Find the geometric mean of 2 and 98.

This is a problem of fact families, but what is fact families? Well it is a family of four things. Two of them are additions and two of them are subtractions. So this question asks about fact families by writing the subtraction fact two ways. So we have:



First way. So let's take the number 10 and explain this problem using triangles. Let's say that we have 10 triangles in the beginning:

Δ Δ Δ Δ Δ
Δ Δ Δ Δ Δ

So I want to take away 3 triangles, then by taking away 3 what is left? Well the answer is 7:

Δ Δ Δ Δ Δ
Δ Δ 

That is, if we subtract 3 from 10 then the result is:



Second way. In this subtraction we take the same 10 triangles:

Δ Δ Δ Δ Δ
Δ Δ Δ Δ Δ

Now I want to take away 7 triangles, then by taking away 7 what is left is 3:

Δ Δ Δ

That is, if we subtract 7 from 10 then the result is: