This document provides several methods for multiplying and squaring numbers mentally using tricks and shortcuts: 1) To multiply numbers, multiply the ones digits first, then cross-multiply and add the tens digits, and finally multiply the hundreds digits. 2) For numbers close to 100, subtract the difference from 100 to get the "base number" and multiply the differences. 3) To multiply by 11, add the digits and insert the sum between them. 4) To square a number close to 100, subtract the difference from 100 for the base number and square the difference. 5) Any number ending in 5 is easy to square, as the answer will end in 25.

1. 20August 2013
MATH
MAGIC

2. MULTIPLICATION
TRICKS

3. CROSS-
MULPLICATION
14
X 12

4. First, to get the last digit in the answer,
multiply the two numbers on the right.
Write the answer, as the rightmost digit in
the problem’s answer.

5. 2x4=8
14
X 12
8

6. Now, get the middle digit, cross-
multiply both sets of numbers, and
then add the together.

7. 1 x 2 = 2
1 x 4 = 4
6
14
X 12
68

8. Lastly to get the last digit, simply
multiply the left digits.

9. 1 x 1= 1
14
X 12
168

10. TRY!
28
X 23
In this case, we will do the carrying procedure.

11. COMPLEMENTARY
MULTIPLICATION
96
x 94

12. First, subtract both numbers in 100
and list the difference.
100 - 96 = 4
100 - 94 = 6

13. Second step is to subtract diagonally.
You will notice there that they will give
the same answer, and this will be your
base number.

14. 96 – 6 = 90
94 – 4 = 90

15. 96
x 94
90

16. Third, multiply the two numbers we
got by figuring the difference
between the original numbers and
100.
4 x 6 = 24

17. •Lastly, write it to the right of the
base number.
96
x 94
9,024

18. •If the number are larger than 100, add
the difference instead of subtracting.
Ex.
103
x 107

19. 103 – 100 = 3
107 – 100 = 7
103 + 7 = 110
107 + 3 = 110

20. •You will arrive with same answer
then write it as the base number.
103
x 107
110

21. •Multiply the 3 and 7, then write it as
the base number.
3 x 7 = 21

22. 103
x 107
11,021

23. This method is applicable also in numbers around
50.
Ex.
46
x 44

24. MULTIPLYING BY 11
18
X 11

25. •Add the two digits and insert the
sum between the digits.
1 + 8 = 9

26. 18
X 11
198

27. 99
X 11
In case that you got a two-digit number, add
that numbers’ left digit to the digit in the
original number.

28. 9 + 9 = 18
99
X 11
1,089

29. SQUARING TRICKS

30. Squaring a number around 100
If the number falls under 100 and above
50, you simply figure the difference
between 100 and the number.
96²

31. •Subtract the difference from the
number being squared, and write the
answer as the first digits in your
answer.
100 – 96 = 4

32. 96²
- 4
92 base number 92(00)

33. •Take the difference between 100
and the number being squared and
square.
100 – 96 = 4
4² = 16

34. •Place that number after the base
number and you have the answer.
96² = 9,216

35. If the number to be squared is
more than 100, add the
difference to the number.

36. Squaring numbers that ends in
5
Any number that ends in 5 is easy to
square to start with, you know that
5 x 5 = 25, so the answer will
automatically end in 25.
Ex. 35²

37. •Add 1 to the first digit, ignore the
rest at the number.
1
+ 3(5)
4

38. •Multiply the result to the first digit
of the original number. This result is
the first part of the answer.
4 x 3 = 12

39. 12 with 25 makes 1, 225.
Try!
85²
115²
65²

40. SHORTCUT AND HELPFUL HINTS
18 X 101 = 1,818
84 X 101 = 8,484
97 X 101 = 9,797
102 X 101 = 10,302
621 X 101 = 62,721

41. Thank you!