What fraction of the elephants is blue?

Someone sent me a nice word problem to solve:

Bob went to the zoo last week and was captivated by the lovely baby elephants. Some were pink and some were blue. When he counted the elephants, he found that the number of pink elephants was 2 1/2 times the number of blue elephants. What fraction of the elephants was blue?
First of all, think: which ones are less, blue or pink? Clearly, the blue ones are less. Make those kind represented by ONE BLOCK or one unit.

So, let's let the BLUE elephants to be |----|  (one block).

Then, the pink ones would be |----|----|--| (2 1/2 times as many)

Now, to get the fraction asked, I could use those little dashed lines in my blocks... See, I made each block have 4 little dashes ---- and the half-block has two.

So, the Blue elephants are "four dashes" and the pink ones are "ten dashes". I know that in reality we don't know how many blue or pink elephants there are, but this won't matter if we only want to know what FRACTION or what PART of the elephants are blue. So we might as well assign some quantities here that fit the problem.

From this, we can write the fraction. Blue elephants are 4, total elephants are 14, so 4/14 of the elephants are blue. This simplifies to 2/7.

You can also get the same answer this way: blue elephants are 1 block, and there are a total of 3 1/2 blocks of elephants. The fraction is 1 / (3 1/2) which is equivalent to 2/7 (multiply both numerator and denominator by 2).


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