Final answer:
The mixed number 3 2/3 is rounded up to 4 because the fractional part, 2/3, is greater than 1/2, which is the standard threshold for rounding up to the next whole number.
Step-by-step explanation:
When considering the mixed number 3 2/3 and deciding whether to round it up to 4 or down to 3, we look at the fractional part of the mixed number. Since we have two-thirds, which is more than one-half, we follow the rule of rounding up if the fraction is one-half or more. Therefore, we round 3 2/3 up to 4.
The concept of rounding up refers to increasing the number to the nearest whole number, while rounding down refers to keeping the number at the current whole number without increasing it. In rounding the fraction 2/3, we can think of it as being more than 1/2 (which is the mid-point), so we round up.