Question

homework 5 - (2nd quarter)
\\(\frac{2}{5}\\) of a loaf of bread
serves 4 people. how
many people can be
served by the whole
loaf?

Explanation:

Step1: Define the relationship

Let \( x \) be the number of people the whole loaf serves. We know that \( \frac{2}{5} \) of the loaf serves 4 people. So we can set up a proportion: \( \frac{2}{5} \) loaf corresponds to 4 people, and 1 whole loaf (which is \( \frac{5}{5} \)) corresponds to \( x \) people. The proportion is \( \frac{\frac{2}{5}}{4}=\frac{1}{x} \) (or we can think in terms of unit rate: find how many people per \( \frac{1}{5} \) of the loaf, then multiply by 5).

Step2: Find people per \( \frac{1}{5} \) loaf

If \( \frac{2}{5} \) loaf serves 4 people, then \( \frac{1}{5} \) loaf serves \( 4\div2 = 2 \) people (since \( \frac{2}{5}\div2=\frac{1}{5} \)).

Step3: Find people for whole loaf

A whole loaf is \( \frac{5}{5} \), so we multiply the number of people per \( \frac{1}{5} \) loaf by 5. So \( 2\times5 = 10 \) people.

Or using the proportion method: Cross - multiply \( \frac{2}{5}x=4\times1 \). Then solve for \( x \): \( x = 4\div\frac{2}{5}=4\times\frac{5}{2}=10 \).

Answer:

10