What fraction of the diagrams below has been coloured? What fraction of the diagrams below has not been coloured?

$$\frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12}$$ $$\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}$$

Since $4 > 3$, then $\frac{4}{12} > \frac{3}{12}$.
Therefore, $\frac{1}{3} > \frac{1}{4}$.
The answer is $\boxed{>}$.

b) Compare $\frac{2}{5}$ and $\frac{3}{6}$.

$$\frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10}$$ $$\frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10}$$

Since $4 < 5$, then $\frac{4}{10} < \frac{5}{10}$.
Therefore, $\frac{2}{5} < \frac{3}{6}$.
The answer is $\boxed{<}$.

c) Compare $\frac{4}{7}$ and $\frac{2}{5}$.

$$\frac{4}{7} = \frac{4 \times 5}{7 \times 5} = \frac{20}{35}$$ $$\frac{2}{5} = \frac{2 \times 7}{5 \times 7} = \frac{14}{35}$$

Since $20 > 14$, then $\frac{20}{35} > \frac{14}{35}$.
Therefore, $\frac{4}{7} > \frac{2}{5}$.
The answer is $\boxed{>}$.

d) Compare $\frac{3}{6}$ and $\frac{2}{4}$.

$$\frac{3}{6} = \frac{1}{2}$$ $$\frac{2}{4} = \frac{1}{2}$$

Since both are equal to $\frac{1}{2}$.
Therefore, $\frac{3}{6} = \frac{2}{4}$.
The answer is $\boxed{=}$.

e) Compare $\frac{2}{8}$ and $\frac{1}{4}$.

Since both are equal to $\frac{1}{4}$.
Therefore, $\frac{2}{8} = \frac{1}{4}$.
The answer is $\boxed{=}$.

f) Compare $\frac{1}{3}$ and $\frac{3}{5}$.

$$\frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15}$$ $$\frac{3}{5} = \frac{3 \times 3}{5 \times 3} = \frac{9}{15}$$

Since $5 < 9$, then $\frac{5}{15} < \frac{9}{15}$.
Therefore, $\frac{1}{3} < \frac{3}{5}$.
The answer is $\boxed{<}$.

2. What fractions are shown by the arrow?

a) The number line is divided into 4 equal parts between 0 and 1. Each part represents $\frac{1}{4}$. The arrow points to the second mark.

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

The fraction is $\boxed{\frac{1}{2}}$.

b) The number line is divided into 4 equal parts between 1 and 2. Each part represents $\frac{1}{4}$. The arrow points to the second mark after 1.

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

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

c) The number line is divided into 4 equal parts between 4 and 5. Each part represents $\frac{1}{4}$. The arrow points to the third mark after 4.

$$4 + \frac{3}{4} = \frac{16}{4} + \frac{3}{4} = \frac{19}{4}$$

The fraction is $\boxed{\frac{19}{4}}$.

d) The number line is divided into 4 equal parts between 5 and 6. Each part represents $\frac{1}{4}$. The arrow points to the second mark after 5.

$$5 + \frac{2}{4} = 5 + \frac{1}{2} = \frac{11}{2}$$

The fraction is $\boxed{\frac{11}{2}}$.