Earlier articles said that division is the opposite of multiplication. Now let's see what that really means — and how one multiplication fact gives you four problems.
Three numbers, four problems
Take three numbers that belong together — for example 3, 4, 12, because 3 × 4 = 12.
From these three numbers you can build four different problems:
3 × 4 = 12
4 × 3 = 12 (thanks to commutativity)
12 ÷ 3 = 4
12 ÷ 4 = 3
We call this trio of numbers a fact family. They're related like a family.
Why this is useful
Less practice, more knowledge. When you remember that 6 × 7 = 42, you immediately also know:
7 × 6 = 42
42 ÷ 6 = 7
42 ÷ 7 = 6
Four facts from one.
Try it yourself
Family 2, 5, 10 (because 2 × 5 = 10):
2 × 5 = 10
5 × 2 = 10
10 ÷ 2 = 5
10 ÷ 5 = 2
Family 4, 6, 24 (because 4 × 6 = 24):
4 × 6 = 24
6 × 4 = 24
24 ÷ 4 = 6
24 ÷ 6 = 4
Family 3, 3, 9 (special — when the factors are the same):
3 × 3 = 9
9 ÷ 3 = 3
When the factors are the same, the family only has 2 problems — one multiplication and one division.
A trick for solving division
When you meet a division whose answer you don't remember, switch to multiplication.
Example: 35 ÷ 5 = ?
Ask yourself: "Five times what equals thirty-five?"
5 × 5 = 25 (too small)
5 × 6 = 30 (too small)
5 × 7 = 35 ✓
So 35 ÷ 5 = 7.
Summary
Three numbers in a fact family make four equations — two multiplications and two divisions.
When you remember one multiplication fact, you automatically know four facts.
For division, ask "X times what = Y?" and switch to multiplication.
When the factors are the same, the family only has 2 problems.
