A) To add 3/4 and 5/6, we need to find a common denominator. The least common multiple of 4 and 6 is 12. We can convert 3/4 to 9/12 by multiplying the numerator and denominator by 3. Similarly, we can convert 5/6 to 10/12 by multiplying the numerator and denominator by 2. Now we have a common denominator of 12, so we can add the fractions:
3/4 + 5/6 = 9/12 + 10/12 = (9 + 10)/12 = 19/12
B) To subtract 1/3 from 4/7, we also need a common denominator. The least common multiple of 3 and 7 is 21. We can convert both fractions to have a denominator of 21:
4/7 = (4/7) * (3/3) = 12/21
1/3 = (1/3) * (7/7) = 7/21
Now we can subtract the fractions:
4/7 - 1/3 = 12/21 - 7/21 = 5/21