Expert: Paul Klarreich - 12/4/2006

Question
i am doing some math problems it is as followed
   2/3=blank/24 & i am a 10 year old trying to figure this out will you please help me thank you

Answer
Questioner:  mr
Category:  Advanced Math
 
Subject:  BUILDING factions
Question:  i am doing some math problems it is as followed
  2/3=blank/24 & i am a 10 year old trying to figure this out will you please help me

thank you
.....................
Hi, mr,

I thought these were marked "For ages 12 to adult" but we will just have to see what we can do.  You are trying to fill this in:
2     ??
--- = ----
3     24

The problem really says:  The number 2/3 [yes, that is a number] can be written in many ways.  That is part of the excitement of doing mathematics.

One of those ways is as a fraction with 24 as the denominator.  In that case, what is the numerator.

The process of writing a fraction with a BIGGER numerator is called BUILDING FRACTIONS TO HIGHER TERMS.  It is the reverse of reducing fractions to lower terms.(So it is a kind of anti-simplification.)

Here is what you do:  To get the bigger denominator, 24, from the smaller one, 3, you must multiply 3 by 8.  Therefore, you will also multiply the numerator by 8:

2   8     16
--- --- = ----
3   8     24

That 16 is the number to fill in the blank.  Of course you will see that 16/24 can be reduced to 2/3; that's what this was all about.