Final answer:
Keiko's calculation is incorrect. Using common denominators and intuitive understanding of fractions, we can determine that the sum of 1/8 + 7/15 is greater than 1/3, as both fractions are less than 1/2 and their sum exceeds the sum of 1/6 + 1/6, which is 1/3.
Step-by-step explanation:
Keiko's claim that 1/8 + 7/15 = 1/3 is not correct. To see why, let's first understand the concept of common denominators. We know that 1/8 is less than 1/2, and 7/15 is less than 1/2 as well. So their sum must be less than 1/2 + 1/2, which is a whole. Now, if 1/8 were to be doubled, we would get 1/4, and doubling it again gives us 1/2. Therefore, it's clear that 1/8 is quite small.
Similarly, if we take 1/3 of a known fraction like 1/2, which is 1/6, we can see that adding 1/8 to it would certainly be more than 1/6, hinting that 1/8 + 7/15 must be greater than 1/6 + 1/6, which is 1/3. Thus, using this intuition, we can conclude that the sum 1/8 + 7/15 has to be greater than 1/3.