Solve (4/3-1/5)*(3/4-1/6)

$$( \frac{ 4 }{ 3 } - \frac{ 1 }{ 5 } ) \times ( \frac{ 3 }{ 4 } - \frac{ 1 }{ 6 } )$$

Evaluate

$$\frac{119}{180}\approx 0.661111111$$

Solution Steps

Least common multiple of 3 and 5 is 15. Convert \frac{4}{3} and \frac{1}{5} to fractions with denominator 15.

$$\left(\frac{20}{15}-\frac{3}{15}\right)\left(\frac{3}{4}-\frac{1}{6}\right)$$

Since \frac{20}{15} and \frac{3}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{20-3}{15}\left(\frac{3}{4}-\frac{1}{6}\right)$$

Subtract 3 from 20 to get 17.

$$\frac{17}{15}\left(\frac{3}{4}-\frac{1}{6}\right)$$

Least common multiple of 4 and 6 is 12. Convert \frac{3}{4} and \frac{1}{6} to fractions with denominator 12.

$$\frac{17}{15}\left(\frac{9}{12}-\frac{2}{12}\right)$$

Since \frac{9}{12} and \frac{2}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{17}{15}\times \frac{9-2}{12}$$

Subtract 2 from 9 to get 7.

$$\frac{17}{15}\times \frac{7}{12}$$

Multiply \frac{17}{15} times \frac{7}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{17\times 7}{15\times 12}$$

Do the multiplications in the fraction \frac{17\times 7}{15\times 12}.

$$\frac{119}{180}$$

Factor

$$\frac{7 \cdot 17}{2 ^ {2} \cdot 3 ^ {2} \cdot 5} = 0.6611111111111111$$