Patterns in the Multiplication Table

We have already seen the many patterns which are visible in products of multiplication products. Let us summarise them for convenience.

1. Each column is a “skip counting” table of a particular number. This is because multiplication turns out to be same in procedure as “repeated addition”. So in column under “4” we get the numbers 0, 4, 8, 12, 16, 20 etc

2. Similarly, each row is also a skip-counting” table, for the same reason.

3. Because of the above reasons, the table is symmetrical both in the horizontal & vertical directions.

4. The diagonals contain all the squares – 1, 4, 9, 16, 25, 36, 49, 64, 81. This is because they are the products of numbers multiplied by themselves – 1X1, 2X2, 3X3 etc

5. All the other products are arranged symmetrically about this diagonal. Hence 3X4 (which is 12) is symmetrical with 4X3 (which is also 12). Hence products (other than the squares) come in pairs.

6. The number of multiplication facts that have to be remembered is quite small!

   1. The total number of facts is 10 X 10 = 100

   2. Tables of 0, 1, 2 & 5 (40 facts) are easy to remember. Hence only 60 need to be remembered

   3. Table of 9 can be seen on our palms! (10 facts). That leaves 50 facts

   4. Each fact has a duplicate. Hence it comes down to 25 facts.

All these patterns make it easy for students to construct a multiplication table from scratch.

They also make it clear that the actual number of multiplication facts that need to be remembered are only quarter of the total facts!

Why do we frighten children about multiplication tables?

Remembering Division Facts

One bonus with the one-page multiplication table is that it helps in practicing division facts also. This is because multiplication and division are mirror images of each other. The division factors of any number which appears in the table can easily be found.

For example, 42 occurs in the table. The row and column under which 42 occurs are 6 & 7. This means that both 6 & 7 can divide 42!