Answer :
To determine which proportion is false, let's check each one step-by-step by comparing both sides of the equation.
1. Check the first proportion:
[tex]\[
\frac{25}{45} = \frac{50}{90}
\][/tex]
We can simplify both fractions:
- Simplifying [tex]\(\frac{25}{45}\)[/tex], we divide both the numerator and denominator by 5: [tex]\(\frac{25 \div 5}{45 \div 5} = \frac{5}{9}\)[/tex].
- Simplifying [tex]\(\frac{50}{90}\)[/tex], we divide both the numerator and denominator by 10: [tex]\(\frac{50 \div 10}{90 \div 10} = \frac{5}{9}\)[/tex].
Both fractions simplify to [tex]\(\frac{5}{9}\)[/tex], so this proportion is true.
2. Check the second proportion:
[tex]\[
\frac{12}{15} = \frac{20}{25}
\][/tex]
Simplify both fractions:
- Simplifying [tex]\(\frac{12}{15}\)[/tex], we divide both the numerator and denominator by 3: [tex]\(\frac{12 \div 3}{15 \div 3} = \frac{4}{5}\)[/tex].
- Simplifying [tex]\(\frac{20}{25}\)[/tex], we divide both the numerator and denominator by 5: [tex]\(\frac{20 \div 5}{25 \div 5} = \frac{4}{5}\)[/tex].
Both fractions simplify to [tex]\(\frac{4}{5}\)[/tex], so this proportion is true.
3. Check the third proportion:
[tex]\[
\frac{18}{48} = \frac{30}{50}
\][/tex]
Simplify both fractions:
- Simplifying [tex]\(\frac{18}{48}\)[/tex], we divide both the numerator and denominator by 6: [tex]\(\frac{18 \div 6}{48 \div 6} = \frac{3}{8}\)[/tex].
- Simplifying [tex]\(\frac{30}{50}\)[/tex], we divide both the numerator and denominator by 10: [tex]\(\frac{30 \div 10}{50 \div 10} = \frac{3}{5}\)[/tex].
The fractions simplify to [tex]\(\frac{3}{8}\)[/tex] and [tex]\(\frac{3}{5}\)[/tex] respectively, which are not equal. Therefore, this proportion is false.
4. Check the fourth proportion:
[tex]\[
\frac{20}{50} = \frac{40}{100}
\][/tex]
Simplify both fractions:
- Simplifying [tex]\(\frac{20}{50}\)[/tex], we divide both the numerator and denominator by 10: [tex]\(\frac{20 \div 10}{50 \div 10} = \frac{2}{5}\)[/tex].
- Simplifying [tex]\(\frac{40}{100}\)[/tex], we divide both the numerator and denominator by 20: [tex]\(\frac{40 \div 20}{100 \div 20} = \frac{2}{5}\)[/tex].
Both fractions simplify to [tex]\(\frac{2}{5}\)[/tex], so this proportion is true.
Therefore, the false proportion is the third one: [tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex].
1. Check the first proportion:
[tex]\[
\frac{25}{45} = \frac{50}{90}
\][/tex]
We can simplify both fractions:
- Simplifying [tex]\(\frac{25}{45}\)[/tex], we divide both the numerator and denominator by 5: [tex]\(\frac{25 \div 5}{45 \div 5} = \frac{5}{9}\)[/tex].
- Simplifying [tex]\(\frac{50}{90}\)[/tex], we divide both the numerator and denominator by 10: [tex]\(\frac{50 \div 10}{90 \div 10} = \frac{5}{9}\)[/tex].
Both fractions simplify to [tex]\(\frac{5}{9}\)[/tex], so this proportion is true.
2. Check the second proportion:
[tex]\[
\frac{12}{15} = \frac{20}{25}
\][/tex]
Simplify both fractions:
- Simplifying [tex]\(\frac{12}{15}\)[/tex], we divide both the numerator and denominator by 3: [tex]\(\frac{12 \div 3}{15 \div 3} = \frac{4}{5}\)[/tex].
- Simplifying [tex]\(\frac{20}{25}\)[/tex], we divide both the numerator and denominator by 5: [tex]\(\frac{20 \div 5}{25 \div 5} = \frac{4}{5}\)[/tex].
Both fractions simplify to [tex]\(\frac{4}{5}\)[/tex], so this proportion is true.
3. Check the third proportion:
[tex]\[
\frac{18}{48} = \frac{30}{50}
\][/tex]
Simplify both fractions:
- Simplifying [tex]\(\frac{18}{48}\)[/tex], we divide both the numerator and denominator by 6: [tex]\(\frac{18 \div 6}{48 \div 6} = \frac{3}{8}\)[/tex].
- Simplifying [tex]\(\frac{30}{50}\)[/tex], we divide both the numerator and denominator by 10: [tex]\(\frac{30 \div 10}{50 \div 10} = \frac{3}{5}\)[/tex].
The fractions simplify to [tex]\(\frac{3}{8}\)[/tex] and [tex]\(\frac{3}{5}\)[/tex] respectively, which are not equal. Therefore, this proportion is false.
4. Check the fourth proportion:
[tex]\[
\frac{20}{50} = \frac{40}{100}
\][/tex]
Simplify both fractions:
- Simplifying [tex]\(\frac{20}{50}\)[/tex], we divide both the numerator and denominator by 10: [tex]\(\frac{20 \div 10}{50 \div 10} = \frac{2}{5}\)[/tex].
- Simplifying [tex]\(\frac{40}{100}\)[/tex], we divide both the numerator and denominator by 20: [tex]\(\frac{40 \div 20}{100 \div 20} = \frac{2}{5}\)[/tex].
Both fractions simplify to [tex]\(\frac{2}{5}\)[/tex], so this proportion is true.
Therefore, the false proportion is the third one: [tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex].
