Len Greenberg, Song Writer
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Fun With Math

Here are some tricks that I show my students to help them with math.

Trick 1

How to divide a number by 5: Double it and take away one decimal place.

What's 734 divided by 5?

Double 734: 1,468

Take away one decimal place:  ANSWER: 146.8

Trick 2

How to multiply a number by 9: Add a zero, then subtract the number you started with.

What's 56 times 9?

Add a zero to 56:  560

Subtract 56: ANSWER: 504

Trick 3

How to square a number that ends in "5": Take the number to the left of the "5", multiply it by one more than itself, then place a "25" to the right of whatever you come up with.

How much is 75 squared?

Multiply 7 by 8: 56
Place "25" to the right: ANSWER: 5,625

Trick 4

How to multiply two numbers whose sum ends in "0:

In the preceding trick, we learned how to square a number that ends in "5".  Situations like that don't arise every day but when they do, it's nice to be able to handle them.

Here's another situation that pops up every once in a while.  Suppose you wanted to multiply two numbers whose sum ends in "0" -- numbers, for example, like 66 and 74, one ending in "6", the other in "4". Wouldn't it be nice to have a short-cut way of handling the calculation?

If the numbers you want to multiply are only two digits long and not very far apart -- less than 25 or so -- it so happens there is such a method.  Here’s how it works:

Step 1

Take half of the difference between the numbers you want to multiply and add it to the smaller of the two.

The difference between 66 and 74 is 8; half of that is "4".  66 plus 4 is "70".

Step 2

Take the two numbers you just came up with (the 4 and the 70) and square them both. 

4  squared is "16"; 70 squared is "4,900".

Step 3

Subtract the smaller square from the larger one.

16 subtracted from 4,900 is "4,884".  That's your
answer. 66 times 74 is 4,884. 

Some of you may be wondering why it’s important that the numbers you wish to multiply have a sum that ends in "0"?  Here's why:  if the sum of two numbers ends in "0", the number halfway between them must end in either a "0" or a "5".  The fact that it ends in a "0" or a "5" makes it easy to square, even though it's two digits long. Squaring a two-digit number ending in "0" can be easily handled in one's head and we just learned in Trick No.
3 how to square numbers ending
in "5".

Experienced Math Tutor

I am available for math tutoring, from the elementary grades through college
level. Please contact me at lennberg@verizon.net for more information.

Younger students enjoy learning with me because I make math fun! Advanced students benefit from my practical approach to learning complex theory and application.

I have taught math at Northern Virginia Community College for the past twelve years. I have a Bachelors Degree in Mathematics from the City College of New York and a Masters Degree in Mathematical Statistics from Columbia University.  For many years I was a statistical consultant for both the government and private industry. I enjoy teaching much more than I did consulting!
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