To solve this problem, let’s work through each step to determine how much paint Hugo has left.

Step 1: Convert all mixed numbers to improper fractions

1. Initial amount of paint: $2 \frac{3}{35}$ litres

   • Convert $2 \frac{3}{35}$ to an improper fraction: $2 \frac{3}{35} = \frac{2 \times 35 + 3}{35} = \frac{70 + 3}{35} = \frac{73}{35}$

2. Paint used on the kitchen walls: $\frac{2}{5}$ litres (already in fraction form).

3. Paint used on the bedroom walls: $1 \frac{1}{7}$ litres

   • Convert $1 \frac{1}{7}$ to an improper fraction: $1 \frac{1}{7} = \frac{1 \times 7 + 1}{7} = \frac{7 + 1}{7} = \frac{8}{7}$

Step 2: Calculate the total amount of paint used

We need to add the fractions $\frac{2}{5}$ and $\frac{8}{7}$.

To add these, we find a common denominator:

• The least common multiple of 5 and 7 is 35.

Convert each fraction to have a denominator of 35: $\frac{2}{5} = \frac{2 \times 7}{5 \times 7} = \frac{14}{35}$ $\frac{8}{7} = \frac{8 \times 5}{7 \times 5} = \frac{40}{35}$

Now add these two fractions: $\frac{14}{35} + \frac{40}{35} = \frac{54}{35}$

So, the total paint used is $\frac{54}{35}$ litres.

Step 3: Subtract the amount of paint used from the initial amount

Now, we subtract $\frac{54}{35}$ from $\frac{73}{35}$: $\frac{73}{35} - \frac{54}{35} = \frac{73 - 54}{35} = \frac{19}{35}$

Answer

Hugo has $\frac{19}{35}$ litres of paint left.

Would you like further details on any part of this solution?

Here are five related questions to expand your understanding:

1. How would the solution change if Hugo used more paint than he originally had?
2. What is the process for adding fractions with different denominators?
3. How do you convert an improper fraction back into a mixed number?
4. How can you simplify fractions after performing operations like addition or subtraction?
5. How can you check your answer to ensure accuracy?

Tip: Always make sure to convert mixed numbers into improper fractions when performing arithmetic operations to simplify calculations.