Solve 1/3<5/4*-1/5>3/9

$$\frac { 1 } { 3 } < \frac { 5 } { 4 } \cdot - \frac { 1 } { 5 } > \frac { 3 } { 9 }$$

Verify

Solution Steps

Multiply \frac{5}{4} times -\frac{1}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{3}<\frac{5\left(-1\right)}{4\times 5}\text{ and }\frac{5}{4}\left(-\frac{1}{5}\right)>\frac{3}{9}$$

Cancel out 5 in both numerator and denominator.

$$\frac{1}{3}<\frac{-1}{4}\text{ and }\frac{5}{4}\left(-\frac{1}{5}\right)>\frac{3}{9}$$

Fraction \frac{-1}{4} can be rewritten as -\frac{1}{4} by extracting the negative sign.

$$\frac{1}{3}<-\frac{1}{4}\text{ and }\frac{5}{4}\left(-\frac{1}{5}\right)>\frac{3}{9}$$

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

$$\frac{4}{12}<-\frac{3}{12}\text{ and }\frac{5}{4}\left(-\frac{1}{5}\right)>\frac{3}{9}$$

Compare \frac{4}{12} and -\frac{3}{12}.

$$\text{false}\text{ and }\frac{5}{4}\left(-\frac{1}{5}\right)>\frac{3}{9}$$

Multiply \frac{5}{4} times -\frac{1}{5} by multiplying numerator times numerator and denominator times denominator.

$$\text{false}\text{ and }\frac{5\left(-1\right)}{4\times 5}>\frac{3}{9}$$

Cancel out 5 in both numerator and denominator.

$$\text{false}\text{ and }\frac{-1}{4}>\frac{3}{9}$$

Fraction \frac{-1}{4} can be rewritten as -\frac{1}{4} by extracting the negative sign.

$$\text{false}\text{ and }-\frac{1}{4}>\frac{3}{9}$$

Reduce the fraction \frac{3}{9} to lowest terms by extracting and canceling out 3.

$$\text{false}\text{ and }-\frac{1}{4}>\frac{1}{3}$$

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

$$\text{false}\text{ and }-\frac{3}{12}>\frac{4}{12}$$

Compare -\frac{3}{12} and \frac{4}{12}.

$$\text{false}\text{ and }\text{false}$$

The conjunction of \text{false} and \text{false} is \text{false}.

$$\text{false}$$