A piece of string is marked in segments of onefourth and onethird the string's length. If the string is then cut at each mark, which of the following lists all the different lengths of the bits of string, in fractions of the original length?
A. 1/12 and 1/4 only B. 1/4 and 1/3 only C. 1/6, 1/4 and 1/3 D. 1/12, 1/6, and 1/4 E. 1/12, 1/6, and 1/3
(D) This is one of those word problems that you should translate into a diagram. You have a piece of string marked into fourths and thirds.
To make things easy, assume that the string is 1 foot long. Whatever the actual length, the relative lengths of the pieces will be the same. 1 foot is also convenient, as it equals 12 inches, and 12 is the least common denominator of the fractions in the problem.
Making cuts every onefourth the length of the string means making cuts every 3 inches. A cut every third the length of the string means a cut every 4 inches. Some of the segments would then be 3 inches long, some are 2, and some are 1, or 1/4, 1/6, 1/12 of the whole.
Choice (A) is wrong because it says "only" and there are other options available. 
How do you know what order to cut the marks in? What if I choose to cut the 1/3 marks before the 1/4 marks?
