This document provides a step-by-step method for multiplying one number over 100 by a number under 100 in 2 steps: 1) Subtract the product of the differences between each number and 100 from 100, and 2) Take the difference between the numbers' differences from 100 and add/subtract it from 99. Examples are worked through, such as 104 x 98 = 10192, by finding the differences, subtracting their product from 100, and adding/subtracting their difference to 99. It is noted the order of subtraction in step 2 is important.

1. Math Magic – Multiplying One Number Over And Under 100 Page 1
Multiply One Number Over 100 By A Number Under 100:
A. From algebra we learn:
(100 + a)(100 - b) = 100(99 + (a-b)) + (100-ab)
B. Using numbers instead of variables we get:
1. For the last set of numbers, multiply the differences between each number and
100. Subtract this value from 100. Write this down (make sure it takes up 2
place values).
2. Take the difference of the number over 100 and subtract it from the difference
of the number under 100. Add this value to 99. Write this down.
C. Examples:
Ex [1] 104 x 98 = _____
a. The difference between the two numbers is 4 and 2 respectively.
4 x 2 = 8. 100 - 8 = 92. Write 92.
b. 4 - 2 = 2. 99 + 2 = 101. Write 101.
c. The answer is 10192.
Ex [2] 92 x 106 = _______
a. The difference between the two numbers is 8 and 6 respectively.
8 x 6 = 48. 100 - 48 = 52. Write 52.
b. 6 - 8 = -2. -2 + 99 = 97. Write 97.
c. The answer is 9752.
d. Notice in step 2, we had to subtract 6 - 8 and not 8 - 6. This trick requires
you to subtract the difference of the number over 100 minus the difference
of the number less than 100.