Why do we "keep, change, flip" or "multiply by the reciprocal" when we divide fractions?

Why Do We Keep, Switch, Flip When Dividing Fractions? (aka Keep, Change, Flip) | Math with Mr. J

Dividing Fractions with KEEP, CHANGE, FLIP | Fractions Rap Song

Dividing fractions - why does Keep Change Flip work?

The truth behind Keep Change Flip

Math Antics - Dividing Fractions

Why can we KEEP, CHANGE and FLIP when dividing by a fraction?

I Hate "Keep Change Flip" when dividing fractions

Dividing Fractions Easily using KEEP-CHANGE-FLIP Method | Tagalog Tutorial | Math 4, 5, 6 Tagalog

Why Keep Change Flip works

Keep Change Flip

8 Dividing Fractions with Keep Change Flip

How to Add, Subtract, Multiply, and Divide Mixed Numbers | Math with Mr. J

How To Divide Fractions | Keep, Change, Flip

Dividing Mixed Numbers | Step by Step | Math with Mr. J

Subtracting Integers | How to Subtract Positive and Negative Integers

Why Do We Flip the Inequality Sign When Multiplying or Dividing by a Negative? | Math with Mr. J

Dividing Fractions without Keep-Change-Flip @AllThisMath

Dividing Algebraic Fractions

Fraction Review | How to Add, Subtract, Multiply, and Divide Fractions