Solve 5/13*4/5-12/13*3/5

$$\frac { 5 } { 13 } \times \frac { 4 } { 5 } - \frac { 12 } { 13 } \times \frac { 3 } { 5 }$$

Evaluate

$$-\frac{16}{65}\approx -0.246153846$$

Solution Steps

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

$$\frac{5\times 4}{13\times 5}-\frac{12}{13}\times \frac{3}{5}$$

Cancel out 5 in both numerator and denominator.

$$\frac{4}{13}-\frac{12}{13}\times \frac{3}{5}$$

Multiply \frac{12}{13} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4}{13}-\frac{12\times 3}{13\times 5}$$

Do the multiplications in the fraction \frac{12\times 3}{13\times 5}.

$$\frac{4}{13}-\frac{36}{65}$$

Least common multiple of 13 and 65 is 65. Convert \frac{4}{13} and \frac{36}{65} to fractions with denominator 65.

$$\frac{20}{65}-\frac{36}{65}$$

Since \frac{20}{65} and \frac{36}{65} have the same denominator, subtract them by subtracting their numerators.

$$\frac{20-36}{65}$$

Subtract 36 from 20 to get -16.

$$-\frac{16}{65}$$

Factor

$$-\frac{16}{65} = -0.24615384615384617$$