Question

lesson 7 practice problems

1. a recipe calls for \\(\frac{1}{2}\\) lb of flour for 1 batch. how many batches can be made with each of the following amounts?

a. 1 lb
b. \\(\frac{3}{4}\\) lb
c. \\(\frac{1}{4}\\) lb

Explanation:

Step1: Understand the problem

We know that 1 batch requires $\frac{1}{2}$ lb of flour. To find the number of batches for a given amount of flour, we use the formula: Number of batches = Amount of flour $\div$ Flour per batch.

Step2: Solve part (a) - 1 lb of flour

We have amount of flour = 1 lb, flour per batch = $\frac{1}{2}$ lb.
Number of batches = $1 \div \frac{1}{2} = 1\times\frac{2}{1} = 2$.

Step3: Solve part (b) - $\frac{3}{4}$ lb of flour

Amount of flour = $\frac{3}{4}$ lb, flour per batch = $\frac{1}{2}$ lb.
Number of batches = $\frac{3}{4} \div \frac{1}{2} = \frac{3}{4}\times\frac{2}{1} = \frac{3\times2}{4\times1} = \frac{6}{4} = \frac{3}{2} = 1.5$.

Step4: Solve part (c) - $\frac{1}{4}$ lb of flour

Amount of flour = $\frac{1}{4}$ lb, flour per batch = $\frac{1}{2}$ lb.
Number of batches = $\frac{1}{4} \div \frac{1}{2} = \frac{1}{4}\times\frac{2}{1} = \frac{2}{4} = \frac{1}{2} = 0.5$.

Answer:

a. 2 batches
b. $\frac{3}{2}$ (or 1.5) batches
c. $\frac{1}{2}$ (or 0.5) batches