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Which of the following proportions is false?

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

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

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

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

Answer :

To determine which proportion is false, let's analyze each pair of fractions:

1. First Pair: [tex]\(\frac{20}{50} = \frac{40}{100}\)[/tex]
- Simplifying both sides:
- [tex]\(\frac{20}{50} = \frac{2}{5}\)[/tex]
- [tex]\(\frac{40}{100} = \frac{4}{10} = \frac{2}{5}\)[/tex]
- Since both fractions simplify to [tex]\(\frac{2}{5}\)[/tex], this proportion is true.

2. Second Pair: [tex]\(\frac{25}{45} = \frac{50}{90}\)[/tex]
- Simplifying both sides:
- [tex]\(\frac{25}{45} = \frac{5}{9}\)[/tex]
- [tex]\(\frac{50}{90} = \frac{5}{9}\)[/tex]
- Since both fractions simplify to [tex]\(\frac{5}{9}\)[/tex], this proportion is true.

3. Third Pair: [tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex]
- Simplifying both sides:
- [tex]\(\frac{18}{48} = \frac{3}{8}\)[/tex]
- [tex]\(\frac{30}{50} = \frac{3}{5}\)[/tex]
- Since the fractions [tex]\(\frac{3}{8}\)[/tex] and [tex]\(\frac{3}{5}\)[/tex] are not equal, this proportion is false.

4. Fourth Pair: [tex]\(\frac{12}{15} = \frac{20}{25}\)[/tex]
- Simplifying both sides:
- [tex]\(\frac{12}{15} = \frac{4}{5}\)[/tex]
- [tex]\(\frac{20}{25} = \frac{4}{5}\)[/tex]
- Since both fractions simplify to [tex]\(\frac{4}{5}\)[/tex], this proportion is true.

Therefore, the false proportion is [tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex].

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