Introduction and the Idea[]
Multiplication (often denoted by the cross symbol " × " and by " * [asterisk]" in computers) is the mathematical operation of scaling one number by another. It is one of the four basic operations in elementary arithmetic (the others being addition, subtraction and division).
To be said in simple words, multiplication is repeated addition of numbers. For example: 2 x 3 = 6 (verbally, 2 times 3 equals 6) can also be written as 3 + 3 = 6 (saying the above in words, 2 x 3 is like 2 times 3) or 2 + 2 + 2 = 6 (also as 3 times 2). So considering table for number 3 from below we can have, 1 time 3 is 3, obviously. 2 times 3 is 6. 3 times 3 is 9 (3+3+3 or 3x3). To make it more clear it is like if you say 4 times 3, then it means like adding four 3's which is 3+3+3+3.
Problem of 3 Boxes[]
Try doing 4 x 5 for practice? You can check if the answer you arrived at is right or not from the table of 4, below.
Properties of Multiplication[]
The following are the properties of multiplication.
Commutative Property[]
Multiplication is commutative, i.e. a x b = b x a (here a and b are variables which represent any number). Further it can be understood as 3 x 2 = 2 x 3.
Associative Property[]
Multiplication is associative, i.e. (a x b) x c = a x (b x c) (here a, b and c are variables which represent any number). Further it can be understood as (3 x 2) x 4 = 3 x (2 x 4).
Closure Property[]
Multiplication holds good with the closure property, i.e. if a x b = c, and a and b are integers, then c is also an integer. Also said as multiplication of two integers will give an integral number as a result. Further it can be understood as 3 x 2 = 6 where 3 and 2 are integers, therefore, 6 is also an integer.
Multiplication Tables[]
Multiplication tables are important for easy and quick calculation. Here are multiplication tables for 1 to 12.
Multiplication Symbol
| 1 | 2 | 3 |
|---|---|---|
| 1 x 1 = 1 | 2 x 1 = 2 | 3 x 1 = 3 |
| 1 x 2 = 2 | 2 x 2 = 4 | 3 x 2 = 6 |
| 1 x 3 = 3 | 2 x 3 = 6 | 3 x 3 = 9 |
|
1 x 4 = 4 |
2 x 4 = 8 | 3 x 4 = 12 |
| 1 x 5 = 5 | 2 x 5 = 10 | 3 x 5 = 15 |
| 1 x 6 = 6 | 2 x 6 = 12 | 3 x 6 = 18 |
| 1 x 7 = 7 | 2 x 7 = 14 | 3 x 7 = 21 |
| 1 x 8 = 8 | 2 x 8 = 16 | 3 x 8 = 24 |
| 1 x 9 = 9 | 2 x 9 = 18 | 3 x 9 = 27 |
| 1 x 10 = 10 | 2 x 10 = 20 | 3 x 10 = 30 |
| 4 | 5 | 6 |
|---|---|---|
| 4 x 1 = 4 | 5 x 1 = 5 | 6 x 1 = 6 |
| 4 x 2 = 8 | 5 x 2 = 10 | 6 x 2 = 12 |
| 4 x 3 = 12 | 5 x 3 = 15 | 6 x 3 = 18 |
| 4 x 4 = 16 | 5 x 4 = 20 | 6 x 4 = 24 |
| 4 x 5 = 20 | 5 x 5 = 25 | 6 x 5 = 30 |
| 4 x 6 = 24 | 5 x 6 = 30 | 6 x 6 = 36 |
| 4 x 7 = 28 | 5 x 7 = 35 | 6 x 7 = 42 |
| 4 x 8 = 32 | 5 x 8 = 40 | 6 x 8 = 48 |
| 4 x 9 = 36 | 5 x 9 = 45 | 6 x 9 = 54 |
| 4 x 10 = 40 | 5 x 10 = 50 | 6 x 10 = 60 |
| 7 | 8 | 9 |
|---|---|---|
| 7 x 1 = 1 | 8 x 1 = 8 | 9 x 1 = 1 |
| 7 x 2 = 14 | 8 x 2 = 16 | 9 x 2 = 18 |
| 7 x 3 = 21 | 8 x 3 = 24 | 9 x 3 = 27 |
| 7 x 4 = 28 | 8 x 4 = 32 | 9 x 4 = 36 |
| 7 x 5 = 35 | 8 x 5 = 40 | 9 x 5 = 45 |
| 7 x 6 = 42 | 8 x 6 = 48 | 9 x 6 = 54 |
| 7 x 7 = 49 | 8 x 7 = 56 | 9 x 7 = 63 |
| 7 x 8 = 56 | 8 x 8 = 64 | 9 x 8 = 73 |
| 7 x 9 = 63 | 8 x 9 = 72 | 9 x 9 = 81 |
| 7 x 10 = 70 | 8 x 10 = 80 | 9 x 10 = 90 |
| 10 | 11 | 12 |
|---|---|---|
|
10 x 1 = 10 |
11 x 1 = 11 | 12 x 1 = 12 |
| 10 x 2 = 20 | 11 x 2 = 22 | 12 x 2 = 24 |
| 10 x 3 = 30 | 11 x 3 = 33 | 12 x 3 = 36 |
| 10 x 4 = 40 | 11 x 4 = 44 | 12 x 4 = 48 |
| 10 x 5 = 50 | 11 x 5 = 55 | 12 x 5 = 60 |
| 10 x 6 = 60 | 11 x 6 = 66 | 12 x 6 = 72 |
| 10 x 7 = 70 | 11 x 7 = 77 | 12 x 7 = 84 |
| 10 x 8 = 80 | 11 x 8 = 88 | 12 x 8 = 96 |
| 10 x 9 = 90 | 11 x 9 = 99 | 12 x 9 = 108 |
| 10 x 10 = 100 | 11 x 10 = 110 | 12 x 10 = 120 |