Fraction word problem

Question

A baker made 2 cakes of the same size. At the end of the day there was 2/3 of a chocolate cake left. There was 5/6 of a strawberry cake left. The baker divided the remaining chocolate cake into 2 equal pieces and the remaining strawberry cake into 3 pieces. Which cake flavor had larger pieces and by how much?

Answer 1

First off, you will want to draw two circles.  For the purposes of this explanation, the first one will be the chocolate cake and the second the strawberry cake.

 

The problem states that there was two thirds of the chocolate cake left.  This means you will divide the first circle into three equal pieces, which will resemble a peace sign.  Now, lightly shade two of the pieces.  This represents the 2/3 that is left.  The baker divided this into two remaining pieces.  This is simple as the two pieces remaining are already of equal size, each being 1/3 of the whole in size.  Therefore, each slice equals 1/3.

 

For the strawberry cake, you will divide it into six equal pieces (think the chocolate cake with each slice divided in half).  As there is 5/6 remaining, you will shade five of the six pieces.  Here comes the tricky part.  The baker divided the remaining 5/6 into 3 equal pieces.  The simplest way to achieve this is to take your denominator (6) times 3 (the number of pieces you need) to get 18. This means you will have to divide the entire circle into 18 total pieces.  This can be achieved by dividing each of the 1/6 slices into 3 pieces.  This will give you the needed 18 pieces.  As you will notice from your shading, only 15 of these new slices are shaded.  This means that the remaining strawberry cake is 15/18 (which equals 5/6 once it is reduced).  Now, if the baker divided the remaining 15 slices into three equal groups, this would mean that each group is made up of 5 slices (which equals 5/18 of the whole cake).  This means that each chunk of strawberry cake is now 5/18 in size.

 

In order to determine which flavor had larger chunks left over we have to have a common denominator for 1/3 and 5/18.  Luckily, 3 goes into 18 six times.  To keep the proportions even, we must multiply the numerator by six as well to get an equivalent fraction of 6/18 (6/18 reduces down to 1/3 and they are therefore equal).  Now you are able to compare the two fractions which, chocolate cake (6/18) compared to strawberry cake (5/18). As 6 out of 18 slices results in a greater piece, the slice of chocolate cake is therefore larger (although not by much!).  To find out how much, you subtract 5/18 from 6/18 which equals 1/18 (your second answer).

 

Hope this helps!  Next time you get stumped, try drawing it out.  I have found that this works for many of my students.  :)