Question

Paula’s salad dressing recipe calls for 8 ounces of oil for every 3 ounces of vinegar. Carlo’s recipe has 1 ounce of vinegar for every 4 ounces of oil. Whose recipe has a smaller ratio of vinegar to oil?

Paula’s dressing ratio of vinegar to oil written as a fraction is
.
Carlo’s dressing ratio of vinegar to oil written as a fraction is
.
A common denominator for these fractions is
.
Whose recipe has a smaller ratio of vinegar to oil?
.

Answer 1

To analyze both Paula’s and Carlo’s salad dressing recipes in terms of the ratio of vinegar to oil, we can express their ratios as fractions.

1. **Paula’s Recipe:**
- Oil = 8 ounces
- Vinegar = 3 ounces
- The ratio of vinegar to oil is:
\[
\frac{\text{Vinegar}}{\text{Oil}} = \frac{3}{8}
\]

2. **Carlo’s Recipe:**
- Oil = 4 ounces
- Vinegar = 1 ounce
- The ratio of vinegar to oil is:
\[
\frac{\text{Vinegar}}{\text{Oil}} = \frac{1}{4}
\]

Next, we will find a common denominator for these fractions to compare them.

3. **Common Denominator:**
- The denominators are 8 and 4.
- A common denominator for these fractions is 8.

4. **Convert Carlo’s Ratio to the Common Denominator:**
\[
\frac{1}{4} = \frac{1 \times 2}{4 \times 2} = \frac{2}{8}
\]

Now we have both ratios:
- Paula’s ratio: \(\frac{3}{8}\)
- Carlo’s ratio: \(\frac{2}{8}\)

5. **Comparison:**
To see which recipe has a smaller ratio of vinegar to oil, we compare the fractions:
- \(\frac{3}{8}\) (Paula) is greater than \(\frac{2}{8}\) (Carlo).

Thus, Carlo’s recipe has a smaller ratio of vinegar to oil.

### Final Answers:
- Paula’s dressing ratio of vinegar to oil written as a fraction is \(\frac{3}{8}\).
- Carlo’s dressing ratio of vinegar to oil written as a fraction is \(\frac{1}{4}\) or \(\frac{2}{8}\).
- A common denominator for these fractions is 8.
- Carlo’s recipe has a smaller ratio of vinegar to oil.