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Answer :
To determine which proportion is false, we can check each pair using the concept of cross multiplication. Two ratios [tex]\(\frac{a}{b}\)[/tex] and [tex]\(\frac{c}{d}\)[/tex] are equivalent if the cross products are equal, which means [tex]\(a \times d\)[/tex] should equal [tex]\(b \times c\)[/tex].
Let's check each proportion:
1. First Proportion: [tex]\(\frac{20}{50} = \frac{40}{100}\)[/tex]
Calculate the cross products:
- [tex]\(20 \times 100 = 2000\)[/tex]
- [tex]\(50 \times 40 = 2000\)[/tex]
Since both cross products are equal, this proportion is true.
2. Second Proportion: [tex]\(\frac{25}{45} = \frac{50}{90}\)[/tex]
Calculate the cross products:
- [tex]\(25 \times 90 = 2250\)[/tex]
- [tex]\(45 \times 50 = 2250\)[/tex]
Since both cross products are equal, this proportion is true.
3. Third Proportion: [tex]\(\frac{12}{15} = \frac{20}{25}\)[/tex]
Calculate the cross products:
- [tex]\(12 \times 25 = 300\)[/tex]
- [tex]\(15 \times 20 = 300\)[/tex]
Since both cross products are equal, this proportion is true.
4. Fourth Proportion: [tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex]
Calculate the cross products:
- [tex]\(18 \times 50 = 900\)[/tex]
- [tex]\(48 \times 30 = 1440\)[/tex]
Since the cross products are not equal, this proportion is false.
Therefore, the false proportion is [tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex].
Let's check each proportion:
1. First Proportion: [tex]\(\frac{20}{50} = \frac{40}{100}\)[/tex]
Calculate the cross products:
- [tex]\(20 \times 100 = 2000\)[/tex]
- [tex]\(50 \times 40 = 2000\)[/tex]
Since both cross products are equal, this proportion is true.
2. Second Proportion: [tex]\(\frac{25}{45} = \frac{50}{90}\)[/tex]
Calculate the cross products:
- [tex]\(25 \times 90 = 2250\)[/tex]
- [tex]\(45 \times 50 = 2250\)[/tex]
Since both cross products are equal, this proportion is true.
3. Third Proportion: [tex]\(\frac{12}{15} = \frac{20}{25}\)[/tex]
Calculate the cross products:
- [tex]\(12 \times 25 = 300\)[/tex]
- [tex]\(15 \times 20 = 300\)[/tex]
Since both cross products are equal, this proportion is true.
4. Fourth Proportion: [tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex]
Calculate the cross products:
- [tex]\(18 \times 50 = 900\)[/tex]
- [tex]\(48 \times 30 = 1440\)[/tex]
Since the cross products are not equal, this proportion is false.
Therefore, the false proportion is [tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex].
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