# Multiplication as Proportional Co-Variation & the Sign Rule

- Author:
- Jonathan J. Crabtree

**Have your friends already heard the REAL reason why -ve x -ve = +ve?**What is multiplication? Really... Well, despite what you may have been told, it's not repeated addition! Multiplication by any number except 1, changes a number. But how? Multiplication can make a number bigger. Yet multiplication can also make a number smaller! OK, can you keep a secret? Whatever we do to 1, the UNIT, to make the MULTIPLIER, you do exactly the same to the MULTIPLICAND, the number being multiplied, to make the PRODUCT or answer. It's that simple! And in case you don't believe me, we'll try it out with -2 x -3.

**-2 x -3 = ?**

**Q.**What did we do to 1 to make -2?

**A.**Simple! We doubled it and changed its sign!

**Q.**What do we do to -3?

**A.**We double it and change its sign! So twice -3 is -6 and changing its sign makes it 6. Easy! Have fun! Jonathan Crabtree Mathematics Researcher: The Evolution of Elementary Mathematics www.j.mp/jcrabtree