Is there a mathematical reason (like a proof) of why this happens? You can do it with examples and it is 'intuitive.' But the proof of why this happens is never shown in pedagogy, we just warn students to remember to flip the inequality when

• multiply or divide by a negative number both sides

$$-2>-3 \implies 2 < 3$$

• take reciprocals of same sign fractions both sides

$$\frac{3}{4} > \frac{1}{2} \implies \frac{4}{3} < 2$$

Post Closed as "Not suitable for this site" by Tommi, user5402, Xander Henderson, JTP - Apologise to Monica, Benjamin Dickman

Is there a mathematical reason (like a proof) of why this happens? You can do it with examples and it is 'intuitive.' But the proof of why this happens is never shown in pedagogy, we just warn students to remember to flip the inequality when

• multiply or divide by a negative number both sides

$$-2>-3 => 2 < 3$$$$-2>-3 \implies 2 < 3$$

• take reciprocals of same sign fractions both sides

$$\frac{3}{4} > \frac{1}{2} => \frac{4}{3} < 2$$$$\frac{3}{4} > \frac{1}{2} \implies \frac{4}{3} < 2$$

Is there a mathematical reason (like a proof) of why this happens? You can do it with examples and it is 'intuitive.' But the proof of why this happens is never shown in pedagogy, we just warn students to remember to flip the inequality when

• multiply or divide by a negative number both sides

$$-2>-3 => 2 < 3$$

• take reciprocals of same sign fractions both sides

$$\frac{3}{4} > \frac{1}{2} => \frac{4}{3} < 2$$