Converting recurring decimals to fractions:
To express the decimal 0.38 recurring and 1.27 recurring as fractions in the form p/q, we can use the following steps:

Step 1: Let x = 0.38
Let x = 0.383838... (recurring decimals are represented by placing a bar over the repeating digits)

Step 2: Multiply x by 100 to shift the decimal two places to the right:
100x = 38.383838...

Step 3: Subtract x from 100x:
100x - x = 38.3838... - 0.3838...
99x = 38
x = 38/99
Therefore, 0.38 recurring can be expressed as 38/99.

Step 4: Let y = 1.27
Let y = 1.277777... (recurring decimals are represented by placing a bar over the repeating digits)

Step 5: Multiply y by 10 to shift the decimal one place to the right:
10y = 12.77777...

Step 6: Subtract y from 10y:
10y - y = 12.7777... - 1.7777...
9y = 12
y = 12/9 = 4/3
Therefore, 1.27 recurring can be expressed as 4/3.

Combining the fractions:
0.38 recurring + 1.27 recurring
= 38/99 + 4/3
To add these fractions, we need to find a common denominator. In this case, the least common multiple of 99 and 3 is 99.
= (38 * 3)/(99 * 3) + (4 * 33)/(3 * 33)
= 114/297 + 132/297
= (114 + 132)/297
= 246/297

Therefore, 0.38 recurring + 1.27 recurring can be expressed as 246/297 in the form p/q.