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Answer :
To determine which of the given proportions is false, let's evaluate each one step-by-step by checking if the fractions are equal:
1. Proportion 1:
[tex]\(\frac{25}{45} = \frac{50}{90}\)[/tex]
To check if these fractions are equal, we simplify both:
- Simplifying [tex]\(\frac{25}{45}\)[/tex]:
[tex]\[
\frac{25}{45} = \frac{5 \times 5}{5 \times 9} = \frac{5}{9}
\][/tex]
- Simplifying [tex]\(\frac{50}{90}\)[/tex]:
[tex]\[
\frac{50}{90} = \frac{5 \times 10}{9 \times 10} = \frac{5}{9}
\][/tex]
Both fractions simplify to [tex]\(\frac{5}{9}\)[/tex], so they are equal.
2. Proportion 2:
[tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex]
To check if these fractions are equal, we simplify both:
- Simplifying [tex]\(\frac{18}{48}\)[/tex]:
[tex]\[
\frac{18}{48} = \frac{6 \times 3}{6 \times 8} = \frac{3}{8}
\][/tex]
- Simplifying [tex]\(\frac{30}{50}\)[/tex]:
[tex]\[
\frac{30}{50} = \frac{10 \times 3}{10 \times 5} = \frac{3}{5}
\][/tex]
These fractions do not simplify to the same value ([tex]\(\frac{3}{8} \neq \frac{3}{5}\)[/tex]), so this proportion is false.
3. Proportion 3:
[tex]\(\frac{12}{15} = \frac{20}{25}\)[/tex]
To check if these fractions are equal, we simplify both:
- Simplifying [tex]\(\frac{12}{15}\)[/tex]:
[tex]\[
\frac{12}{15} = \frac{3 \times 4}{3 \times 5} = \frac{4}{5}
\][/tex]
- Simplifying [tex]\(\frac{20}{25}\)[/tex]:
[tex]\[
\frac{20}{25} = \frac{5 \times 4}{5 \times 5} = \frac{4}{5}
\][/tex]
Both fractions simplify to [tex]\(\frac{4}{5}\)[/tex], so they are equal.
4. Proportion 4:
[tex]\(\frac{20}{50} = \frac{40}{100}\)[/tex]
To check if these fractions are equal, we simplify both:
- Simplifying [tex]\(\frac{20}{50}\)[/tex]:
[tex]\[
\frac{20}{50} = \frac{10 \times 2}{10 \times 5} = \frac{2}{5}
\][/tex]
- Simplifying [tex]\(\frac{40}{100}\)[/tex]:
[tex]\[
\frac{40}{100} = \frac{20 \times 2}{20 \times 5} = \frac{2}{5}
\][/tex]
Both fractions simplify to [tex]\(\frac{2}{5}\)[/tex], so they are equal.
Therefore, the false proportion is [tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex].
1. Proportion 1:
[tex]\(\frac{25}{45} = \frac{50}{90}\)[/tex]
To check if these fractions are equal, we simplify both:
- Simplifying [tex]\(\frac{25}{45}\)[/tex]:
[tex]\[
\frac{25}{45} = \frac{5 \times 5}{5 \times 9} = \frac{5}{9}
\][/tex]
- Simplifying [tex]\(\frac{50}{90}\)[/tex]:
[tex]\[
\frac{50}{90} = \frac{5 \times 10}{9 \times 10} = \frac{5}{9}
\][/tex]
Both fractions simplify to [tex]\(\frac{5}{9}\)[/tex], so they are equal.
2. Proportion 2:
[tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex]
To check if these fractions are equal, we simplify both:
- Simplifying [tex]\(\frac{18}{48}\)[/tex]:
[tex]\[
\frac{18}{48} = \frac{6 \times 3}{6 \times 8} = \frac{3}{8}
\][/tex]
- Simplifying [tex]\(\frac{30}{50}\)[/tex]:
[tex]\[
\frac{30}{50} = \frac{10 \times 3}{10 \times 5} = \frac{3}{5}
\][/tex]
These fractions do not simplify to the same value ([tex]\(\frac{3}{8} \neq \frac{3}{5}\)[/tex]), so this proportion is false.
3. Proportion 3:
[tex]\(\frac{12}{15} = \frac{20}{25}\)[/tex]
To check if these fractions are equal, we simplify both:
- Simplifying [tex]\(\frac{12}{15}\)[/tex]:
[tex]\[
\frac{12}{15} = \frac{3 \times 4}{3 \times 5} = \frac{4}{5}
\][/tex]
- Simplifying [tex]\(\frac{20}{25}\)[/tex]:
[tex]\[
\frac{20}{25} = \frac{5 \times 4}{5 \times 5} = \frac{4}{5}
\][/tex]
Both fractions simplify to [tex]\(\frac{4}{5}\)[/tex], so they are equal.
4. Proportion 4:
[tex]\(\frac{20}{50} = \frac{40}{100}\)[/tex]
To check if these fractions are equal, we simplify both:
- Simplifying [tex]\(\frac{20}{50}\)[/tex]:
[tex]\[
\frac{20}{50} = \frac{10 \times 2}{10 \times 5} = \frac{2}{5}
\][/tex]
- Simplifying [tex]\(\frac{40}{100}\)[/tex]:
[tex]\[
\frac{40}{100} = \frac{20 \times 2}{20 \times 5} = \frac{2}{5}
\][/tex]
Both fractions simplify to [tex]\(\frac{2}{5}\)[/tex], so they are equal.
Therefore, the false proportion is [tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex].
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