Answer :
To determine which proportion is false, we will examine each pair of fractions to see if they are equivalent. We can check the equivalence of two fractions by cross-multiplying. If the cross-products are equal, then the fractions are equivalent.
Let's check each proportion one by one:
1. Proportion: [tex]\(\frac{25}{45} = \frac{50}{90}\)[/tex]
- Cross-multiply: [tex]\(25 \times 90\)[/tex] and [tex]\(50 \times 45\)[/tex]
- Calculate:
- [tex]\(25 \times 90 = 2250\)[/tex]
- [tex]\(50 \times 45 = 2250\)[/tex]
- The cross-products are equal, so these fractions are equivalent.
2. Proportion: [tex]\(\frac{20}{50} = \frac{40}{100}\)[/tex]
- Cross-multiply: [tex]\(20 \times 100\)[/tex] and [tex]\(40 \times 50\)[/tex]
- Calculate:
- [tex]\(20 \times 100 = 2000\)[/tex]
- [tex]\(40 \times 50 = 2000\)[/tex]
- The cross-products are equal, so these fractions are equivalent.
3. Proportion: [tex]\(\frac{12}{15} = \frac{20}{25}\)[/tex]
- Cross-multiply: [tex]\(12 \times 25\)[/tex] and [tex]\(20 \times 15\)[/tex]
- Calculate:
- [tex]\(12 \times 25 = 300\)[/tex]
- [tex]\(20 \times 15 = 300\)[/tex]
- The cross-products are equal, so these fractions are equivalent.
4. Proportion: [tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex]
- Cross-multiply: [tex]\(18 \times 50\)[/tex] and [tex]\(30 \times 48\)[/tex]
- Calculate:
- [tex]\(18 \times 50 = 900\)[/tex]
- [tex]\(30 \times 48 = 1440\)[/tex]
- The cross-products are not equal, so these fractions are not equivalent.
Therefore, the false proportion is the fourth one:
[tex]\(\frac{18}{48} \neq \frac{30}{50}\)[/tex].
Let's check each proportion one by one:
1. Proportion: [tex]\(\frac{25}{45} = \frac{50}{90}\)[/tex]
- Cross-multiply: [tex]\(25 \times 90\)[/tex] and [tex]\(50 \times 45\)[/tex]
- Calculate:
- [tex]\(25 \times 90 = 2250\)[/tex]
- [tex]\(50 \times 45 = 2250\)[/tex]
- The cross-products are equal, so these fractions are equivalent.
2. Proportion: [tex]\(\frac{20}{50} = \frac{40}{100}\)[/tex]
- Cross-multiply: [tex]\(20 \times 100\)[/tex] and [tex]\(40 \times 50\)[/tex]
- Calculate:
- [tex]\(20 \times 100 = 2000\)[/tex]
- [tex]\(40 \times 50 = 2000\)[/tex]
- The cross-products are equal, so these fractions are equivalent.
3. Proportion: [tex]\(\frac{12}{15} = \frac{20}{25}\)[/tex]
- Cross-multiply: [tex]\(12 \times 25\)[/tex] and [tex]\(20 \times 15\)[/tex]
- Calculate:
- [tex]\(12 \times 25 = 300\)[/tex]
- [tex]\(20 \times 15 = 300\)[/tex]
- The cross-products are equal, so these fractions are equivalent.
4. Proportion: [tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex]
- Cross-multiply: [tex]\(18 \times 50\)[/tex] and [tex]\(30 \times 48\)[/tex]
- Calculate:
- [tex]\(18 \times 50 = 900\)[/tex]
- [tex]\(30 \times 48 = 1440\)[/tex]
- The cross-products are not equal, so these fractions are not equivalent.
Therefore, the false proportion is the fourth one:
[tex]\(\frac{18}{48} \neq \frac{30}{50}\)[/tex].
