Fact Family – Truth Mafia or Math Term?

Have you heard of a fact family? Does it make you think of the math mob? Or the truth police? Here's what it is, really.
Have you heard of a fact family? Does it make you think of the math mob? Or the truth police? Here’s what it is, really.

“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:

8 = 3 + 5
5 = 8 - 3
3 = 8 - 5

And here’s another one I’m fond of:

42 = 6 \times 7
6 = 42 \div 7
7 = 42 \div 6

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 (G,\bigstar) be a group and a, b and c in G so that a \bigstar b=c. Then we say a, b and c form a fact family and we can write

a\bigstar b=c b=-a\bigstar c a = c\bigstar -b

A Casual Definition

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

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

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

I feel so much better. 🙂
SignatureBon

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