Answer :
To determine which of the given proportions is false, we'll check each pair of fractions to see if they are equivalent.
1. First proportion: [tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex]
To check if the fractions are equal, we can cross-multiply:
[tex]\[ 18 \times 50 = 900 \][/tex]
[tex]\[ 48 \times 30 = 1440 \][/tex]
Since [tex]\(900 \neq 1440\)[/tex], [tex]\(\frac{18}{48}\)[/tex] is not equal to [tex]\(\frac{30}{50}\)[/tex].
2. Second proportion: [tex]\(\frac{20}{50} = \frac{40}{100}\)[/tex]
Again, using cross-multiplication:
[tex]\[ 20 \times 100 = 2000 \][/tex]
[tex]\[ 50 \times 40 = 2000 \][/tex]
Since [tex]\(2000 = 2000\)[/tex], [tex]\(\frac{20}{50}\)[/tex] is equal to [tex]\(\frac{40}{100}\)[/tex].
3. Third proportion: [tex]\(\frac{12}{15} = \frac{20}{25}\)[/tex]
Checking by cross-multiplying:
[tex]\[ 12 \times 25 = 300 \][/tex]
[tex]\[ 15 \times 20 = 300 \][/tex]
Since [tex]\(300 = 300\)[/tex], [tex]\(\frac{12}{15}\)[/tex] is equal to [tex]\(\frac{20}{25}\)[/tex].
4. Fourth proportion: [tex]\(\frac{25}{45} = \frac{50}{90}\)[/tex]
And again, using cross-multiplication:
[tex]\[ 25 \times 90 = 2250 \][/tex]
[tex]\[ 45 \times 50 = 2250 \][/tex]
Since [tex]\(2250 = 2250\)[/tex], [tex]\(\frac{25}{45}\)[/tex] is equal to [tex]\(\frac{50}{90}\)[/tex].
Based on this analysis, the first proportion, [tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex], is false. Consequently, the correct answer is the first option.
1. First proportion: [tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex]
To check if the fractions are equal, we can cross-multiply:
[tex]\[ 18 \times 50 = 900 \][/tex]
[tex]\[ 48 \times 30 = 1440 \][/tex]
Since [tex]\(900 \neq 1440\)[/tex], [tex]\(\frac{18}{48}\)[/tex] is not equal to [tex]\(\frac{30}{50}\)[/tex].
2. Second proportion: [tex]\(\frac{20}{50} = \frac{40}{100}\)[/tex]
Again, using cross-multiplication:
[tex]\[ 20 \times 100 = 2000 \][/tex]
[tex]\[ 50 \times 40 = 2000 \][/tex]
Since [tex]\(2000 = 2000\)[/tex], [tex]\(\frac{20}{50}\)[/tex] is equal to [tex]\(\frac{40}{100}\)[/tex].
3. Third proportion: [tex]\(\frac{12}{15} = \frac{20}{25}\)[/tex]
Checking by cross-multiplying:
[tex]\[ 12 \times 25 = 300 \][/tex]
[tex]\[ 15 \times 20 = 300 \][/tex]
Since [tex]\(300 = 300\)[/tex], [tex]\(\frac{12}{15}\)[/tex] is equal to [tex]\(\frac{20}{25}\)[/tex].
4. Fourth proportion: [tex]\(\frac{25}{45} = \frac{50}{90}\)[/tex]
And again, using cross-multiplication:
[tex]\[ 25 \times 90 = 2250 \][/tex]
[tex]\[ 45 \times 50 = 2250 \][/tex]
Since [tex]\(2250 = 2250\)[/tex], [tex]\(\frac{25}{45}\)[/tex] is equal to [tex]\(\frac{50}{90}\)[/tex].
Based on this analysis, the first proportion, [tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex], is false. Consequently, the correct answer is the first option.
