why do some fact families have only two facts? give an example.
Some fact families have only two facts because they involve subtraction or division, which have a different relationship compared to addition or multiplication. In addition and multiplication fact families, there are always three related facts that involve the same set of numbers. However, in subtraction and division fact families, there are only two related facts because the operations are not commutative like addition and multiplication.
For example, let's consider the fact family with the numbers 8, 4, and 2. In addition and multiplication, we would have:
8 + 4 = 12
4 + 8 = 12 (commutative property)
8 × 2 = 16
2 × 8 = 16 (commutative property)
This fact family involves four related facts because addition and multiplication are commutative operations. Now, let's look at the subtraction and division fact family with the same numbers:
8 - 4 = 4
8 ÷ 4 = 2
In this case, we have only two related facts because subtraction and division do not have the commutative property.