Question
Do the ratios \( 23: 1 \) and \( 58: 2 \) form a proportion? yes Submit
Ask by George Warner. in the United States
Mar 06,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The ratios \(23:1\) and \(58:2\) do not form a proportion.
Solution
Below is a step-by-step explanation:
### Step 1: Write the Ratios as Fractions
The ratios \(23:1\) and \(58:2\) can be written as the fractions:
\[
\frac{23}{1} \quad \text{and} \quad \frac{58}{2}
\]
### Step 2: Simplify the Fractions (if necessary)
Simplify the fraction \(\frac{58}{2}\):
\[
\frac{58}{2} = 29
\]
The fraction \(\frac{23}{1}\) is simply \(23\).
### Step 3: Compare the Two Fractions
For two ratios to form a proportion, they must be equal. In other words, we need to check if:
\[
23 = 29
\]
Since this is not true, the ratios are not equal.
### Step 4: Conclude
Since \(23 \neq 29\), the ratios \(23:1\) and \(58:2\) do **not** form a proportion.
### Final Answer
No, the ratios do not form a proportion.
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Simplify this solution Beyond the Answer
To determine if \( 23:1 \) and \( 58:2 \) form a proportion, we can cross-multiply. This means we multiply the means and the extremes: \( 23 \times 2 \) and \( 58 \times 1 \). Calculating these gives us \( 46 \) and \( 58 \). Since \( 46 \) is not equal to \( 58 \), the two ratios do not form a proportion. In practical terms, proportions are all about balancing things out. Think of it like portions for a recipe: if you’re making a dish and your ingredients don’t follow the same ratio, your dish might end up tasting quite different than intended!
