Final answer:
After spending 1/4 of a $800 monthly budget on food and 1/5 on entertainment, the fraction leftover for clothing should be 11/20 when the fractions are combined and simplified. However, this answer does not match any of the provided multiple-choice options, indicating a possible error in the question or the answer choices.
Step-by-step explanation:
When determining the fraction of the budget left for other expenses like clothing after spending on certain categories, you'd want to subtract the fractions dedicated to those categories from the whole. Starting with $800 per month, spending 1/4 on food and 1/5 on entertainment, you will first need to find a common denominator to combine the fractions. That denominator is 20, so we convert 1/4 to 5/20 and 1/5 to 4/20, and add them together to get 9/20. Therefore, 20/20 (the whole budget) minus 9/20 (food and entertainment) leaves 11/20 for other expenses. However, we're looking for a match among the multiple-choice answers given (a) 7/20 b) 3/10 c) 4/5 d) 2/5).
To match one of these choices, we must simplify 11/20. We can divide both numerator and denominator by the largest common factor they share, which is 1, so the fraction is already in its simplest form. As none of the multiple-choice answers are equivalent to 11/20, it seems there may have been an error in the question or answer choices provided. To answer this question effectively, we need to revisit the answer choices or the initial fractions allocated to food and entertainment to ensure accuracy.