This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

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Here are the solutions to the problems:
2. Calculate the following.
a) Step 1: Add the numerators since the denominators are the same. Step 2: Simplify the fraction. The answer is .
b) Step 1: Add the numerators since the denominators are the same. The answer is .
c) Step 1: Add the numerators since the denominators are the same. The answer is .
d) Step 1: Add the numerators since the denominators are the same. The answer is .
e) Step 1: Add the numerators since the denominators are the same. The answer is .
f) Step 1: Add the numerators since the denominators are the same. The answer is .
g) Step 1: Add the numerators since the denominators are the same. The answer is .
h) Step 1: Add the numerators since the denominators are the same. Step 2: Simplify the fraction. The answer is .
i) Step 1: Add the numerators since the denominators are the same. Step 2: Simplify the fraction. The answer is .
j) Step 1: Add the numerators since the denominators are the same. The answer is .
Thinking fractions: Make a sum for each diagram.
First diagram (rectangle with 6 parts): The rectangle is divided into 6 equal parts. There are 2 red, 1 orange, 1 purple, and 2 green parts.
Second diagram (rectangle with 4 parts): The rectangle is divided into 4 equal parts. There are 2 green and 2 pink parts.
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This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.