Primer—Five's Conjugate

Adding and Subtracting Five is Easy

I will frequently use the term "five's conjugate". The word conjugate means yoked together or coupled. The five's conjugate are pairs of numbers whose difference is five—that's the coupling. The five’s conjugate of 1 is 6, of 2 is 7, of 3 is 8, etc. The five's conjugate of 6 is 1, of 7 is 2, of 8 is 3, etc. 

The easiest way to think of the five's conjugate is with your hands. Each hand has a relative finger count (1-5). Both hands combined have an absolute finger count (1-10). Martian mathematics is largely single-digit mathematics, so we are mostly interested in the single-digits (0-9); therefore, we think of ten as zero.

Let's say you want the five's conjugate of 7. Hold up both hands with the left hand's fingers fully extended. That is five. On the right hand, extend the thumb and index finger. You now have seven fingers. Now, make your left hand into a fist. You are left with only two fingers. The five's conjugate of 7 is 2. 

Let's say you want the five's conjugate of 3. Make your left hand into a fist. That's zero. On your right hand, extend your thumb, index finger, and middle finger. That's 3. Now open your left hand fully. You should see eight fingers extended. The five's conjugate of 3 is 8. 

Practice this until you instantly recognize all the five's conjugate pairs. When you see 9, you should immediately think of 4 and vice-versa. Now you can add or subtract five to a number as easily as you can add or subtract one. 

Consider 37 ± 5. Both answers (37 + 5 and 37 – 5) will have the five's conjugate in the ones' place. You know that 37 + 5 must be greater than 37, so increment the tens' place to get 42. You also know that 37 – 5 is less than 37. Since 32 fits the bill, there is no need to decrement the tens' place.  Let's try one more. 

Consider 32 ± 5. Both answers (32 + 5 and 32 – 5) will have the five's conjugate in the ones' place. You know that 32 + 5 > 32, and since 37 > 32, there is no need to increment the tens' place. Similarly, since 32 – 5 < 32, you need to decrement the tens' place to get 32 – 5 = 27. 

Now you can try on your own. You can quickly check yourself with the answer key at the bottom.

In the next post, I will talk about adding and subtracting 3. If you want to get a head start, then study a telephone number pad. Thanks for reading.
© 2019 David W. Ward, All Rights Reserved.