Solve 5/13*3/5-(-4/5)*2/13

$$\frac { 5 } { 13 } \times \frac { 3 } { 5 } - ( - \frac { 4 } { 5 } ) \times \frac { 2 } { 13 }$$

Evaluate

$$\frac{23}{65}\approx 0.353846154$$

Solution Steps

Multiply \frac{5}{13} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 3}{13\times 5}-\left(-\frac{4}{5}\times \frac{2}{13}\right)$$

Cancel out 5 in both numerator and denominator.

$$\frac{3}{13}-\left(-\frac{4}{5}\times \frac{2}{13}\right)$$

Multiply -\frac{4}{5} times \frac{2}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{13}-\frac{-4\times 2}{5\times 13}$$

Do the multiplications in the fraction \frac{-4\times 2}{5\times 13}.

$$\frac{3}{13}-\frac{-8}{65}$$

Fraction \frac{-8}{65} can be rewritten as -\frac{8}{65} by extracting the negative sign.

$$\frac{3}{13}-\left(-\frac{8}{65}\right)$$

The opposite of -\frac{8}{65} is \frac{8}{65}.

$$\frac{3}{13}+\frac{8}{65}$$

Least common multiple of 13 and 65 is 65. Convert \frac{3}{13} and \frac{8}{65} to fractions with denominator 65.

$$\frac{15}{65}+\frac{8}{65}$$

Since \frac{15}{65} and \frac{8}{65} have the same denominator, add them by adding their numerators.

$$\frac{15+8}{65}$$

Add 15 and 8 to get 23.

$$\frac{23}{65}$$

Factor

$$\frac{23}{5 \cdot 13} = 0.35384615384615387$$