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?

Question

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.