23% of 45 is what percent of 69?

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!

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