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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Answer
Here are the solutions for adding the fractions:
a)
Step 1: Add the numerators since the denominators are the same.
Step 2: Simplify the fraction.
\frac{1+1}{3} = \frac{2{3}}
The image shows one-third shaded in the first shape and one-third shaded in the second, totaling two-thirds.
b)
Step 1: Add the numerators since the denominators are the same.
Step 2: Simplify the fraction.
\frac{2+1}{4} = \frac{3{4}}
The image shows two-fourths shaded in the first shape and one-fourth shaded in the second, totaling three-fourths.
c)
Step 1: Add the numerators since the denominators are the same.
Step 2: Simplify the fraction.
\frac{1+2}{4} = \frac{3{4}}
The image shows one-fourth shaded in the first shape and two-fourths shaded in the second, totaling three-fourths.
d)
Step 1: Add the numerators since the denominators are the same.
Step 2: Simplify the fraction.
\frac{1+3}{5} = \frac{4{5}}
The image shows one-fifth shaded in the first shape and three-fifths shaded in the second, totaling four-fifths.
e)
Step 1: Add the numerators since the denominators are the same.
Step 2: Simplify the fraction.
\frac{2+3}{6} = \frac{5{6}}
The image shows two-sixths shaded in the first shape and three-sixths shaded in the second, totaling five-sixths.
f)
Step 1: Add the numerators since the denominators are the same.
Step 2: Simplify the fraction.
Step 3: Reduce the fraction to its simplest form by dividing the numerator and denominator by their greatest common divisor, which is 2.
\frac{6 \div 2}{8 \div 2} = \frac{3{4}}
The image shows four-eighths shaded in the first shape and two-eighths shaded in the second, totaling six-eighths, which simplifies to three-fourths.
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a) Step 1: Add the numerators since the denominators are the same. (1)/(3) + (1)/(3) = (1+1)/(3) Step 2: Simplify the fraction.
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.