   SEARCH HOME Math Central Quandaries & Queries  Question from Shazia, a parent: When does a fact family not have 4 related facts? Give an example. Shazia,
Go to the Quandaries and Queries page on Math Central and use the Quick Search to search for the term fact family. Look at the list of questions that are returned. Two of them have responses that should
help.

Harley

Shazia wrote back

Hi,

I still can't find the answer even from those questions. I am talking about multiplication and division not addition and subtraction. I need four unrelated facts.

Shazia,

Maybe you can approach this by asking "How can there be fewer that 4 facts?" and then saying that there are 4 facts unless ....

Here is a 4 fact, fact family

7 × 5 = 35
5 × 7 = 35
35 ÷ 5 = 7
35 ÷ 7 = 5

From the above example a fact family has three numbers, I am going to call them a, b and c and the facts are

a × b = c
b × a = c
c ÷ b = a
c ÷ a = b

Look at the first two equations. These would be identical is a and b were the same number, for example

5 × 5 = 25.

How many facts are in this fact family?

This makes me wonder. What if a and c were the same number, for example 5 × b = 5? Then b would have to be 1 to give

5 × 1 = 5

How many facts are in this fact family?

What if b and c were the same number?

What is a, b and c are all the same number?

I hope this helps,
Harley     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.