Solve 2/5*1/2geq4/3*-2/3

$$\frac { 2 } { 5 } \times \frac { 1 } { 2 } \geq \frac { 4 } { 3 } \times \frac { - 2 } { 3 }$$

Verify

Solution Steps

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

$$\frac{2\times 1}{5\times 2}\geq \frac{4}{3}\times \frac{-2}{3}$$

Cancel out 2 in both numerator and denominator.

$$\frac{1}{5}\geq \frac{4}{3}\times \frac{-2}{3}$$

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

$$\frac{1}{5}\geq \frac{4}{3}\left(-\frac{2}{3}\right)$$

Multiply \frac{4}{3} times -\frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{5}\geq \frac{4\left(-2\right)}{3\times 3}$$

Do the multiplications in the fraction \frac{4\left(-2\right)}{3\times 3}.

$$\frac{1}{5}\geq \frac{-8}{9}$$

Fraction \frac{-8}{9} can be rewritten as -\frac{8}{9} by extracting the negative sign.

$$\frac{1}{5}\geq -\frac{8}{9}$$

Least common multiple of 5 and 9 is 45. Convert \frac{1}{5} and -\frac{8}{9} to fractions with denominator 45.

$$\frac{9}{45}\geq -\frac{40}{45}$$

Compare \frac{9}{45} and -\frac{40}{45}.

$$\text{true}$$