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------------------------------------------------ Which of the following proportions is false?

A. [tex]\frac{25}{45} = \frac{50}{90}[/tex]

B. [tex]\frac{20}{50} = \frac{40}{100}[/tex]

C. [tex]\frac{12}{15} = \frac{20}{25}[/tex]

D. [tex]\frac{18}{48} = \frac{30}{50}[/tex]

Sure! Let's check each proportion step by step to determine which one is false.

### Proportion 1:
[tex]\[
\frac{25}{45} = \frac{50}{90}
\][/tex]
To verify, we can cross-multiply:
[tex]\[
25 \times 90 = 2250
\][/tex]
[tex]\[
45 \times 50 = 2250
\][/tex]
Since [tex]\(2250 = 2250\)[/tex], this proportion is correct.

### Proportion 2:
[tex]\[
\frac{20}{50} = \frac{40}{100}
\][/tex]
Cross-multiplying, we get:
[tex]\[
20 \times 100 = 2000
\][/tex]
[tex]\[
50 \times 40 = 2000
\][/tex]
Since [tex]\(2000 = 2000\)[/tex], this proportion is correct.

### Proportion 3:
[tex]\[
\frac{12}{15} = \frac{20}{25}
\][/tex]
Cross-multiplying:
[tex]\[
12 \times 25 = 300
\][/tex]
[tex]\[
15 \times 20 = 300
\][/tex]
Since [tex]\(300 = 300\)[/tex], this proportion is correct.

### Proportion 4:
[tex]\[
\frac{18}{48} = \frac{30}{50}
\][/tex]
Cross-multiplying, we obtain:
[tex]\[
18 \times 50 = 900
\][/tex]
[tex]\[
48 \times 30 = 1440
\][/tex]
Since [tex]\(900 \neq 1440\)[/tex], this proportion is incorrect.

So, the false proportion is:
[tex]\[
\frac{18}{48} = \frac{30}{50}
\][/tex]