Skip to main content

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.
Labels:

Comments

Post a Comment

Popular posts from this blog

Why Martian Mathematics

Martian Mathematics  I call this Martian mathematics because if you saw someone doing math this way, you would probably think they were from Mars.  87 × 8, no problem. That's just 670 + 26.  Weird, huh? Not everything here is "out of this world," but a good bit of it will seem strange at first. With that said, I developed this system of mental mathematics for my children. Innumeracy is a growing problem worldwide and dependence on machines for calculation is the rate-limiting step in analytical thinking. These shortcomings are what I hope to alleviate with my system. In short, the methods you will find here are intended to unshackle mathematics from pen and paper. I am, of course, not the first person to do mental mathematics. There is much to be learned from Arthur Benjamin, Scott Flansburg, and Jakow Trachtenberg. I will visit them here as well. You should follow this blog if you are interested in fast mental math or homeschooling your children in mathematics. ...
36 comments
Read more

Foundations-Multiplying by Half of Ten

The Multiplication Workhorse Let's begin again with a problem. Can you easily multiply 484 ×  5 in your head? If so, then how about  3261  ×  5? By the end of this post, you will be able to easily multiply any number by five provided you have mastered doubling and halving discussed in my previous posts. Multiplication by five is the workhorse of martian mathematics. At least it is for the intermediate methods of multiplying times 3, 4, 5, 6, and 7. More on that in a later post. I think that everyone would agree that aside from multiplying by one, nothing is easier than multiplying by ten—just add a zero onto the end of the number. For example, 37  × 10 = 37 0 , 271  × 10 = 271 0 , and hell   × 10 = hell 0 . Well, maybe not that last one, but you get the idea: just tack a zero onto the back of the number when multiplying by ten.  Multiplying by five is almost as easy as multiplying by ten because five is just half of ten.  Usi...
1 comment
Read more

Foundations-Doubling

Doubling is ×2 Before we begin, I would like you to try your hand at the following multiplication problem (in your head): 2  × 734829.  If you would like to be able to multiply this as easily as reading of the digits, then read on.  We are all familiar with doubling. If you have  N  items in a bag and you double it, then it is like adding a second identical bag so that now we have twice as many as we did before ( 2N ).  In martian mathematics you need to know the following doubles: What about the numbers 5-9? We will get to that in a moment, but first let's take what we have out for a ride.  If we want to double a number of any size then we just read it from left-to-right one digit at a time, doubling as we go. Easy, huh? Now let's tackle the other five doubles you need to know. For the most part, martian math is a single-digit technique and we can ignore anything not in the ones' place. For this reason, when we double a number great...
1 comment
Read more