A concert audience of 600 people has 3/10 males and 5/6 older than 10. Calculate the fraction of females, fraction younger than 10, number of females, and number younger than 10.

If $\frac{3}{10}$ are male, the rest are female. $\text{Fraction female} = 1 - \frac{3}{10}$ $\text{Fraction female} = \frac{10}{10} - \frac{3}{10} = \frac{7}{10}$ The fraction of the audience that is female is $\boxed{\frac{7}{10}}$.

• b) What fraction of the audience is younger than 10 years of age?

If $\frac{5}{6}$ are older than 10, the rest are younger than 10. $\text{Fraction younger than 10} = 1 - \frac{5}{6}$ $\text{Fraction younger than 10} = \frac{6}{6} - \frac{5}{6} = \frac{1}{6}$ The fraction of the audience younger than 10 years of age is $\boxed{\frac{1}{6}}$.

• c) How many people in the audience are female?

$$
\text{Number of females} = \frac{7}{10} \times 600
$$
$$
\text{Number of females} = 7 \times 60 = 420
$$
There are $\boxed{420}$ female people in the audience.

• d) How many people are younger than 10 years of age?

$$
\text{Number of people younger than 10} = \frac{1}{6} \times 600
$$
$$
\text{Number of people younger than 10} = 1 \times 100 = 100
$$
There are $\boxed{100}$ people younger than 10 years of age.

2. Jane has walked $2\frac{4}{5}$ km from her home towards the shops. She has to walk a further $1\frac{3}{5}$ km to get there. What is the total distance from her house to the shops?

The total distance from her house to the shops is $\boxed{4\frac{2}{5} \text{ km}}$.

3. We are erecting safety fencing around our swimming pool. The total length of fencing is $20\frac{3}{8}$ m. The builders have already erected two pieces. One is $3\frac{2}{8}$ m, the next is $4\frac{5}{8}$ m. How much fencing do they still need to erect?

They still need to erect $\boxed{12\frac{1}{2} \text{ m}}$ of fencing.

4. a) What fraction of an hour is 40 minutes, in its simplest form?

Form the fraction.

40 minutes is $\boxed{\frac{2}{3}}$ of an hour.

4. b) I sleep 8 hours a night. What fraction of a day is this?

Form the fraction.

8 hours is $\boxed{\frac{1}{3}}$ of a day.

4. c) How many hours is $\frac{1}{4}$ of a day? How many hours is $\frac{3}{4}$ of a day?

$\frac{1}{4}$ of a day is $\boxed{6 \text{ hours}}$ and $\frac{3}{4}$ of a day is $\boxed{18 \text{ hours}}$.

5. Mila has saved R208. She decides to spend $\frac{5}{8}$ of her money on a new skirt.

• a) How much did the skirt cost?

$$
\text{Skirt cost} = \frac{5}{8} \times \text{R}208
$$
$$
\text{Skirt cost} = 5 \times \frac{208}{8}
$$
$$
\text{Skirt cost} = 5 \times 26 = \text{R}130
$$
The skirt cost $\boxed{\text{R}130}$.

• b) How much money has she got left?

$$
\text{Money left} = \text{R}208 - \text{R}130
$$
$$
\text{Money left} = \text{R}78
$$
She has $\boxed{\text{R}78}$ left.

6. Thando had 24 sweets. He ate one-quarter of his sweets and gave half of what was left to a friend.

• a) How many sweets did he eat?

$$
\text{Sweets eaten} = \frac{1}{4} \times 24
$$
$$
\text{Sweets eaten} = 6
$$
He ate $\boxed{6}$ sweets.

• b) How many sweets did he give to his friend?

$$
\text{Sweets given to friend} = \frac{1}{2} \times 18
$$
$$
\text{Sweets given to friend} = 9
$$
He gave $\boxed{9}$ sweets to his friend.

7. Joe had R150. He spent $\frac{2}{5}$ of the money on a shirt, and then he spent $\frac{2}{3}$ of the money that was left to buy a cap.

• a) How much did the shirt cost?

$$
\text{Shirt cost} = \frac{2}{5} \times \text{R}150
$$
$$
\text{Shirt cost} = 2 \times \frac{150}{5}
$$
$$
\text{Shirt cost} = 2 \times 30 = \text{R}60
$$
The shirt cost $\boxed{\text{R}60}$.

• b) How much did