Why would it? One "whole" is one sandwich. She cut each sandwich into four pieces, giving her 8/4 (pieces of) sandwiches (which simplies to "2", as sense would require). If she now has five pieces, then these are five of the one-fourth-of-a-sandwich pieces, which is 5/4 of a sandwich (or one and one-fourth).[/SIZE]
@stapel
The problem is that the question did not ask "How much of a sandwich is left." It asked "How much of the sandwiches are left."
What do we find in the first sentence: an indefinite article referring to a standard or perhaps platonically ideal sandwich, a singular noun consistent with the indefinite article, and a singular verb consistent with a singular subject. What do we find in the second sentence,
which is the actual question that the student is asked to parse: a definite article (referring, according to the rules of English grammar, to previously identified exemplars of the indicated class), a plural noun (consistent with two sandwiches having been cut), and a plural verb consistent with a plural subject.
Others have been kinder than I am and have said that the wording of the problem is ambiguous. I disagree. According to the
basic rules of English grammar, "the sandwiches are" indicates specific sandwiches identifiable by context, not an abstract idealized sandwich. The only correct answer to the question asked is 5/8 of the two original sandwiches. The answer given by the text book is to a question that the text failed to ask.
It is all very well to say that is a stupid question. I agree. Probably, the author of the text book meant "How much of a sandwich is left." But it is ridiculous to blame the reader's confusion on the author's inability to express that intended meaning in English. The value of word problems is that they require translating issues presented in a natural language into the language of mathematics, a skill critical to applying mathematics to any practical purpose. The least we should require (although obviously not anything we can expect from the current educational establishment) is that the word problems posed to English-speaking students of arithmetic follow the rules of English grammar, not some language that looks like English but follows some grammar known only to the author.
One of the problems in following this thread is that, for perfectly good reasons, a chunk of it has been transferred into a separate thread.