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Michael and Sondra are mixing lemonade. In Michael’s lemonade, the ratio of lemons to water is 1:4. In Sondra’s lemonade, the ratio of lemons to water is 2:6. Several equivalent ratios for each mixture are shown in the ratio tables.

Michael
Lemons
Cups of Water
1
4
3
12
4
16

Sondra
Lemons
Cups of Water
2
6
4
12
6
18

Imagine that you want to compare Michael’s ratio to Sondra’s ratio. Which two ratios in the tables shown have a common denominator you could use to compare?
Three-fourths and StartFraction 6 Over 4 EndFraction
StartFraction 3 Over 12 EndFraction and StartFraction 4 Over 12 EndFraction
StartFraction 16 Over 4 EndFraction and StartFraction 18 Over 6 EndFraction
StartFraction 1 Over 12 EndFraction and StartFraction 4 Over 18 EndFraction

1 answer

To compare Michael's and Sondra's lemonade ratios, we need to find two fractions from the provided tables that have a common denominator.

Let's examine the fractional representations of their ratios:

Michael's lemonade (lemons:water = 1:4):

  • For Michael:
    • 1 lemon and 4 cups of water = \( \frac{1}{4} \)
    • 3 lemons and 12 cups of water = \( \frac{3}{12} \) (which simplifies to \( \frac{1}{4} \))
    • 4 lemons and 16 cups of water = \( \frac{4}{16} \) (which simplifies to \( \frac{1}{4} \))

Sondra's lemonade (lemons:water = 2:6):

  • For Sondra:
    • 2 lemons and 6 cups of water = \( \frac{2}{6} \) (which simplifies to \( \frac{1}{3} \))
    • 4 lemons and 12 cups of water = \( \frac{4}{12} \) (which simplifies to \( \frac{1}{3} \))
    • 6 lemons and 18 cups of water = \( \frac{6}{18} \) (which simplifies to \( \frac{1}{3} \))

Now we evaluate the choices provided:

  1. Three-fourths and \( \frac{6}{4} \) → not present in tables.
  2. \( \frac{3}{12} \) and \( \frac{4}{12} \) → both can be expressed over the common denominator of 12.
  3. \( \frac{16}{4} \) and \( \frac{18}{6} \) → not simplified and don't reflect the mix accurately.
  4. \( \frac{1}{12} \) and \( \frac{4}{18} \) → not present in tables.

Thus, the appropriate pair with a common denominator that can be compared is \( \frac{3}{12} \) and \( \frac{4}{12} \).

The correct answer is: StartFraction 3 Over 12 EndFraction and StartFraction 4 Over 12 EndFraction.