First let's look at rounding with decimals:
Round 3.47 to the nearest tenth.
The tenths place is the 4. Does it stay 4 or round up to 5?
Look at the next digit over- 7. 7 is greater than or equal to 5, so the 4 rounds up to 5.
3.5
The thing to remember there is that we round up starting with 5, the half way mark from 0 to 10.
So, if we're rounding with a fraction, we round up starting half way between units of that fraction.
Example with fractions:
Round 1/8 to the nearest 1/4.
1/8 is between 0 (0 * 1/4) and 1/4 (1 * 1/4), so 1/8 either rounds up to 1/4 or rounds down to 0.
1/8 is half way between 0 and 1/4, so it's like when we round up, say, 2.5 to 3 instead of down to 2.
1/8 rounds up to the nearest 1/4.
1/8 rounded to the nearest 1/4 is 1/4.
For this problem we're asked to round 6 7/8 to the nearest 1/4.
6 7/8 is half way between 6 3/4 and 7, so it rounds up to 7.
Answer: 7
For the other problem we're asked to round 11 1/2 to the nearest 1/4.
11 1/2 is divisible by 1/4, so it's already rounded to the nearest 1/4.
Answer: 11 1/2