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Answer :
To determine which proportion is false, we need to check the equality of each given pair of fractions.
Let's examine each proportion one by one:
1. Proportion 1: [tex]\(\frac{18}{48} = \frac{20}{50}\)[/tex]
- Simplifying both fractions:
- [tex]\(\frac{18}{48}\)[/tex] simplifies to [tex]\(\frac{3}{8}\)[/tex].
- [tex]\(\frac{20}{50}\)[/tex] simplifies to [tex]\(\frac{2}{5}\)[/tex].
- Comparing [tex]\(\frac{3}{8}\)[/tex] and [tex]\(\frac{2}{5}\)[/tex], these fractions are not equal.
Therefore, this proportion is false.
2. Proportion 2: [tex]\(\frac{25}{45} = \frac{75}{135}\)[/tex]
- Simplifying both fractions:
- [tex]\(\frac{25}{45} = \frac{5}{9}\)[/tex] after dividing by 5.
- [tex]\(\frac{75}{135} = \frac{5}{9}\)[/tex] after dividing by 15.
- Since both fractions simplify to [tex]\(\frac{5}{9}\)[/tex], they are equal.
Therefore, this proportion is true.
3. Proportion 3: [tex]\(\frac{10}{25} = \frac{40}{100}\)[/tex]
- Simplifying both fractions:
- [tex]\(\frac{10}{25} = \frac{2}{5}\)[/tex] after dividing by 5.
- [tex]\(\frac{40}{100} = \frac{2}{5}\)[/tex] after dividing by 20.
- Since both fractions simplify to [tex]\(\frac{2}{5}\)[/tex], they are equal.
Therefore, this proportion is true.
4. Proportion 4: [tex]\(\frac{24}{30} = \frac{20}{25}\)[/tex]
- Simplifying both fractions:
- [tex]\(\frac{24}{30} = \frac{4}{5}\)[/tex] after dividing by 6.
- [tex]\(\frac{20}{25} = \frac{4}{5}\)[/tex] after dividing by 5.
- Since both fractions simplify to [tex]\(\frac{4}{5}\)[/tex], they are equal.
Therefore, this proportion is true.
Based on the analysis, the false proportion is the first one: [tex]\(\frac{18}{48} = \frac{20}{50}\)[/tex].
Let's examine each proportion one by one:
1. Proportion 1: [tex]\(\frac{18}{48} = \frac{20}{50}\)[/tex]
- Simplifying both fractions:
- [tex]\(\frac{18}{48}\)[/tex] simplifies to [tex]\(\frac{3}{8}\)[/tex].
- [tex]\(\frac{20}{50}\)[/tex] simplifies to [tex]\(\frac{2}{5}\)[/tex].
- Comparing [tex]\(\frac{3}{8}\)[/tex] and [tex]\(\frac{2}{5}\)[/tex], these fractions are not equal.
Therefore, this proportion is false.
2. Proportion 2: [tex]\(\frac{25}{45} = \frac{75}{135}\)[/tex]
- Simplifying both fractions:
- [tex]\(\frac{25}{45} = \frac{5}{9}\)[/tex] after dividing by 5.
- [tex]\(\frac{75}{135} = \frac{5}{9}\)[/tex] after dividing by 15.
- Since both fractions simplify to [tex]\(\frac{5}{9}\)[/tex], they are equal.
Therefore, this proportion is true.
3. Proportion 3: [tex]\(\frac{10}{25} = \frac{40}{100}\)[/tex]
- Simplifying both fractions:
- [tex]\(\frac{10}{25} = \frac{2}{5}\)[/tex] after dividing by 5.
- [tex]\(\frac{40}{100} = \frac{2}{5}\)[/tex] after dividing by 20.
- Since both fractions simplify to [tex]\(\frac{2}{5}\)[/tex], they are equal.
Therefore, this proportion is true.
4. Proportion 4: [tex]\(\frac{24}{30} = \frac{20}{25}\)[/tex]
- Simplifying both fractions:
- [tex]\(\frac{24}{30} = \frac{4}{5}\)[/tex] after dividing by 6.
- [tex]\(\frac{20}{25} = \frac{4}{5}\)[/tex] after dividing by 5.
- Since both fractions simplify to [tex]\(\frac{4}{5}\)[/tex], they are equal.
Therefore, this proportion is true.
Based on the analysis, the false proportion is the first one: [tex]\(\frac{18}{48} = \frac{20}{50}\)[/tex].
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