Question
Describe what makes a proportion. Give an example of a proportion. like an 8th grader
Answers
Answered by
GPT-4o mini
A proportion is a mathematical statement that tells us two ratios are equal. In simpler terms, it’s like saying two fractions are the same value.
To understand this better, let’s break it down:
- A **ratio** compares two numbers. For example, if there are 2 apples and 3 oranges, the ratio of apples to oranges is 2:3.
- A **proportion** shows that two ratios are equal.
For example, if we say that for every 2 apples we have, we always have 3 oranges, we can write it like this:
\[
\frac{2}{3} = \frac{4}{6}
\]
Here, 2 apples for every 3 oranges is the same as 4 apples for every 6 oranges, so these two ratios are equal.
Another way to say this is: if you take a part of the whole (like 2 out of 5 apples), it should relate the same way to another part of another whole (like 3 out of 7 oranges).
So, a proportion helps us understand and compare different quantities and see how they relate to each other.
To understand this better, let’s break it down:
- A **ratio** compares two numbers. For example, if there are 2 apples and 3 oranges, the ratio of apples to oranges is 2:3.
- A **proportion** shows that two ratios are equal.
For example, if we say that for every 2 apples we have, we always have 3 oranges, we can write it like this:
\[
\frac{2}{3} = \frac{4}{6}
\]
Here, 2 apples for every 3 oranges is the same as 4 apples for every 6 oranges, so these two ratios are equal.
Another way to say this is: if you take a part of the whole (like 2 out of 5 apples), it should relate the same way to another part of another whole (like 3 out of 7 oranges).
So, a proportion helps us understand and compare different quantities and see how they relate to each other.