Question

Determine if 2.5/10 =? 12/48 or 2.5/2 =? 12/24 is a proportion.

Answer 1

To determine if the given ratios are equal, we can simplify both sides of the proposed equalities.

1. **First comparison: \( \frac{2.5}{10} \) and \( \frac{12}{48} \)**

Let's simplify both fractions:

- For \( \frac{2.5}{10} \):
\[
\frac{2.5}{10} = \frac{25}{100} = \frac{1}{4} \quad (\text{by multiplying numerator and denominator by 10})
\]

- For \( \frac{12}{48} \):
\[
\frac{12}{48} = \frac{1}{4} \quad (\text{by dividing numerator and denominator by 12})
\]

Since \( \frac{2.5}{10} = \frac{1}{4} \) and \( \frac{12}{48} = \frac{1}{4} \), we have:
\[
\frac{2.5}{10} = \frac{12}{48}
\]

Therefore, the first comparison **is a proportion**.

2. **Second comparison: \( \frac{2.5}{2} \) and \( \frac{12}{24} \)**

Let's simplify both fractions:

- For \( \frac{2.5}{2} \):
\[
\frac{2.5}{2} = 1.25
\]

- For \( \frac{12}{24} \):
\[
\frac{12}{24} = \frac{1}{2} \quad (\text{by dividing numerator and denominator by 12})
\]

Since \( 1.25 \) is not equal to \( 0.5 \), we have:
\[
\frac{2.5}{2} \neq \frac{12}{24}
\]

Therefore, the second comparison **is not a proportion**.

In summary:
- \( \frac{2.5}{10} = \frac{12}{48} \) is a proportion.
- \( \frac{2.5}{2} \neq \frac{12}{24} \) is not a proportion.