Which of the following proportions is false?

A. [tex]\(\frac{10}{25}=\frac{40}{100}\)[/tex]

B. [tex]\(\frac{18}{48}=\frac{20}{50}\)[/tex]

C. [tex]\(\frac{25}{45}=\frac{75}{135}\)[/tex]

D. [tex]\(\frac{24}{30}=\frac{20}{25}\)[/tex]

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.