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Answer :
To determine which of the given proportions is false, we need to compare each pair of fractions and check if they are equal. Here's a step-by-step solution to find out:
1. Check the first proportion:
- [tex]\(\frac{10}{25}\)[/tex] and [tex]\(\frac{40}{100}\)[/tex]
- Simplify both fractions:
- [tex]\(\frac{10}{25} = \frac{2}{5}\)[/tex]
- [tex]\(\frac{40}{100} = \frac{2}{5}\)[/tex]
- Since both fractions simplify to [tex]\(\frac{2}{5}\)[/tex], they are equal. This proportion is true.
2. Check the second proportion:
- [tex]\(\frac{18}{48}\)[/tex] and [tex]\(\frac{20}{50}\)[/tex]
- Simplify both fractions:
- [tex]\(\frac{18}{48} = \frac{3}{8}\)[/tex]
- [tex]\(\frac{20}{50} = \frac{2}{5}\)[/tex]
- The simplified forms [tex]\(\frac{3}{8}\)[/tex] and [tex]\(\frac{2}{5}\)[/tex] are not equal, so this proportion is false.
3. Check the third proportion:
- [tex]\(\frac{25}{45}\)[/tex] and [tex]\(\frac{75}{135}\)[/tex]
- Simplify both fractions:
- [tex]\(\frac{25}{45} = \frac{5}{9}\)[/tex]
- [tex]\(\frac{75}{135} = \frac{5}{9}\)[/tex]
- Both fractions simplify to [tex]\(\frac{5}{9}\)[/tex], so they are equal. This proportion is true.
4. Check the fourth proportion:
- [tex]\(\frac{24}{30}\)[/tex] and [tex]\(\frac{20}{25}\)[/tex]
- Simplify both fractions:
- [tex]\(\frac{24}{30} = \frac{4}{5}\)[/tex]
- [tex]\(\frac{20}{25} = \frac{4}{5}\)[/tex]
- Both fractions simplify to [tex]\(\frac{4}{5}\)[/tex], so they are equal. This proportion is true.
Based on these checks, we find that the second proportion, [tex]\(\frac{18}{48} = \frac{20}{50}\)[/tex], is false.
1. Check the first proportion:
- [tex]\(\frac{10}{25}\)[/tex] and [tex]\(\frac{40}{100}\)[/tex]
- Simplify both fractions:
- [tex]\(\frac{10}{25} = \frac{2}{5}\)[/tex]
- [tex]\(\frac{40}{100} = \frac{2}{5}\)[/tex]
- Since both fractions simplify to [tex]\(\frac{2}{5}\)[/tex], they are equal. This proportion is true.
2. Check the second proportion:
- [tex]\(\frac{18}{48}\)[/tex] and [tex]\(\frac{20}{50}\)[/tex]
- Simplify both fractions:
- [tex]\(\frac{18}{48} = \frac{3}{8}\)[/tex]
- [tex]\(\frac{20}{50} = \frac{2}{5}\)[/tex]
- The simplified forms [tex]\(\frac{3}{8}\)[/tex] and [tex]\(\frac{2}{5}\)[/tex] are not equal, so this proportion is false.
3. Check the third proportion:
- [tex]\(\frac{25}{45}\)[/tex] and [tex]\(\frac{75}{135}\)[/tex]
- Simplify both fractions:
- [tex]\(\frac{25}{45} = \frac{5}{9}\)[/tex]
- [tex]\(\frac{75}{135} = \frac{5}{9}\)[/tex]
- Both fractions simplify to [tex]\(\frac{5}{9}\)[/tex], so they are equal. This proportion is true.
4. Check the fourth proportion:
- [tex]\(\frac{24}{30}\)[/tex] and [tex]\(\frac{20}{25}\)[/tex]
- Simplify both fractions:
- [tex]\(\frac{24}{30} = \frac{4}{5}\)[/tex]
- [tex]\(\frac{20}{25} = \frac{4}{5}\)[/tex]
- Both fractions simplify to [tex]\(\frac{4}{5}\)[/tex], so they are equal. This proportion is true.
Based on these checks, we find that the second proportion, [tex]\(\frac{18}{48} = \frac{20}{50}\)[/tex], is false.
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