“What the heck is a *fact family*?” I asked the first time I read the term.

And the second, third, fourth and fifth times.

“Fact families” – both the term and the families – seem to be everywhere these days.

### So what IS a fact family?

Well, it’s a family of facts. But not parents or cousins. More like siblings.

Here’s a nice one I’ve known for years:

And here’s another one I’m fond of:

### Is that a real thing in math?

The short answer is “no.”

When you look it up on WolframAlpha.com, you don’t get a definition. It gives you the definition of “family.”

And according to that definition, any collection of facts (totally random, even) can be a “fact family.”

### So is it a real thing?

The long answer is “yes.”

A nice little collection of related facts is called a fact family.

But sometimes we get even sloppier and say that 8, 3 and 5 are a fact family. The numbers aren’t the facts, but, as grownups, we know what we mean.

I’ve mentioned a number of times that mathematicians just make this crap up. So even WE can play a mathematician and create…

### A Formal Definition *bum-bum-buum*

Ahem… pardon me while I geek out a moment…

Let be a group and , and in so that . Then we say , and form a * fact family* and we can write

### A Casual Definition

We can call any three numbers , and , that make , a fact family. And we know that not only does , but also and .

Likewise with multiplication, we can call any three numbers , and , that make , a fact family. And we know that not only does , but also and .

So there you have it. Fact Family formally and casually defined.

I feel so much better. 🙂

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