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Answer :
To solve the problem, we need to determine which proportion among the provided options is false. Let's check each proportion one by one:
1. Proportion 1: [tex]\(\frac{25}{45} = \frac{50}{90}\)[/tex]
To check if these fractions are equal, we can simplify both to their lowest terms:
- [tex]\(\frac{25}{45}\)[/tex] can be simplified by dividing both the numerator and the denominator by 5, resulting in [tex]\(\frac{5}{9}\)[/tex].
- [tex]\(\frac{50}{90}\)[/tex] can also be simplified by dividing both the numerator and the denominator by 10, resulting in [tex]\(\frac{5}{9}\)[/tex].
Since both fractions simplify to [tex]\(\frac{5}{9}\)[/tex], they are equal.
2. Proportion 2: [tex]\(\frac{20}{50} = \frac{40}{100}\)[/tex]
Simplifying both fractions:
- [tex]\(\frac{20}{50}\)[/tex] can be simplified by dividing both the numerator and the denominator by 10, resulting in [tex]\(\frac{2}{5}\)[/tex].
- [tex]\(\frac{40}{100}\)[/tex] can be simplified by dividing both the numerator and the denominator by 20, resulting in [tex]\(\frac{2}{5}\)[/tex].
Since both fractions simplify to [tex]\(\frac{2}{5}\)[/tex], they are equal.
3. Proportion 3: [tex]\(\frac{12}{15} = \frac{20}{25}\)[/tex]
Simplifying both fractions:
- [tex]\(\frac{12}{15}\)[/tex] can be simplified by dividing both the numerator and the denominator by 3, resulting in [tex]\(\frac{4}{5}\)[/tex].
- [tex]\(\frac{20}{25}\)[/tex] can be simplified by dividing both the numerator and the denominator by 5, resulting in [tex]\(\frac{4}{5}\)[/tex].
Since both fractions simplify to [tex]\(\frac{4}{5}\)[/tex], they are equal.
4. Proportion 4: [tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex]
Simplifying both fractions:
- [tex]\(\frac{18}{48}\)[/tex] can be simplified by dividing both the numerator and the denominator by 6, resulting in [tex]\(\frac{3}{8}\)[/tex].
- [tex]\(\frac{30}{50}\)[/tex] can be simplified by dividing both the numerator and the denominator by 10, resulting in [tex]\(\frac{3}{5}\)[/tex].
Since [tex]\(\frac{3}{8}\)[/tex] and [tex]\(\frac{3}{5}\)[/tex] do not simplify to the same fraction, they are not equal.
Thus, Proportion 4, [tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex], is the false proportion.
1. Proportion 1: [tex]\(\frac{25}{45} = \frac{50}{90}\)[/tex]
To check if these fractions are equal, we can simplify both to their lowest terms:
- [tex]\(\frac{25}{45}\)[/tex] can be simplified by dividing both the numerator and the denominator by 5, resulting in [tex]\(\frac{5}{9}\)[/tex].
- [tex]\(\frac{50}{90}\)[/tex] can also be simplified by dividing both the numerator and the denominator by 10, resulting in [tex]\(\frac{5}{9}\)[/tex].
Since both fractions simplify to [tex]\(\frac{5}{9}\)[/tex], they are equal.
2. Proportion 2: [tex]\(\frac{20}{50} = \frac{40}{100}\)[/tex]
Simplifying both fractions:
- [tex]\(\frac{20}{50}\)[/tex] can be simplified by dividing both the numerator and the denominator by 10, resulting in [tex]\(\frac{2}{5}\)[/tex].
- [tex]\(\frac{40}{100}\)[/tex] can be simplified by dividing both the numerator and the denominator by 20, resulting in [tex]\(\frac{2}{5}\)[/tex].
Since both fractions simplify to [tex]\(\frac{2}{5}\)[/tex], they are equal.
3. Proportion 3: [tex]\(\frac{12}{15} = \frac{20}{25}\)[/tex]
Simplifying both fractions:
- [tex]\(\frac{12}{15}\)[/tex] can be simplified by dividing both the numerator and the denominator by 3, resulting in [tex]\(\frac{4}{5}\)[/tex].
- [tex]\(\frac{20}{25}\)[/tex] can be simplified by dividing both the numerator and the denominator by 5, resulting in [tex]\(\frac{4}{5}\)[/tex].
Since both fractions simplify to [tex]\(\frac{4}{5}\)[/tex], they are equal.
4. Proportion 4: [tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex]
Simplifying both fractions:
- [tex]\(\frac{18}{48}\)[/tex] can be simplified by dividing both the numerator and the denominator by 6, resulting in [tex]\(\frac{3}{8}\)[/tex].
- [tex]\(\frac{30}{50}\)[/tex] can be simplified by dividing both the numerator and the denominator by 10, resulting in [tex]\(\frac{3}{5}\)[/tex].
Since [tex]\(\frac{3}{8}\)[/tex] and [tex]\(\frac{3}{5}\)[/tex] do not simplify to the same fraction, they are not equal.
Thus, Proportion 4, [tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex], is the false proportion.
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