Calculate the following.

$$\frac{4}{6} = \frac{2}{3}$$

The answer is $\boxed{\frac{2}{3}}$.

$$\frac{1}{3} + \frac{1}{3} = \frac{1+1}{3} = \frac{2}{3}$$

The answer is $\boxed{\frac{2}{3}}$.

$$\frac{1}{3} + \frac{1}{3} = \frac{1+1}{3} = \frac{2}{3}$$

The answer is $\boxed{\frac{2}{3}}$.

$$\frac{2}{4} + \frac{1}{4} = \frac{2+1}{4} = \frac{3}{4}$$

The answer is $\boxed{\frac{3}{4}}$.

$$\frac{1}{4} + \frac{2}{4} = \frac{1+2}{4} = \frac{3}{4}$$

The answer is $\boxed{\frac{3}{4}}$.

$$\frac{1}{5} + \frac{3}{5} = \frac{1+3}{5} = \frac{4}{5}$$

The answer is $\boxed{\frac{4}{5}}$.

$$\frac{2}{6} + \frac{3}{6} = \frac{2+3}{6} = \frac{5}{6}$$

The answer is $\boxed{\frac{5}{6}}$.

$$\frac{6}{8} = \frac{3}{4}$$

The answer is $\boxed{\frac{3}{4}}$.

$$\frac{4}{6} = \frac{2}{3}$$

The answer is $\boxed{\frac{2}{3}}$.

j)

$$\frac{3}{8} + \frac{2}{8} = \frac{3+2}{8} = \frac{5}{8}$$

The answer is $\boxed{\frac{5}{8}}$.

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.

  $$\frac{2}{6} + \frac{1}{6} + \frac{1}{6} + \frac{2}{6} = \frac{6}{6} = \boxed{1}$$

• Second diagram (rectangle with 4 parts): The rectangle is divided into 4 equal parts. There are 2 green and 2 pink parts.

  $$\frac{2}{4} + \frac{2}{4} = \frac{4}{4} = \boxed{1}$$