\frac{2}{5}\times \frac{-3}{7})$$

Fraction \frac{-1}{9} can be rewritten as -\frac{1}{9} by extracting the negative sign.

$$Re(-\frac{2}{5}\left(-\frac{1}{9}\right)+\frac{2}{5}\times \frac{-3}{7})$$

Multiply -\frac{2}{5} times -\frac{1}{9} by multiplying numerator times numerator and denominator times denominator.

$$Re(\frac{-2\left(-1\right)}{5\times 9}+\frac{2}{5}\times \frac{-3}{7})$$

Do the multiplications in the fraction \frac{-2\left(-1\right)}{5\times 9}.

$$Re(\frac{2}{45}+\frac{2}{5}\times \frac{-3}{7})$$

Fraction \frac{-3}{7} can be rewritten as -\frac{3}{7} by extracting the negative sign.

$$Re(\frac{2}{45}+\frac{2}{5}\left(-\frac{3}{7}\right))$$

Multiply \frac{2}{5} times -\frac{3}{7} by multiplying numerator times numerator and denominator times denominator.

$$Re(\frac{2}{45}+\frac{2\left(-3\right)}{5\times 7})$$

Do the multiplications in the fraction \frac{2\left(-3\right)}{5\times 7}.

$$Re(\frac{2}{45}+\frac{-6}{35})$$

Fraction \frac{-6}{35} can be rewritten as -\frac{6}{35} by extracting the negative sign.

$$Re(\frac{2}{45}-\frac{6}{35})$$

Least common multiple of 45 and 35 is 315. Convert \frac{2}{45} and \frac{6}{35} to fractions with denominator 315.

$$Re(\frac{14}{315}-\frac{54}{315})$$

Since \frac{14}{315} and \frac{54}{315} have the same denominator, subtract them by subtracting their numerators.

$$Re(\frac{14-54}{315})$$

Subtract 54 from 14 to get -40.

$$Re(\frac{-40}{315})$$

Reduce the fraction \frac{-40}{315} to lowest terms by extracting and canceling out 5.

$$Re(-\frac{8}{63})$$

The real part of -\frac{8}{63} is -\frac{8}{63}.

$$-\frac{8}{63}$$