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Multiplication Tricks

Method 1: Numbers Near 100
A quick way to multiply numbers close to 100.

Example: Find
106 × 107

1

Find the differences from 100

For
106
, the difference is
+6
.
For
107
, the difference is
+7
.
2

Multiply the differences

Multiply the differences:
6 × 7 = 42
. This will be the last two digits of your answer.
3

Cross-add one number and the other's difference

Add one number to the other's difference:
106 + 7 = 113
(or
107 + 6 = 113
). This will be the first part of your answer.

Result

Combine the two parts:
113
and
42
gives you 11342.

Example (with carry-over): Find
112 × 103

1

Find differences from 100

For
112
it's
+12
. For
103
it's
+3
.
2

Multiply differences

12 × 3 = 36
. This is the last part.
3

Cross-add

112 + 3 = 115
. This is the first part.

Result

Combine:
115
and
36
gives 11536.

Example (below 100): Find
96 × 89

1

Find differences from 100

For
96
it's
-4
. For
89
it's
-11
.
2

Multiply differences

(-4) × (-11) = 44
. This is the last part.
3

Cross-subtract

96 - 11 = 85
(or
89 - 4 = 85
). This is the first part.

Result

Combine:
85
and
44
gives 8544.

Example (mixed): Find
93 × 105

1

Find differences from 100

For
93
it's
-7
. For
105
it's
+5
.
2

Cross-add/subtract

93 + 5 = 98
(or
105 - 7 = 98
). Append two zeros:
9800
.
3

Multiply differences and subtract

Multiply the differences:
(-7) × 5 = -35
. Subtract this from the previous result:
9800 - 35 = 9765
.

Result

The answer is 9765.
Method 2: Multiplication of Successive Numbers
Rule: (Smaller Number)² + (Smaller Number)

Example:
11 × 12

Result

11² + 11
=
121 + 11
= 132.

Example:
12 × 13

Result

12² + 12
=
144 + 12
= 156.

Example:
13 × 14

Result

13² + 13
=
169 + 13
= 182.
Method 3: Numbers Near 50
Base is 50, but addition/subtraction is from 25.

Example: Find
48 × 56

1

Find differences from 50

For
48
it's
-2
. For
56
it's
+6
.
2

Cross-add/subtract and halve

48 + 6 = 54
. Half of this is
27
. Append two zeros:
2700
.
3

Multiply differences and combine

(-2) × 6 = -12
. Subtract this from the previous result:
2700 - 12 = 2688
.

Result

The answer is 2688.

Example: Find
56 × 58

1

Find differences from 50

For
56
it's
+6
. For
58
it's
+8
.
2

Multiply differences

6 × 8 = 48
. This is the last part.
3

Cross-add and halve

56 + 8 = 64
. Half is
32
. This is the first part.

Result

Combine: 3248.

Example: Find
42 × 46

1

Find differences from 50

For
42
it's
-8
. For
46
it's
-4
.
2

Multiply differences

(-8) × (-4) = 32
. This is the last part.
3

Cross-subtract and halve

42 - 4 = 38
. Half is
19
. This is the first part.

Result

Combine: 1932.
Method 4: Universal (Criss-Cross) Method
Works for any two-digit numbers.

Example:
32 × 21

1

Multiply Units Digits (Right to Left)

2 × 1 = 2
. This is the unit digit of the answer.
2

Criss-Cross Multiply and Add

(
3 × 1
) + (
2 × 2
) =
3 + 4 = 7
. This is the tens digit.
3

Multiply Tens Digits

3 × 2 = 6
. This is the hundreds digit.

Result

Combine from right to left: 672.

Example (with carry-over):
65 × 43

1

Units Digits

5 × 3 = 15
. Write down
5
, carry over
1
.
2

Criss-Cross

(
6 × 3
) + (
5 × 4
) + carry
1
=
18 + 20 + 1 = 39
. Write down
9
, carry over
3
.
3

Tens Digits

6 × 4
+ carry
3
=
24 + 3 = 27
.

Result

Combine: 2795.
Method 5: Unit Digits Sum to 10
For numbers where tens digits are the same and unit digits sum to 10.

Example:
32 × 38

1

Multiply the Unit Digits

The unit digits are 2 and 8.
2 × 8 = 16
. This forms the last two digits.
2

Multiply Tens Digit by Next Number

The tens digit is 3. The next consecutive number is 4.
3 × 4 = 12
. This forms the first part.

Result

Combine the parts: 1216.

Example:
73 × 77

Result

Last part:
3 × 7 = 21
. First part:
7 × 8 = 56
. Answer: 5621.

Example (Squares ending in 5):
45 × 45

Result

Last part:
5 × 5 = 25
. First part:
4 × 5 = 20
. Answer: 2025.
Method 6: Multiplying by 9, 99, 999...
A simple subtraction trick.

Example:
12345 × 999

1

Add Zeros

Since we are multiplying by 999 (3 nines), add 3 zeros to the number:
12345000
.
2

Subtract Original Number

Subtract the original number from the new number:
12345000 - 12345
.

Result

The answer is 12332655.