Question: Charlie had $2 \frac{2}{45}$ litres of paint.
He used $\frac{2}{5}$ litres of the paint on his bedroom walls and $1 \frac{2}{9}$ litres of the paint on his kitchen walls.
How many litres of paint does he have left?
Give your answer in its simplest form.
1. **State the problem:**
Charlie starts with $2 \frac{2}{45}$ litres of paint. He uses $\frac{2}{5}$ litres on bedroom walls and $1 \frac{2}{9}$ litres on kitchen walls. We need to find how much paint remains.
2. **Convert mixed numbers to improper fractions:**
$$2 \frac{2}{45} = \frac{2 \times 45 + 2}{45} = \frac{90 + 2}{45} = \frac{92}{45}$$
$$1 \frac{2}{9} = \frac{1 \times 9 + 2}{9} = \frac{9 + 2}{9} = \frac{11}{9}$$
3. **Sum the paint used:**
Add $\frac{2}{5}$ and $\frac{11}{9}$:
Find common denominator for $5$ and $9$ which is $45$.
$$\frac{2}{5} = \frac{2 \times 9}{5 \times 9} = \frac{18}{45}$$
$$\frac{11}{9} = \frac{11 \times 5}{9 \times 5} = \frac{55}{45}$$
Sum:
$$\frac{18}{45} + \frac{55}{45} = \frac{18 + 55}{45} = \frac{73}{45}$$
4. **Calculate paint left:**
Subtract paint used from total paint:
$$\frac{92}{45} - \frac{73}{45} = \frac{92 - 73}{45} = \frac{19}{45}$$
5. **Simplify the fraction:**
$19$ and $45$ have no common factors other than $1$, so $\frac{19}{45}$ is already in simplest form.
**Final answer:**
Charlie has $\frac{19}{45}$ litres of paint left.