mental math

“Go fast slowly” – Clarence Stephens

Number Circuits are an original puzzle that I came up with a few years ago.  They are number sense puzzles that require you to arrange a set of numbers in a designated pattern.  I used magic squares as a theme using shapes other than squares. In all, I was able to develop over 200 puzzles all with this same theme.  Fortunately, Mindware liked the puzzles and published two books.  I was pretty excited (and still am).  The books differ in difficulty, although neither set of puzzles are too difficult (although all puzzle are challenging when you can’t solve them!).  Below are four puzzles, two from each book.  I believe they’re representatve of each collection and Number Circuit puzzles in general.  Click each picture to open a full sized pdf image of each puzzle in a new window.

from Number Circuits A	from Number Circuits B

As always, I hope you enjoyed these puzzles. Please pass them onto others who may enjoy them and please click LIKE below if you like them! 

MIndware currently has the books for sale for only $3.95 (that a 69% savings!).  If interested in purchasing either book just click below:

Number Circuits A (Beginner Puzzles)

Number Circuits B (Advanced Puzzles)

“There is no greatness where there is not simplicity, goodness, and truth.”
― Leo Tolstoy

Dividing by 5 mentally can be accomplished very easily. The best part is that there’s no division required. That’s right, there’s no division required to mentally divide a number by 5!  That sounds almost too good to be true.

All you need to do is multiply the number by 2 and then shift the decimal point left 1 place. That’s right, just two steps, multiplying by 2 and then shifting the decimal point of the product. Let me put them in bullet format:

 step 1: multiply the number by 2

 step 2: shift the decimal point left 1 place
 

So, if you want to divide 120 by 5, just do the following:

So 120 ÷ 5 = 24.  That’s pretty easy, isn’t it?  Well, it’s easy if you can quickly multiply numbers by 2 mentally.  This is referred to as “doubling” a number and it’s the basis of a lot of mental arithmetic techniques.  So in order to mentally divide by 5, first master doubling numbers mentally.  Let’s look at another example using a decimal number instead of an integer.   To divide 3246.4 by 5, just do the following: 

So 3246.4 ÷ 5 = 649.28.  Again, that’s pretty easy, isn’t it?  You may be asking “Why does it work?”.  Well, 5 is equal to 10 ÷ 2.  So when dividing by 5, it’s equivalent to dividing by “10 ÷ 2″.  This in turn is equivalent to multiplying by 2 and then dividing by 10.  In our base 10 (decimal) number system, dividing by 10 can be accomplished by shifting the decimal point left 1 place.  There we have it, instead of dividing by 5, we can just double and shift.

Give it a try on some other problems.  Start with integers that are easy to double (like 111 or 234) to get the idea.  Once you’re comfortable with those problems try a bit more challenging problems (like 756 or 1867) which are more difficult to double. 

Remember, mastering doubling numbers mentally is the key.  Practice and master that first and then dividing by 5 mentally will come easily.  Check out my Mental Math Anti-Calculator where you can practice your doubling of numbers and dividing by 5 interactively.  Access will be free to everyone until the end of March.  After that, contact me and I can set up an account for you.  Good luck and remember to practice doubling.