Complementary numbers are numbers with the same initial digits and the sum of the last digits equal to 10.

The technique in multiplying complementary numbers is similar to that of squaring numbers ending in **5 (By one more than the one before)** except that the right hand part is not **25 **but** the product of the last digits**

Example 16.1: Find **46 x 44**

** = 4 x 5 | 6 x 4**

** = 20 | 24**

** = 2,024**

P16: Let t = the common ten’s digit; a, b = the units digit such that a + b = 10
(10t + a)(10t + b) = (10t)(10t) + 10ta + 10tb + ab = 100t = 100t = 100(t = 100 t(t + 1)+ ab |

Example 16.2: Find **39 x 31**

**= 3 x 4 | 9 x 1**

**= 12|09 **Note that the right part has two digits,** 09 **not** 9. **

**= 1,209**

Again, this can be applied to decimals and fractions as long as they have the same whole number part and their decimal and fractional parts total to **1**.

Example 16.3: **8.3 x 8.7 = 8 x 9 | .3 x .7 = 72.21**

Example 16.4: **4 2/7 x 4 5/7 = 4 x 5 | 2/7 x 5/7 = 20 10/49**

Example 16.5: **699 x 601**

Since 99 + 01 = 100, we can also apply complimentary rule

**699 x 601 = 6 x 7 | 99 x 01 = 42| 0099 = 420,099**

** **Exercise 16:

- ) 24 x 26 =
- ) 73 x77 =
- ) 81 x 89 =
- ) 998 x 992 =
- ) 4.3 x 4.7 =
- ) 7.4 x 7.6 =
- ) 3 3/7 x 3 4/7 =
- ) 4 1/6 x 4 5/6 =
- ) 2 4/9 x 2 5/9 =
- ) 297 x 203 =

Answers to all exercises are found in the answer key.

Discover the 25 Math Short Cuts ( 25 MSC )!

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