Twin Facts and Commutative Law
On this journey, we will colour the facts that we can easily figure out without memorising them.
Look at the blue-coloured part of the table. Every fact in this part has a twin in the other part of the table. The twin gives the same answer.
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
1 | 1 x 1 = 1 | 1 x 2 = 2 | 1 x 3 = 3 | 1 x 4 = 4 | 1 x 5 = 5 | 1 x 6 = 6 | 1 x 7 = 7 | 1 x 8 = 8 | 1 x 9 = 9 | 1 x 10 = 10 |
2 | 2 x 1 = 2 | 2 x 2 = 4 | 2 x 3 = 6 | 2 x 4 = 8 | 2 x 5 = 10 | 2 x 6 = 12 | 2 x 7 = 14 | 2 x 8 = 16 | 2 x 9 = 18 | 2 x 10 = 20 |
3 | 3 x 1 = 3 | 3 x 2 = 6 | 3 x 3 = 9 | 3 x 4 = 12 | 3 x 5 = 15 | 3 x 6 = 18 | 3 x 7 = 21 | 3 x 8 = 24 | 3 x 9 = 27 | 3 x 10 = 30 |
4 | 4 x 1 = 4 | 4 x 2 = 8 | 4 x 3 = 12 | 4 x 4 = 16 | 4 x 5 = 20 | 4 x 6 = 24 | 4 x 7 = 28 | 4 x 8 = 32 | 4 x 9 = 36 | 4 x 10 = 40 |
5 | 5 x 1 = 5 | 5 x 2 = 10 | 5 x 3 = 15 | 5 x 4 = 20 | 5 x 5 = 25 | 5 x 6 = 30 | 5 x 7 = 35 | 5 x 8 = 40 | 5 x 9 = 45 | 5 x 10 = 50 |
6 | 6 x 1 = 6 | 6 x 2 = 12 | 6 x 3 = 18 | 6 x 4 = 24 | 6 x 5 = 30 | 6 x 6 = 36 | 6 x 7 = 42 | 6 x 8 = 48 | 6 x 9 = 54 | 6 x 10 = 60 |
7 | 7 x 1 = 7 | 7 x 2 = 14 | 7 x 3 = 21 | 7 x 4 = 28 | 7 x 5 = 35 | 7 x 6 = 42 | 7 x 7 = 49 | 7 x 8 = 56 | 7 x 9 = 63 | 7 x 10 = 70 |
8 | 8 x 1 = 8 | 8 x 2 = 16 | 8 x 3 = 24 | 8 x 4 = 32 | 8 x 5 = 40 | 8 x 6 = 48 | 8 x 7 = 56 | 8 x 8 = 64 | 8 x 9 = 72 | 8 x 10 = 80 |
9 | 9 x 1 = 9 | 9 x 2 = 18 | 9 x 3 = 27 | 9 x 4 = 36 | 9 x 5 = 45 | 9 x 6 = 54 | 9 x 7 = 63 | 9 x 8 = 72 | 9 x 9 = 81 | 9 x 10 = 90 |
10 | 10 x 1 = 10 | 10 x 2 = 20 | 10 x 3 = 30 | 10 x 4 = 40 | 10 x 5 = 50 | 10 x 6 = 60 | 10 x 7 = 70 | 10 x 8 = 80 | 10 x 9 = 90 | 10 x 10 = 100 |
For example, 3 x 5 = 15 and 5 x 3 = 15.
If you remember 5 x 3, then you will know 3 x 5. This means that you do not have to memorise a major chunk of the multiplication tables.
This law is called the Commutative Law of Multiplication
where a x b = b x a
for any numbers a and b.
Twin Facts and Commutative Law Times One for Free
Reproduced with permission from Maria Droujkova, Natural Math
Redesigned by "Parenting the Next Generation"