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In my math classroom there hangs on the wall a poster I made, which looks something like this:

It usually takes quite awhile for my students to figure out the significance of the image. For one thing, they start out not knowing anything about the multiplicative property of inequality. When they ask me about it, I assure them that they'll learn over the course of the year a variety of properties of multiplication, and then they'll understand the poster.

What is the multiplicative property of inequality? The multiplicative property of inequality says that if you have an inequality, and you multiply both sides of the inequality by the same positive quantity, you will have an equivalent inequality. If you mutliply both sides by the same negative quanity, and change the direction of the inequality symbol, you still have an equivalent inequality.

Once my students understand this property, they look at the poster again, and since they all hate fractions, it doesn't take them long to decide they want to multiply both sides of the inequality by 3. This is a positive quantity, so they don't have to reverse the inequality sign. The result the obtain is:

I <3 U, which is an online shorthand for I love you (I - HEART - YOU).

Oh, those crazy, romantic, mathematicians!

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