Answer :
To figure out which proportion is false, we need to check if the two fractions in each pair are equivalent. A quick way to do this is by cross-multiplying the fractions and comparing the results for equality. Let's evaluate each pair step by step:
1. First Pair: [tex]\(\frac{25}{45} = \frac{50}{90}\)[/tex]
- Cross-multiply: [tex]\(25 \times 90 = 2250\)[/tex] and [tex]\(45 \times 50 = 2250\)[/tex]
- The results are equal, so this proportion is true.
2. Second Pair: [tex]\(\frac{20}{50} = \frac{40}{100}\)[/tex]
- Cross-multiply: [tex]\(20 \times 100 = 2000\)[/tex] and [tex]\(50 \times 40 = 2000\)[/tex]
- The results are equal, so this proportion is true.
3. Third Pair: [tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex]
- Cross-multiply: [tex]\(18 \times 50 = 900\)[/tex] and [tex]\(48 \times 30 = 1440\)[/tex]
- The results are not equal, so this proportion is false.
4. Fourth Pair: [tex]\(\frac{12}{15} = \frac{20}{25}\)[/tex]
- Cross-multiply: [tex]\(12 \times 25 = 300\)[/tex] and [tex]\(15 \times 20 = 300\)[/tex]
- The results are equal, so this proportion is true.
After checking each pair, we find that the third proportion, [tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex], is false. The cross-multiplication results are not equal, indicating that these fractions are not equivalent.
1. First Pair: [tex]\(\frac{25}{45} = \frac{50}{90}\)[/tex]
- Cross-multiply: [tex]\(25 \times 90 = 2250\)[/tex] and [tex]\(45 \times 50 = 2250\)[/tex]
- The results are equal, so this proportion is true.
2. Second Pair: [tex]\(\frac{20}{50} = \frac{40}{100}\)[/tex]
- Cross-multiply: [tex]\(20 \times 100 = 2000\)[/tex] and [tex]\(50 \times 40 = 2000\)[/tex]
- The results are equal, so this proportion is true.
3. Third Pair: [tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex]
- Cross-multiply: [tex]\(18 \times 50 = 900\)[/tex] and [tex]\(48 \times 30 = 1440\)[/tex]
- The results are not equal, so this proportion is false.
4. Fourth Pair: [tex]\(\frac{12}{15} = \frac{20}{25}\)[/tex]
- Cross-multiply: [tex]\(12 \times 25 = 300\)[/tex] and [tex]\(15 \times 20 = 300\)[/tex]
- The results are equal, so this proportion is true.
After checking each pair, we find that the third proportion, [tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex], is false. The cross-multiplication results are not equal, indicating that these fractions are not equivalent.
