Determine if the following ratios form a proportion. Also, write the middle terms and extreme terms where the ratios form a proportion.
39 litres : 65 litres and 6 bottles : 10 bottles

Answer

To determine if the given ratios form a proportion, we need to check if the two ratios are equal. The ratios given are:

1. 39 litres : 65 litres
2. 6 bottles : 10 bottles

### Step 1: Write the ratios in fractional form
We can express the ratios as fractions:

- For the first ratio:
\[ \frac{39}{65} \]

- For the second ratio:
\[ \frac{6}{10} \]

### Step 2: Simplify both fractions
Now, we will simplify both fractions to see if they are equal.

**For the first ratio:**
\[ \frac{39}{65} = \frac{39 \div 13}{65 \div 13} = \frac{3}{5} \]

**For the second ratio:**
\[ \frac{6}{10} = \frac{6 \div 2}{10 \div 2} = \frac{3}{5} \]

### Step 3: Compare the simplified fractions
Now we compare the simplified fractions:
\[ \frac{3}{5} \text{ and } \frac{3}{5} \]
Since both fractions are equal, we can conclude that the ratios form a proportion.

### Step 4: Identify the middle terms and extreme terms
In a proportion, the terms can be arranged as follows:
\[ \frac{a}{b} = \frac{c}{d} \]
Where \(a\) and \(d\) are the extreme terms, and \(b\) and \(c\) are the middle terms.

For our ratios:
- Extreme terms: 39 litres and 10 bottles
- Middle terms: 65 litres and 6 bottles

### Final Conclusion
Thus, the given ratios \(39 \text{ litres} : 65 \text{ litres}\) and \(6 \text{ bottles} : 10 \text{ bottles}\) are in proportion.

### Summary of Terms
- **Middle Terms:** 65 litres, 6 bottles
- **Extreme Terms:** 39 litres, 10 bottles

---