To scale the recipe for 1 1/4 batches, we need to multiply each ingredient by 1.25 (which is equivalent to 1 1/4). Let's calculate the new amounts for each ingredient:

Recipe for 1 1/4 Batches:

1. Margarine:
   $\frac{3}{4} \text{ cup} \times 1.25 = \frac{15}{16} \text{ cup} = 0.9375 \text{ cups}$
   New amount: 15/16 cup or 0.9375 cups

2. Water:
   $3 \text{ tablespoons} \times 1.25 = 3.75 \text{ tablespoons}$
   New amount: 3 3/4 tablespoons

3. Butter-flavor shortening:
   $\frac{3}{4} \text{ cup} \times 1.25 = \frac{15}{16} \text{ cup} = 0.9375 \text{ cups}$
   New amount: 15/16 cup or 0.9375 cups

4. Vanilla:
   $3 \text{ teaspoons} \times 1.25 = 3.75 \text{ teaspoons}$
   New amount: 3 3/4 teaspoons

5. Brown sugar:
   $1 \frac{1}{2} \text{ cups} \times 1.25 = 1.875 \text{ cups}$
   New amount: 1 7/8 cups

6. Flour:
   $3 \frac{3}{4} \text{ cups} \times 1.25 = 4.6875 \text{ cups}$
   New amount: 4 11/16 cups or 4.6875 cups

7. Sugar:
   $\frac{3}{4} \text{ cup} \times 1.25 = 0.9375 \text{ cups}$
   New amount: 15/16 cup or 0.9375 cups

8. Baking soda:
   $1 \frac{1}{2} \text{ teaspoons} \times 1.25 = 1.875 \text{ teaspoons}$
   New amount: 1 7/8 teaspoons

9. Eggs:
   $3 \text{ eggs} \times 1.25 = 3.75 \text{ eggs}$
   New amount: 3 3/4 eggs

10. Salt:
    $\frac{3}{4} \text{ teaspoon} \times 1.25 = 0.9375 \text{ teaspoons}$
    New amount: 15/16 teaspoon or 0.9375 teaspoons

11. Light corn syrup:
    $3 \text{ tablespoons} \times 1.25 = 3.75 \text{ tablespoons}$
    New amount: 3 3/4 tablespoons

12. Milk chocolate chips:
    $3 \text{ cups} \times 1.25 = 3.75 \text{ cups}$
    New amount: 3 3/4 cups

Adjusted Recipe for 1 1/4 Batches:

• 15/16 cup margarine, softened
• 3 3/4 tablespoons water
• 15/16 cup butter-flavor shortening
• 3 3/4 teaspoons vanilla
• 1 7/8 cups brown sugar, lightly packed
• 4 11/16 cups flour
• 15/16 cup sugar
• 1 7/8 teaspoons baking soda
• 3 3/4 eggs
• 15/16 teaspoon salt
• 3 3/4 tablespoons light corn syrup
• 3 3/4 cups milk chocolate chips

Would you like further explanation or help with any other details?

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Here are some related questions to explore further:

1. How do you simplify fractional measurements when baking?
2. How do you adjust cooking times for scaled-up recipes?
3. What’s the difference between butter and butter-flavor shortening in baking?
4. How do changes in egg quantity affect the consistency of baked goods?
5. What is the purpose of corn syrup in a cookie recipe?

Tip: When scaling recipes, using a kitchen scale for accurate measurements can ensure better consistency in results!