Answer :
To determine which of the given proportions is false, let's evaluate each one step-by-step:
1. Proportion 1: [tex]\(\frac{20}{50} = \frac{40}{100}\)[/tex]
- Simplifying the fractions:
- [tex]\(\frac{20}{50}\)[/tex] simplifies to [tex]\(\frac{2}{5}\)[/tex].
- [tex]\(\frac{40}{100}\)[/tex] also simplifies to [tex]\(\frac{2}{5}\)[/tex].
- Since both fractions simplify to [tex]\(\frac{2}{5}\)[/tex], this proportion is true.
2. Proportion 2: [tex]\(\frac{12}{15} = \frac{20}{25}\)[/tex]
- Simplifying the fractions:
- [tex]\(\frac{12}{15}\)[/tex] simplifies to [tex]\(\frac{4}{5}\)[/tex].
- [tex]\(\frac{20}{25}\)[/tex] also simplifies to [tex]\(\frac{4}{5}\)[/tex].
- Since both fractions simplify to [tex]\(\frac{4}{5}\)[/tex], this proportion is true.
3. Proportion 3: [tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex]
- Simplifying the fractions:
- [tex]\(\frac{18}{48}\)[/tex] simplifies to [tex]\(\frac{3}{8}\)[/tex].
- [tex]\(\frac{30}{50}\)[/tex] simplifies to [tex]\(\frac{3}{5}\)[/tex].
- Since [tex]\(\frac{3}{8}\)[/tex] is not equal to [tex]\(\frac{3}{5}\)[/tex], this proportion is false.
4. Proportion 4: [tex]\(\frac{25}{45} = \frac{50}{90}\)[/tex]
- Simplifying the fractions:
- [tex]\(\frac{25}{45}\)[/tex] simplifies to [tex]\(\frac{5}{9}\)[/tex].
- [tex]\(\frac{50}{90}\)[/tex] also simplifies to [tex]\(\frac{5}{9}\)[/tex].
- Since both fractions simplify to [tex]\(\frac{5}{9}\)[/tex], this proportion is true.
Based on the evaluation, the false proportion is Proportion 3: [tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex].
1. Proportion 1: [tex]\(\frac{20}{50} = \frac{40}{100}\)[/tex]
- Simplifying the fractions:
- [tex]\(\frac{20}{50}\)[/tex] simplifies to [tex]\(\frac{2}{5}\)[/tex].
- [tex]\(\frac{40}{100}\)[/tex] also simplifies to [tex]\(\frac{2}{5}\)[/tex].
- Since both fractions simplify to [tex]\(\frac{2}{5}\)[/tex], this proportion is true.
2. Proportion 2: [tex]\(\frac{12}{15} = \frac{20}{25}\)[/tex]
- Simplifying the fractions:
- [tex]\(\frac{12}{15}\)[/tex] simplifies to [tex]\(\frac{4}{5}\)[/tex].
- [tex]\(\frac{20}{25}\)[/tex] also simplifies to [tex]\(\frac{4}{5}\)[/tex].
- Since both fractions simplify to [tex]\(\frac{4}{5}\)[/tex], this proportion is true.
3. Proportion 3: [tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex]
- Simplifying the fractions:
- [tex]\(\frac{18}{48}\)[/tex] simplifies to [tex]\(\frac{3}{8}\)[/tex].
- [tex]\(\frac{30}{50}\)[/tex] simplifies to [tex]\(\frac{3}{5}\)[/tex].
- Since [tex]\(\frac{3}{8}\)[/tex] is not equal to [tex]\(\frac{3}{5}\)[/tex], this proportion is false.
4. Proportion 4: [tex]\(\frac{25}{45} = \frac{50}{90}\)[/tex]
- Simplifying the fractions:
- [tex]\(\frac{25}{45}\)[/tex] simplifies to [tex]\(\frac{5}{9}\)[/tex].
- [tex]\(\frac{50}{90}\)[/tex] also simplifies to [tex]\(\frac{5}{9}\)[/tex].
- Since both fractions simplify to [tex]\(\frac{5}{9}\)[/tex], this proportion is true.
Based on the evaluation, the false proportion is Proportion 3: [tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex].
