1. To solve 1/4x27, we can simply multiply the two numbers to get the result:

1/4 x 27 = 1 x 27 / 4 = 27/4

2. To add 2/9 and 7/8, we need to find a common denominator. The least common multiple of 9 and 8 is 72. Using this, we can rewrite the fractions:

(2/9) + (7/8) = (16/72) + (63/72) = 79/72

3. To find 1/2 of 1/3, we multiply 1/3 by 1/2:

(1/2) * (1/3) = 1/6

4. To find the product of 3/4 and 2/5, we multiply the numerators to get the new numerator, and multiply the denominators to get the new denominator:

(3/4) * (2/5) = (3*2) / (4*5) = 6/20 = 3/10

5. To find the product of 3/4 and 1/2, we multiply the numerators to get the new numerator, and multiply the denominators to get the new denominator:

(3/4) * (1/2) = (3*1) / (4*2) = 3/8