To determine which proportion is false, we need to compare each set of fractions step-by-step.
1. Check the first proportion:
[tex]\[
\frac{18}{48} \quad \text{and} \quad \frac{30}{50}
\][/tex]
To compare these, we simplify each fraction:
- Simplifying [tex]\(\frac{18}{48}\)[/tex]:
[tex]\[
\frac{18}{48} = \frac{18 \div 6}{48 \div 6} = \frac{3}{8}
\][/tex]
- Simplifying [tex]\(\frac{30}{50}\)[/tex]:
[tex]\[
\frac{30}{50} = \frac{30 \div 10}{50 \div 10} = \frac{3}{5}
\][/tex]
Since [tex]\(\frac{3}{8} \neq \frac{3}{5}\)[/tex], the first proportion is false.
2. Check the second proportion:
[tex]\[
\frac{12}{15} \quad \text{and} \quad \frac{20}{25}
\][/tex]
- Simplifying [tex]\(\frac{12}{15}\)[/tex]:
[tex]\[
\frac{12}{15} = \frac{12 \div 3}{15 \div 3} = \frac{4}{5}
\][/tex]
- Simplifying [tex]\(\frac{20}{25}\)[/tex]:
[tex]\[
\frac{20}{25} = \frac{20 \div 5}{25 \div 5} = \frac{4}{5}
\][/tex]
Since [tex]\(\frac{4}{5} = \frac{4}{5}\)[/tex], the second proportion is true.
3. Check the third proportion:
[tex]\[
\frac{25}{45} \quad \text{and} \quad \frac{50}{90}
\][/tex]
- Simplifying [tex]\(\frac{25}{45}\)[/tex]:
[tex]\[
\frac{25}{45} = \frac{25 \div 5}{45 \div 5} = \frac{5}{9}
\][/tex]
- Simplifying [tex]\(\frac{50}{90}\)[/tex]:
[tex]\[
\frac{50}{90} = \frac{50 \div 10}{90 \div 10} = \frac{5}{9}
\][/tex]
Since [tex]\(\frac{5}{9} = \frac{5}{9}\)[/tex], the third proportion is true.
4. Check the fourth proportion:
[tex]\[
\frac{20}{50} \quad \text{and} \quad \frac{40}{100}
\][/tex]
- Simplifying [tex]\(\frac{20}{50}\)[/tex]:
[tex]\[
\frac{20}{50} = \frac{20 \div 10}{50 \div 10} = \frac{2}{5}
\][/tex]
- Simplifying [tex]\(\frac{40}{100}\)[/tex]:
[tex]\[
\frac{40}{100} = \frac{40 \div 20}{100 \div 20} = \frac{2}{5}
\][/tex]
Since [tex]\(\frac{2}{5} = \frac{2}{5}\)[/tex], the fourth proportion is true.
Having analyzed each proportion, it turns out that the first proportion:
[tex]\[
\frac{18}{48} \neq \frac{30}{50}
\][/tex]
is false.
Thus, the false proportion is the first one.
