Answer :
To determine which proportion is false, we need to check if each pair of fractions is equal. Let's simplify each fraction and compare them step-by-step.
1. Proportion 1: [tex]\(\frac{20}{50} = \frac{40}{100}\)[/tex]
- Simplifying [tex]\(\frac{20}{50}\)[/tex]: Divide both the numerator and the denominator by 10.
[tex]\[
\frac{20}{50} = \frac{2}{5}
\][/tex]
- Simplifying [tex]\(\frac{40}{100}\)[/tex]: Divide both the numerator and the denominator by 20.
[tex]\[
\frac{40}{100} = \frac{2}{5}
\][/tex]
- The fractions are equal: [tex]\(\frac{20}{50} = \frac{40}{100}\)[/tex].
2. Proportion 2: [tex]\(\frac{25}{45} = \frac{50}{90}\)[/tex]
- Simplifying [tex]\(\frac{25}{45}\)[/tex]: Divide both the numerator and the denominator by 5.
[tex]\[
\frac{25}{45} = \frac{5}{9}
\][/tex]
- Simplifying [tex]\(\frac{50}{90}\)[/tex]: Divide both the numerator and the denominator by 10.
[tex]\[
\frac{50}{90} = \frac{5}{9}
\][/tex]
- The fractions are equal: [tex]\(\frac{25}{45} = \frac{50}{90}\)[/tex].
3. Proportion 3: [tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex]
- Simplifying [tex]\(\frac{18}{48}\)[/tex]: Divide both the numerator and the denominator by 6.
[tex]\[
\frac{18}{48} = \frac{3}{8}
\][/tex]
- Simplifying [tex]\(\frac{30}{50}\)[/tex]: Divide both the numerator and the denominator by 10.
[tex]\[
\frac{30}{50} = \frac{3}{5}
\][/tex]
- The fractions are not equal: [tex]\(\frac{18}{48} \neq \frac{30}{50}\)[/tex].
4. Proportion 4: [tex]\(\frac{12}{15} = \frac{20}{25}\)[/tex]
- Simplifying [tex]\(\frac{12}{15}\)[/tex]: Divide both the numerator and the denominator by 3.
[tex]\[
\frac{12}{15} = \frac{4}{5}
\][/tex]
- Simplifying [tex]\(\frac{20}{25}\)[/tex]: Divide both the numerator and the denominator by 5.
[tex]\[
\frac{20}{25} = \frac{4}{5}
\][/tex]
- The fractions are equal: [tex]\(\frac{12}{15} = \frac{20}{25}\)[/tex].
After simplifying and comparing all the given proportions, we find that the third proportion, [tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex], is false. Therefore, the false proportion is option 3.
1. Proportion 1: [tex]\(\frac{20}{50} = \frac{40}{100}\)[/tex]
- Simplifying [tex]\(\frac{20}{50}\)[/tex]: Divide both the numerator and the denominator by 10.
[tex]\[
\frac{20}{50} = \frac{2}{5}
\][/tex]
- Simplifying [tex]\(\frac{40}{100}\)[/tex]: Divide both the numerator and the denominator by 20.
[tex]\[
\frac{40}{100} = \frac{2}{5}
\][/tex]
- The fractions are equal: [tex]\(\frac{20}{50} = \frac{40}{100}\)[/tex].
2. Proportion 2: [tex]\(\frac{25}{45} = \frac{50}{90}\)[/tex]
- Simplifying [tex]\(\frac{25}{45}\)[/tex]: Divide both the numerator and the denominator by 5.
[tex]\[
\frac{25}{45} = \frac{5}{9}
\][/tex]
- Simplifying [tex]\(\frac{50}{90}\)[/tex]: Divide both the numerator and the denominator by 10.
[tex]\[
\frac{50}{90} = \frac{5}{9}
\][/tex]
- The fractions are equal: [tex]\(\frac{25}{45} = \frac{50}{90}\)[/tex].
3. Proportion 3: [tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex]
- Simplifying [tex]\(\frac{18}{48}\)[/tex]: Divide both the numerator and the denominator by 6.
[tex]\[
\frac{18}{48} = \frac{3}{8}
\][/tex]
- Simplifying [tex]\(\frac{30}{50}\)[/tex]: Divide both the numerator and the denominator by 10.
[tex]\[
\frac{30}{50} = \frac{3}{5}
\][/tex]
- The fractions are not equal: [tex]\(\frac{18}{48} \neq \frac{30}{50}\)[/tex].
4. Proportion 4: [tex]\(\frac{12}{15} = \frac{20}{25}\)[/tex]
- Simplifying [tex]\(\frac{12}{15}\)[/tex]: Divide both the numerator and the denominator by 3.
[tex]\[
\frac{12}{15} = \frac{4}{5}
\][/tex]
- Simplifying [tex]\(\frac{20}{25}\)[/tex]: Divide both the numerator and the denominator by 5.
[tex]\[
\frac{20}{25} = \frac{4}{5}
\][/tex]
- The fractions are equal: [tex]\(\frac{12}{15} = \frac{20}{25}\)[/tex].
After simplifying and comparing all the given proportions, we find that the third proportion, [tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex], is false. Therefore, the false proportion is option 3.
