Question
Describe what makes a proportion. Give an example of a proportion.
Answer middle school form.
Answer middle school form.
Answers
Answered by
GPT-4o mini
A proportion is a special kind of equation that shows two ratios are equal to each other. Ratios are comparisons of two quantities, like fractions, and they can be shown as "a/b" where "a" is the part and "b" is the whole.
For example, let's say you have a recipe that calls for 2 cups of flour for every 3 cups of sugar. We can write this as a ratio:
- Flour to Sugar = 2/3
Now, if you wanted to find out how many cups of flour you would need if you used 6 cups of sugar, you can set up a proportion:
\[
\frac{2 \text{ (cups of flour)}}{3 \text{ (cups of sugar)}} = \frac{x \text{ (cups of flour)}}{6 \text{ (cups of sugar)}}
\]
Here, \(x\) is the unknown amount of flour you need. To solve it, you can cross-multiply:
\[
2 \times 6 = 3 \times x
\]
That gives you:
\[
12 = 3x
\]
Now, divide both sides by 3:
\[
x = 4
\]
So, if you use 6 cups of sugar, you'll need 4 cups of flour. This shows how a proportion helps us understand the relationship between different quantities!
For example, let's say you have a recipe that calls for 2 cups of flour for every 3 cups of sugar. We can write this as a ratio:
- Flour to Sugar = 2/3
Now, if you wanted to find out how many cups of flour you would need if you used 6 cups of sugar, you can set up a proportion:
\[
\frac{2 \text{ (cups of flour)}}{3 \text{ (cups of sugar)}} = \frac{x \text{ (cups of flour)}}{6 \text{ (cups of sugar)}}
\]
Here, \(x\) is the unknown amount of flour you need. To solve it, you can cross-multiply:
\[
2 \times 6 = 3 \times x
\]
That gives you:
\[
12 = 3x
\]
Now, divide both sides by 3:
\[
x = 4
\]
So, if you use 6 cups of sugar, you'll need 4 cups of flour. This shows how a proportion helps us understand the relationship between different quantities!