Which of the following proportions is true?

A. [tex]\(\frac{25}{40} = \frac{48}{80}\)[/tex]

B. [tex]\(\frac{18}{48} = \frac{27}{72}\)[/tex]

C. [tex]\(\frac{12}{15} = \frac{21}{25}\)[/tex]

D. [tex]\(\frac{20}{48} = \frac{40}{98}\)[/tex]



Answer :

To determine which of the given proportions is true, let's analyze each proportion step by step:

1. First Proportion:
[tex]\[ \frac{25}{40} = \frac{48}{80} \][/tex]
To check this, we can cross-multiply:
[tex]\[ 25 \times 80 = 2000 \text{ and } 40 \times 48 = 1920 \][/tex]
Since [tex]\(2000 \neq 1920\)[/tex], the first proportion is not true.

2. Second Proportion:
[tex]\[ \frac{18}{48} = \frac{27}{72} \][/tex]
We cross-multiply:
[tex]\[ 18 \times 72 = 1296 \text{ and } 48 \times 27 = 1296 \][/tex]
Since [tex]\(1296 = 1296\)[/tex], the second proportion is true.

3. Third Proportion:
[tex]\[ \frac{12}{15} = \frac{21}{25} \][/tex]
We cross-multiply:
[tex]\[ 12 \times 25 = 300 \text{ and } 15 \times 21 = 315 \][/tex]
Since [tex]\(300 \neq 315\)[/tex], the third proportion is not true.

4. Fourth Proportion:
[tex]\[ \frac{20}{48} = \frac{40}{98} \][/tex]
We cross-multiply:
[tex]\[ 20 \times 98 = 1960 \text{ and } 48 \times 40 = 1920 \][/tex]
Since [tex]\(1960 \neq 1920\)[/tex], the fourth proportion is not true.

After analyzing all the proportions, we find that only the second proportion is true:

[tex]\[ \frac{18}{48} = \frac{27}{72} \][/tex]

So the correct answer is:
[tex]\[ \boxed{2} \][/tex]