Final answer:
The sum of 1/3 and 4/7 is greater than 1/2 but less than 1, therefore the best estimate for their sum is close to 1.
Step-by-step explanation:
When estimating the sum of 1/3 and 4/7, we can use intuitive reasoning to find the best estimate. Since 1/3 is less than 1/2 and 4/7 is more than 1/2 (since 3.5/7 would be exactly 1/2), when combined, these fractions are likely to add up to a value that is greater than 1/2 but less than 1. Specifically, since one-third is smaller than one-half, their sum must certainly be less than one whole, which can be understood using the logic that three thirds make a whole 'one'. Therefore, the sum of 1/3 and 4/7 will be close to but not equal to one.