Answer :
To determine which proportion is false, we can check each proportion by comparing the two fractions for equality. This can be simply done by cross-multiplying the terms of each proportion and comparing the products.
1. Proportion: [tex]\(\frac{12}{15} = \frac{20}{25}\)[/tex]
- Cross-multiply: [tex]\(12 \times 25\)[/tex] and [tex]\(15 \times 20\)[/tex].
- Calculate the products: [tex]\(12 \times 25 = 300\)[/tex] and [tex]\(15 \times 20 = 300\)[/tex].
- Since both products are equal, this proportion is true.
2. Proportion: [tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex]
- Cross-multiply: [tex]\(18 \times 50\)[/tex] and [tex]\(48 \times 30\)[/tex].
- Calculate the products: [tex]\(18 \times 50 = 900\)[/tex] and [tex]\(48 \times 30 = 1440\)[/tex].
- Since the products are not equal, this proportion is false.
3. Proportion: [tex]\(\frac{25}{45} = \frac{50}{90}\)[/tex]
- Cross-multiply: [tex]\(25 \times 90\)[/tex] and [tex]\(45 \times 50\)[/tex].
- Calculate the products: [tex]\(25 \times 90 = 2250\)[/tex] and [tex]\(45 \times 50 = 2250\)[/tex].
- Since both products are equal, this proportion is true.
4. Proportion: [tex]\(\frac{20}{50} = \frac{40}{100}\)[/tex]
- Cross-multiply: [tex]\(20 \times 100\)[/tex] and [tex]\(50 \times 40\)[/tex].
- Calculate the products: [tex]\(20 \times 100 = 2000\)[/tex] and [tex]\(50 \times 40 = 2000\)[/tex].
- Since both products are equal, this proportion is true.
After examining all proportions, we find that only the second proportion, [tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex], is false.
1. Proportion: [tex]\(\frac{12}{15} = \frac{20}{25}\)[/tex]
- Cross-multiply: [tex]\(12 \times 25\)[/tex] and [tex]\(15 \times 20\)[/tex].
- Calculate the products: [tex]\(12 \times 25 = 300\)[/tex] and [tex]\(15 \times 20 = 300\)[/tex].
- Since both products are equal, this proportion is true.
2. Proportion: [tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex]
- Cross-multiply: [tex]\(18 \times 50\)[/tex] and [tex]\(48 \times 30\)[/tex].
- Calculate the products: [tex]\(18 \times 50 = 900\)[/tex] and [tex]\(48 \times 30 = 1440\)[/tex].
- Since the products are not equal, this proportion is false.
3. Proportion: [tex]\(\frac{25}{45} = \frac{50}{90}\)[/tex]
- Cross-multiply: [tex]\(25 \times 90\)[/tex] and [tex]\(45 \times 50\)[/tex].
- Calculate the products: [tex]\(25 \times 90 = 2250\)[/tex] and [tex]\(45 \times 50 = 2250\)[/tex].
- Since both products are equal, this proportion is true.
4. Proportion: [tex]\(\frac{20}{50} = \frac{40}{100}\)[/tex]
- Cross-multiply: [tex]\(20 \times 100\)[/tex] and [tex]\(50 \times 40\)[/tex].
- Calculate the products: [tex]\(20 \times 100 = 2000\)[/tex] and [tex]\(50 \times 40 = 2000\)[/tex].
- Since both products are equal, this proportion is true.
After examining all proportions, we find that only the second proportion, [tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex], is false.
