Answer :
To determine which proportion is false among the given options, we compare each pair of fractions to see if they are equivalent.
1. First Proportion: [tex]\(\frac{25}{45}=\frac{75}{135}\)[/tex]
- Simplify [tex]\(\frac{25}{45}\)[/tex]: Both 25 and 45 are divisible by 5. So, [tex]\(\frac{25}{45} = \frac{5}{9}\)[/tex].
- Simplify [tex]\(\frac{75}{135}\)[/tex]: Both 75 and 135 are divisible by 15. So, [tex]\(\frac{75}{135} = \frac{5}{9}\)[/tex].
- Both fractions simplify to [tex]\(\frac{5}{9}\)[/tex], so they are equivalent.
2. Second Proportion: [tex]\(\frac{18}{48}=\frac{20}{50}\)[/tex]
- Simplify [tex]\(\frac{18}{48}\)[/tex]: Both 18 and 48 are divisible by 6. So, [tex]\(\frac{18}{48} = \frac{3}{8}\)[/tex].
- Simplify [tex]\(\frac{20}{50}\)[/tex]: Both 20 and 50 are divisible by 10. So, [tex]\(\frac{20}{50} = \frac{2}{5}\)[/tex].
- The fractions [tex]\(\frac{3}{8}\)[/tex] and [tex]\(\frac{2}{5}\)[/tex] are not equivalent.
3. Third Proportion: [tex]\(\frac{24}{30}=\frac{20}{25}\)[/tex]
- Simplify [tex]\(\frac{24}{30}\)[/tex]: Both 24 and 30 are divisible by 6. So, [tex]\(\frac{24}{30} = \frac{4}{5}\)[/tex].
- Simplify [tex]\(\frac{20}{25}\)[/tex]: Both 20 and 25 are divisible by 5. So, [tex]\(\frac{20}{25} = \frac{4}{5}\)[/tex].
- Both fractions simplify to [tex]\(\frac{4}{5}\)[/tex], so they are equivalent.
4. Fourth Proportion: [tex]\(\frac{10}{25}=\frac{40}{100}\)[/tex]
- Simplify [tex]\(\frac{10}{25}\)[/tex]: Both 10 and 25 are divisible by 5. So, [tex]\(\frac{10}{25} = \frac{2}{5}\)[/tex].
- Simplify [tex]\(\frac{40}{100}\)[/tex]: Both 40 and 100 are divisible by 20. So, [tex]\(\frac{40}{100} = \frac{2}{5}\)[/tex].
- Both fractions simplify to [tex]\(\frac{2}{5}\)[/tex], so they are equivalent.
After checking each proportion, we find that the second proportion [tex]\(\frac{18}{48} = \frac{20}{50}\)[/tex] is not true. Therefore, this is the false proportion.
1. First Proportion: [tex]\(\frac{25}{45}=\frac{75}{135}\)[/tex]
- Simplify [tex]\(\frac{25}{45}\)[/tex]: Both 25 and 45 are divisible by 5. So, [tex]\(\frac{25}{45} = \frac{5}{9}\)[/tex].
- Simplify [tex]\(\frac{75}{135}\)[/tex]: Both 75 and 135 are divisible by 15. So, [tex]\(\frac{75}{135} = \frac{5}{9}\)[/tex].
- Both fractions simplify to [tex]\(\frac{5}{9}\)[/tex], so they are equivalent.
2. Second Proportion: [tex]\(\frac{18}{48}=\frac{20}{50}\)[/tex]
- Simplify [tex]\(\frac{18}{48}\)[/tex]: Both 18 and 48 are divisible by 6. So, [tex]\(\frac{18}{48} = \frac{3}{8}\)[/tex].
- Simplify [tex]\(\frac{20}{50}\)[/tex]: Both 20 and 50 are divisible by 10. So, [tex]\(\frac{20}{50} = \frac{2}{5}\)[/tex].
- The fractions [tex]\(\frac{3}{8}\)[/tex] and [tex]\(\frac{2}{5}\)[/tex] are not equivalent.
3. Third Proportion: [tex]\(\frac{24}{30}=\frac{20}{25}\)[/tex]
- Simplify [tex]\(\frac{24}{30}\)[/tex]: Both 24 and 30 are divisible by 6. So, [tex]\(\frac{24}{30} = \frac{4}{5}\)[/tex].
- Simplify [tex]\(\frac{20}{25}\)[/tex]: Both 20 and 25 are divisible by 5. So, [tex]\(\frac{20}{25} = \frac{4}{5}\)[/tex].
- Both fractions simplify to [tex]\(\frac{4}{5}\)[/tex], so they are equivalent.
4. Fourth Proportion: [tex]\(\frac{10}{25}=\frac{40}{100}\)[/tex]
- Simplify [tex]\(\frac{10}{25}\)[/tex]: Both 10 and 25 are divisible by 5. So, [tex]\(\frac{10}{25} = \frac{2}{5}\)[/tex].
- Simplify [tex]\(\frac{40}{100}\)[/tex]: Both 40 and 100 are divisible by 20. So, [tex]\(\frac{40}{100} = \frac{2}{5}\)[/tex].
- Both fractions simplify to [tex]\(\frac{2}{5}\)[/tex], so they are equivalent.
After checking each proportion, we find that the second proportion [tex]\(\frac{18}{48} = \frac{20}{50}\)[/tex] is not true. Therefore, this is the false proportion.
