Answer :
Let's examine each of the proportions to determine which one is false:
1. [tex]\(\frac{20}{50} = \frac{40}{100}\)[/tex]
2. [tex]\(\frac{12}{15} = \frac{20}{25}\)[/tex]
3. [tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex]
4. [tex]\(\frac{25}{45} = \frac{50}{90}\)[/tex]
### Checking the Proportions
1. [tex]\(\frac{20}{50} = \frac{40}{100}\)[/tex]
- Simplify both fractions:
- [tex]\(\frac{20}{50} = \frac{2}{5}\)[/tex]
- [tex]\(\frac{40}{100} = \frac{2}{5}\)[/tex]
- Both fractions are equal, so this proportion is true.
2. [tex]\(\frac{12}{15} = \frac{20}{25}\)[/tex]
- Simplify both fractions:
- [tex]\(\frac{12}{15} = \frac{4}{5}\)[/tex]
- [tex]\(\frac{20}{25} = \frac{4}{5}\)[/tex]
- Both fractions are equal, so this proportion is true.
3. [tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex]
- Simplify both fractions:
- [tex]\(\frac{18}{48} = \frac{3}{8}\)[/tex]
- [tex]\(\frac{30}{50} = \frac{3}{5}\)[/tex]
- [tex]\(\frac{3}{8}\)[/tex] is not equal to [tex]\(\frac{3}{5}\)[/tex], so this proportion is false.
4. [tex]\(\frac{25}{45} = \frac{50}{90}\)[/tex]
- Simplify both fractions:
- [tex]\(\frac{25}{45} = \frac{5}{9}\)[/tex]
- [tex]\(\frac{50}{90} = \frac{5}{9}\)[/tex]
- Both fractions are equal, so this proportion is true.
### Conclusion
The false proportion is:
[tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex]
So, the false proportion is the third one.
1. [tex]\(\frac{20}{50} = \frac{40}{100}\)[/tex]
2. [tex]\(\frac{12}{15} = \frac{20}{25}\)[/tex]
3. [tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex]
4. [tex]\(\frac{25}{45} = \frac{50}{90}\)[/tex]
### Checking the Proportions
1. [tex]\(\frac{20}{50} = \frac{40}{100}\)[/tex]
- Simplify both fractions:
- [tex]\(\frac{20}{50} = \frac{2}{5}\)[/tex]
- [tex]\(\frac{40}{100} = \frac{2}{5}\)[/tex]
- Both fractions are equal, so this proportion is true.
2. [tex]\(\frac{12}{15} = \frac{20}{25}\)[/tex]
- Simplify both fractions:
- [tex]\(\frac{12}{15} = \frac{4}{5}\)[/tex]
- [tex]\(\frac{20}{25} = \frac{4}{5}\)[/tex]
- Both fractions are equal, so this proportion is true.
3. [tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex]
- Simplify both fractions:
- [tex]\(\frac{18}{48} = \frac{3}{8}\)[/tex]
- [tex]\(\frac{30}{50} = \frac{3}{5}\)[/tex]
- [tex]\(\frac{3}{8}\)[/tex] is not equal to [tex]\(\frac{3}{5}\)[/tex], so this proportion is false.
4. [tex]\(\frac{25}{45} = \frac{50}{90}\)[/tex]
- Simplify both fractions:
- [tex]\(\frac{25}{45} = \frac{5}{9}\)[/tex]
- [tex]\(\frac{50}{90} = \frac{5}{9}\)[/tex]
- Both fractions are equal, so this proportion is true.
### Conclusion
The false proportion is:
[tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex]
So, the false proportion is the third one.
