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Answer :
To determine which proportion is false, we can use the method of cross-multiplication. This involves multiplying the numerator of one fraction by the denominator of the other fraction and comparing the products to see if they are equal. Let's go through each proportion one by one:
1. [tex]\(\frac{12}{15} = \frac{20}{25}\)[/tex]
- Cross-multiply: [tex]\(12 \times 25 = 300\)[/tex] and [tex]\(15 \times 20 = 300\)[/tex]
- Both products are equal, so this proportion is true.
2. [tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex]
- Cross-multiply: [tex]\(18 \times 50 = 900\)[/tex] and [tex]\(48 \times 30 = 1440\)[/tex]
- The products are not equal (900 ≠ 1440), so this proportion is false.
3. [tex]\(\frac{25}{45} = \frac{50}{90}\)[/tex]
- Cross-multiply: [tex]\(25 \times 90 = 2250\)[/tex] and [tex]\(45 \times 50 = 2250\)[/tex]
- Both products are equal, so this proportion is true.
4. [tex]\(\frac{20}{50} = \frac{40}{100}\)[/tex]
- Cross-multiply: [tex]\(20 \times 100 = 2000\)[/tex] and [tex]\(50 \times 40 = 2000\)[/tex]
- Both products are equal, so this proportion is true.
Based on the cross-multiplication method, the proportion [tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex] is false.
1. [tex]\(\frac{12}{15} = \frac{20}{25}\)[/tex]
- Cross-multiply: [tex]\(12 \times 25 = 300\)[/tex] and [tex]\(15 \times 20 = 300\)[/tex]
- Both products are equal, so this proportion is true.
2. [tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex]
- Cross-multiply: [tex]\(18 \times 50 = 900\)[/tex] and [tex]\(48 \times 30 = 1440\)[/tex]
- The products are not equal (900 ≠ 1440), so this proportion is false.
3. [tex]\(\frac{25}{45} = \frac{50}{90}\)[/tex]
- Cross-multiply: [tex]\(25 \times 90 = 2250\)[/tex] and [tex]\(45 \times 50 = 2250\)[/tex]
- Both products are equal, so this proportion is true.
4. [tex]\(\frac{20}{50} = \frac{40}{100}\)[/tex]
- Cross-multiply: [tex]\(20 \times 100 = 2000\)[/tex] and [tex]\(50 \times 40 = 2000\)[/tex]
- Both products are equal, so this proportion is true.
Based on the cross-multiplication method, the proportion [tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex] is false.
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