Question

Describe what makes a proportion. Give an example of a proportion.(2 points)

(make it sound like a high schooler and show your work)

Answer 1

A proportion is a mathematical equation that states that two ratios are equal. It usually shows the relationship between two sets of numbers in a way that allows us to compare them. When we say two ratios are proportional, it means that the way they are related holds true across a consistent relationship.

For example, let's take a simple proportion involving the ratios of boys and girls in a classroom. Suppose there are 10 boys and 15 girls. The ratio of boys to girls can be written as:

- Ratio of boys to girls = \( \frac{10}{15} \)

Now, let's say we find another classroom with 20 boys and 30 girls. We can write the ratio for this second classroom as:

- Ratio of boys to girls = \( \frac{20}{30} \)

To check if these two ratios are proportional, we can simplify both ratios:

1. Simplify \( \frac{10}{15} \):
- Divide both the numerator and the denominator by 5:
- \( \frac{10 \div 5}{15 \div 5} = \frac{2}{3} \)

2. Simplify \( \frac{20}{30} \):
- Divide both the numerator and the denominator by 10:
- \( \frac{20 \div 10}{30 \div 10} = \frac{2}{3} \)

Since both simplified ratios are equal (\( \frac{2}{3} \)), we can write the proportion as:

\[ \frac{10}{15} = \frac{20}{30} \]

This shows that the number of boys and girls in both classrooms maintains the same ratio, which makes them proportional.

So, a proportion is basically a way of saying that two different groups or sets of numbers have a consistent relationship relative to one another!