Solve [25/8*2/5]-[3/5*-10/9]

$$[ \frac { 25 } { 8 } \times \frac { 2 } { 5 } ] - [ \frac { 3 } { 5 } \times \frac { - 10 } { 9 } ]$$

Evaluate

$$\frac{23}{12}\approx 1.916666667$$

Solution Steps

Multiply \frac{25}{8} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{25\times 2}{8\times 5}-\frac{3}{5}\times \frac{-10}{9}$$

Do the multiplications in the fraction \frac{25\times 2}{8\times 5}.

$$\frac{50}{40}-\frac{3}{5}\times \frac{-10}{9}$$

Reduce the fraction \frac{50}{40} to lowest terms by extracting and canceling out 10.

$$\frac{5}{4}-\frac{3}{5}\times \frac{-10}{9}$$

Fraction \frac{-10}{9} can be rewritten as -\frac{10}{9} by extracting the negative sign.

$$\frac{5}{4}-\frac{3}{5}\left(-\frac{10}{9}\right)$$

Multiply \frac{3}{5} times -\frac{10}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5}{4}-\frac{3\left(-10\right)}{5\times 9}$$

Do the multiplications in the fraction \frac{3\left(-10\right)}{5\times 9}.

$$\frac{5}{4}-\frac{-30}{45}$$

Reduce the fraction \frac{-30}{45} to lowest terms by extracting and canceling out 15.

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

The opposite of -\frac{2}{3} is \frac{2}{3}.

$$\frac{5}{4}+\frac{2}{3}$$

Least common multiple of 4 and 3 is 12. Convert \frac{5}{4} and \frac{2}{3} to fractions with denominator 12.

$$\frac{15}{12}+\frac{8}{12}$$

Since \frac{15}{12} and \frac{8}{12} have the same denominator, add them by adding their numerators.

$$\frac{15+8}{12}$$

Add 15 and 8 to get 23.

$$\frac{23}{12}$$

Factor

$$\frac{23}{2 ^ {2} \cdot 3} = 1\frac{11}{12} = 1.9166666666666667$$