Scaling a Recipe

Part of the Factors & Fractions section of Coddy's Pre-Algebra journey. Lesson 52 of 58.

A recipe needs 2/3 cup of sugar, and you want to make 1 and 1/2 times the recipe. Scaling a recipe multiplies every amount by the same number, the scale factor. Use s for sugar: s = (2/3) × (3/2), because 1 and 1/2 is 3/2.

Then multiply tops and bottoms: s = 6/6, which is s = 1. You need exactly 1 cup of sugar. As in the last chapter, a mixed scale factor is turned into an improper fraction before multiplying, never split into its whole and fraction parts.

Why multiply? Making the recipe twice means each amount twice, and making it half means each amount halved. A factor between 1 and 2 lands in between: more than the recipe asks, but less than double. That gives a quick check on any answer.

Challenge

A pancake recipe uses 3/4 cup of flour. You make 2 and 1/2 times the recipe. Find the amount of flour f, in cups. Write the scale factor as an improper fraction, then work it down to one fraction.