2016 November

Calculator Fun 2

by | Math is Fun! | No Comments
  • Think of a three digit number
  • Multiply it successively by 7, 11 and 13
  • What is the result?

For example, if your three digit number is 168

     168 x 7  = 1176
    1176 x 11 = 12936
   12936 x 13 = 168168

It is the original three digit number repeated twice!

Why it works

Since 7 x 11 x 13 = 1001, then any three digit number abc x 1001 = abcabc

      abc		   349
   x 1001		x 1001
      abc		   349
       0		    0
      0			   0
   abc   		349   
   abcabc 		349349

It is math Made Simple and Cool!

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23% of 45 is what percent of 69?

by | Competition Math, Math Made Fast! | No Comments

This is a typical grade 4 competition Math problem

23% of 45 is what percent of 69?

The conventional solution is to simply do the arithmetic

23% of 45 = 0.23 x 45 = 10.35 (By long multiplication)
10.35/69 = 0.15 = 15% (by long division)

This is actually algebra, but instead of asking the student for the value of x  we asked “what percent of.”  But that is another story.  🙂

An imaginative MATH-Inic student will have an alternative solution using logic.

Notice that 23 is 1/3 of 69 and remember that 45 is 3 * 15.  Mentally, our MATH-Inic student will think:

  • 23% of 45 = 23/3 % of 3*15
  • which is the same as 69% of 15
  • which is the same as 15% of 69
  • which means 15% is our answer

Effectively, he gave the answer from logic instead of from long multiplication and long division!