Math Problem Statement

How much of each ingredient is needed to make 3 recipes? How much of each ingredient is needed to make 3/4 of the recipe? How much of each ingredient is needed to make 4 2/3 recipes? How much of each ingredient is needed to make one single cookie?

Solution

Let's analyze the recipe and solve the problems step by step. Here's a summary of the ingredients for one recipe:

  • 2 ¾ cups of margarine
  • 1 ⅓ cups of sugar
  • 2 teaspoons of vanilla extract
  • 3 ¾ cups of flour
  • 1 teaspoon of baking powder
  • ¼ teaspoon of salt
  • 8 ⅓ oz of chocolate chips

Now, let's go over the questions:

1. How much of each ingredient is needed to make 3 recipes?

To find the amount for 3 recipes, simply multiply each ingredient by 3.

  • Margarine: 234×3=8142 \frac{3}{4} \times 3 = 8 \frac{1}{4} cups
  • Sugar: 113×3=41 \frac{1}{3} \times 3 = 4 cups
  • Vanilla Extract: 2×3=62 \times 3 = 6 teaspoons
  • Flour: 334×3=11143 \frac{3}{4} \times 3 = 11 \frac{1}{4} cups
  • Baking Powder: 1×3=31 \times 3 = 3 teaspoons
  • Salt: 14×3=34\frac{1}{4} \times 3 = \frac{3}{4} teaspoon
  • Chocolate Chips: 813×3=258 \frac{1}{3} \times 3 = 25 oz

2. How much of each ingredient is needed to make 34\frac{3}{4} of the recipe?

To find the amount for 34\frac{3}{4} of the recipe, multiply each ingredient by 34\frac{3}{4}.

  • Margarine: 234×34=21122 \frac{3}{4} \times \frac{3}{4} = 2 \frac{1}{12} cups
  • Sugar: 113×34=11121 \frac{1}{3} \times \frac{3}{4} = 1 \frac{1}{12} cups
  • Vanilla Extract: 2×34=1122 \times \frac{3}{4} = 1 \frac{1}{2} teaspoons
  • Flour: 334×34=27123 \frac{3}{4} \times \frac{3}{4} = 2 \frac{7}{12} cups
  • Baking Powder: 1×34=341 \times \frac{3}{4} = \frac{3}{4} teaspoon
  • Salt: 14×34=316\frac{1}{4} \times \frac{3}{4} = \frac{3}{16} teaspoon
  • Chocolate Chips: 813×34=61128 \frac{1}{3} \times \frac{3}{4} = 6 \frac{1}{12} oz

3. How much of each ingredient is needed to make 4234 \frac{2}{3} recipes?

To find the amount for 4234 \frac{2}{3} recipes, multiply each ingredient by 4234 \frac{2}{3}.

  • Margarine: 234×423=12142 \frac{3}{4} \times 4 \frac{2}{3} = 12 \frac{1}{4} cups
  • Sugar: 113×423=61 \frac{1}{3} \times 4 \frac{2}{3} = 6 cups
  • Vanilla Extract: 2×423=9132 \times 4 \frac{2}{3} = 9 \frac{1}{3} teaspoons
  • Flour: 334×423=17143 \frac{3}{4} \times 4 \frac{2}{3} = 17 \frac{1}{4} cups
  • Baking Powder: 1×423=4231 \times 4 \frac{2}{3} = 4 \frac{2}{3} teaspoons
  • Salt: 14×423=1112\frac{1}{4} \times 4 \frac{2}{3} = 1 \frac{1}{12} teaspoons
  • Chocolate Chips: 813×423=388 \frac{1}{3} \times 4 \frac{2}{3} = 38 oz

4. How much of each ingredient is needed to make one single cookie?

To find the amount for one cookie, divide each ingredient by 12 (since the recipe makes 12 cookies).

  • Margarine: 234÷12=11482 \frac{3}{4} \div 12 = \frac{11}{48} cups
  • Sugar: 113÷12=436=191 \frac{1}{3} \div 12 = \frac{4}{36} = \frac{1}{9} cups
  • Vanilla Extract: 2÷12=162 \div 12 = \frac{1}{6} teaspoons
  • Flour: 334÷12=1548=5163 \frac{3}{4} \div 12 = \frac{15}{48} = \frac{5}{16} cups
  • Baking Powder: 1÷12=1121 \div 12 = \frac{1}{12} teaspoon
  • Salt: 14÷12=148\frac{1}{4} \div 12 = \frac{1}{48} teaspoon
  • Chocolate Chips: 813÷12=25368 \frac{1}{3} \div 12 = \frac{25}{36} oz

Let me know if you'd like more details or further explanations!

Related Questions:

  1. How would you adjust the ingredients for 5 recipes?
  2. How do you scale the recipe for a half-size batch?
  3. What are the benefits of scaling recipes when baking?
  4. How do you convert measurements between cups, teaspoons, and ounces?
  5. How do you deal with rounding when working with fractional quantities in recipes?

Tip: When multiplying fractions, it's helpful to convert mixed numbers into improper fractions before multiplying for ease.

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Math Problem Analysis

Mathematical Concepts

Fractions
Multiplying Fractions
Dividing Fractions

Formulas

Multiplying fractions: a/b * c/d = ac/bd
Dividing fractions: a/b ÷ c/d = a/b * d/c

Theorems

Scaling recipes with fractions

Suitable Grade Level

Grades 6-8