Multiplication is the mathematical operation of scaling one number by another. It is defined for whole numbers in terms of repeated addition.

For example, 4 multiplied by 5 (often also said as "4 times 5) can be calculated by adding 4 copies of 5 together:

4 × 5 = 5 + 5 + 5 + 5 = 20

• One digit number multiplication can refer to the below basic multiplication table

  ×	1	2	3	4	5	6	7	8	9
  1	1	2	3	4	5	6	7	8	9
  2	2	4	6	8	10	12	14	16	18
  3	3	6	9	12	15	18	21	24	27
  4	4	8	12	16	20	24	28	32	36
  5	5	10	15	20	25	30	35	40	45
  6	6	12	18	24	30	36	42	48	54
  7	7	14	21	28	35	42	49	56	63
  8	8	16	24	32	40	48	56	64	72
  9	9	18	27	36	45	54	63	72	81

• Two or more digit number multiplication can be done with a vertical form. Some of the examples are below:

  1 9 × 1 1     1 9   1 9     2 0 9

  1 8 × 1 2     3 6   1 8     2 1 6

  1 7 × 1 3     5 1   1 7     2 2 1

  1 6 × 1 4     6 4   1 6     2 2 4

  1 5 × 1 5     7 5   1 5     2 2 5

• Properties of Multiplication
  • Zero multiplied by any number or any number multiplied by zero is still equal to zero:

    0 × 0 = 0

    65 × 0 = 0

    0 × 406 = 0

    4200 × 0 = 0

    0 × 149812 = 0

  • Any number multiplied by one does not change the value:

    1 × 1 = 1

    72 × 1 = 72

    1 × 657 = 657

    21523 × 1 = 21523

    1 × 65353 = 65353

  • Commutative Property of Multiplication: ab = ba

    2 × 8 = 8 × 2 = 16

    25 × 7 × 4 = 25 × 4 × 7 = 100 × 7 = 700

  • Associative Property of Multiplication: abc = (ab)c = a(bc) = (ac)b

    2 × 8 × 5 = (2 × 5) × 8 = (10) × 8 = 80

    7 × 25 × 4 = 7(25 × 4) = 7(100) = 700

  • Distributive Property of Multiplication: a(b + c) = ab + ac or (b + c)a = ba + ca

    7(10 + 5) = 7 × 10 + 7 × 5 = 70 + 35 = 105

    (100 + 1) × 9 = 100 × 9 + 1 × 9 = 900 + 9 = 909

• Square numbers and square roots

  112 = 121	122 = 144	132 = 169	142 = 196	152 = 225
  162 = 256	172 = 289	182 = 324	192 = 361	202 = 400

For example: 121,144,169,...are square numbers, and 11, 12, 13, ...are square roots of the corresponding square numbers.
• Shortcut with multiplication
  • Utilize associative property 25 × 9 × 4 = (25 × 4) × 9 = (100) × 9 = 900
  • Utilize distribution property 101 × 9 = (100 + 1) × 9 = 100 × 9 + 1 × 9 = 909
  • Two digits number with same tens digit and the single digits sum is 10

    1 7 × 1 3     5 1   1 7     2 2 1

    2 6 × 2 4   1 0 4   5 2     6 2 4

    3 3 × 3 7   2 3 1   9 9   1 2 2 1

    4 7 × 4 3   1 4 1 1 8 8   2 0 2 1

    5 6 × 5 4   2 2 4 2 8 0   3 0 2 4

  • The difference of the two numbers to be multiplied is 2, their product will be the square of their medium number minus 1.
    14 × 16 = 15² − 1 = 224
    19 × 21 = 20² − 1 = 399
  • Multiply by 11
    25 × 11 = 2(2 + 5)5 = 275
    123 × 11 = 1(12 + 23)3 = 1353
    79 × 11 = 7(7 + 9)9 = 869
    653 × 11 = 6(65 + 53)3 = 7183