# MSC 16 – Multiplying Complementary Numbers

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 = 100t2 + 10t(a + b) + ab = 100t2 + 10t(10) + ab = 100(t2 + t)+ ab = 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:

1. ) 24 x 26 =
2. ) 73 x77 =
3. ) 81 x 89 =
4. ) 998 x 992 =
5. ) 4.3 x 4.7 =
6. ) 7.4 x 7.6 =
7. ) 3 3/7 x 3 4/7 =
8. ) 4 1/6 x 4 5/6 =
9. ) 2 4/9 x 2 5/9 =
10. ) 297 x 203 =