Praxis Core Academic Skills for Educators: Mathematics (5733)Number and QuantityMedium
A chef is preparing a large batch of soup. The recipe calls for 3/4 cup of broth for every 2 servings. If the chef wants to make 10 servings, how many cups of broth are needed?
- A1 1/2 cups
- B7 1/2 cups
- C3 3/4 cups
- D2 1/4 cups
Show answer & explanationAnswer & explanation
Correct answer: C. 3 3/4 cups
Set up a proportion: (3/4 cup) / (2 servings) = (x cups) / (10 servings). Cross-multiply and solve for x. (3/4) * 10 = 2 * x, which simplifies to 30/4 = 2x, or 7.5 = 2x. Dividing by 2 gives x = 3.75, which is 3 3/4 cups.
Why the other options are wrong
- A. This would be the amount for 4 servings.
- B. This would be the amount for 20 servings.
- D. This is an incorrect calculation, possibly from dividing 10 by 2 then multiplying by 3/4 and then by 2 again.
Proportions with Fractions
A proportion is an equation stating that two ratios are equal. When one or more terms in a proportion are fractions, cross-multiplication can be used to solve for an unknown value.
- A ratio compares two quantities.
- In a proportion a/b = c/d, the cross products are equal (ad = bc).
- Fractions can be terms in a ratio or the ratio itself.
Memory trick: Ratios equal, cross-multiply and solve.