Convert fractions of metres to cm and fractions of hours to minutes.

To find the number of cm, use the conversion $1 \text{ metre} = 100 \text{ cm}$.

a) $\frac{1}{2}$ of 1 metre

$$\frac{1}{2} \times 100 \text{ cm} = 50 \text{ cm}$$

The answer is $\boxed{\mathbf{50 \text{ cm}}}$.

b) $\frac{1}{4}$ of 1 metre

$$\frac{1}{4} \times 100 \text{ cm} = 25 \text{ cm}$$

The answer is $\boxed{\mathbf{25 \text{ cm}}}$.

c) $\frac{1}{5}$ of 1 metre

$$\frac{1}{5} \times 100 \text{ cm} = 20 \text{ cm}$$

The answer is $\boxed{\mathbf{20 \text{ cm}}}$.

d) $\frac{7}{10}$ of 1 metre

$$\frac{7}{10} \times 100 \text{ cm} = 7 \times 10 \text{ cm} = 70 \text{ cm}$$

The answer is $\boxed{\mathbf{70 \text{ cm}}}$.

e) $\frac{1}{8}$ of 2 metres
First, convert 2 metres to cm: $2 \times 100 \text{ cm} = 200 \text{ cm}$.

$$\frac{1}{8} \times 200 \text{ cm} = 25 \text{ cm}$$

The answer is $\boxed{\mathbf{25 \text{ cm}}}$.

f) $\frac{3}{5}$ of 1 metre

$$\frac{3}{5} \times 100 \text{ cm} = 3 \times 20 \text{ cm} = 60 \text{ cm}$$

The answer is $\boxed{\mathbf{60 \text{ cm}}}$.

To find the number of minutes, use the conversion $1 \text{ hour} = 60 \text{ minutes}$.

a) $\frac{1}{5}$ hour

$$\frac{1}{5} \times 60 \text{ minutes} = 12 \text{ minutes}$$

The answer is $\boxed{\mathbf{12 \text{ minutes}}}$.

b) $\frac{1}{6}$ hour

$$\frac{1}{6} \times 60 \text{ minutes} = 10 \text{ minutes}$$

The answer is $\boxed{\mathbf{10 \text{ minutes}}}$.

c) $\frac{1}{10}$ hour

$$\frac{1}{10} \times 60 \text{ minutes} = 6 \text{ minutes}$$

The answer is $\boxed{\mathbf{6 \text{ minutes}}}$.

d) $\frac{2}{3}$ hour

$$\frac{2}{3} \times 60 \text{ minutes} = 2 \times 20 \text{ minutes} = 40 \text{ minutes}$$

The answer is $\boxed{\mathbf{40 \text{ minutes}}}$.

e) $\frac{1}{20}$ of 2 hours
First, convert 2 hours to minutes: $2 \times 60 \text{ minutes} = 120 \text{ minutes}$.

$$\frac{1}{20} \times 120 \text{ minutes} = 6 \text{ minutes}$$

The answer is $\boxed{\mathbf{6 \text{ minutes}}}$.

f) $\frac{2}{15}$ of 2 hours
First, convert 2 hours to minutes: $2 \times 60 \text{ minutes} = 120 \text{ minutes}$.

$$\frac{2}{15} \times 120 \text{ minutes} = 2 \times 8 \text{ minutes} = 16 \text{ minutes}$$

The answer is $\boxed{\mathbf{16 \text{ minutes}}}$.