Answer :
To determine which proportion is false, we can compare each pair by using cross multiplication. If the cross products are equal, the proportion is true; otherwise, it's false.
Let's examine each proportion one by one:
1. Proportion: [tex]\(\frac{18}{48} = \frac{20}{50}\)[/tex]
- Cross multiply: [tex]\(18 \times 50\)[/tex] and [tex]\(48 \times 20\)[/tex]
- Calculate: [tex]\(18 \times 50 = 900\)[/tex] and [tex]\(48 \times 20 = 960\)[/tex]
- Since [tex]\(900 \neq 960\)[/tex], this proportion is false.
2. Proportion: [tex]\(\frac{24}{30} = \frac{20}{25}\)[/tex]
- Cross multiply: [tex]\(24 \times 25\)[/tex] and [tex]\(30 \times 20\)[/tex]
- Calculate: [tex]\(24 \times 25 = 600\)[/tex] and [tex]\(30 \times 20 = 600\)[/tex]
- Since [tex]\(600 = 600\)[/tex], this proportion is true.
3. Proportion: [tex]\(\frac{25}{45} = \frac{75}{135}\)[/tex]
- Cross multiply: [tex]\(25 \times 135\)[/tex] and [tex]\(45 \times 75\)[/tex]
- Calculate: [tex]\(25 \times 135 = 3375\)[/tex] and [tex]\(45 \times 75 = 3375\)[/tex]
- Since [tex]\(3375 = 3375\)[/tex], this proportion is true.
4. Proportion: [tex]\(\frac{10}{25} = \frac{40}{100}\)[/tex]
- Cross multiply: [tex]\(10 \times 100\)[/tex] and [tex]\(25 \times 40\)[/tex]
- Calculate: [tex]\(10 \times 100 = 1000\)[/tex] and [tex]\(25 \times 40 = 1000\)[/tex]
- Since [tex]\(1000 = 1000\)[/tex], this proportion is true.
After cross checking each proportion, we see that the first proportion, [tex]\(\frac{18}{48} = \frac{20}{50}\)[/tex], is false.
Let's examine each proportion one by one:
1. Proportion: [tex]\(\frac{18}{48} = \frac{20}{50}\)[/tex]
- Cross multiply: [tex]\(18 \times 50\)[/tex] and [tex]\(48 \times 20\)[/tex]
- Calculate: [tex]\(18 \times 50 = 900\)[/tex] and [tex]\(48 \times 20 = 960\)[/tex]
- Since [tex]\(900 \neq 960\)[/tex], this proportion is false.
2. Proportion: [tex]\(\frac{24}{30} = \frac{20}{25}\)[/tex]
- Cross multiply: [tex]\(24 \times 25\)[/tex] and [tex]\(30 \times 20\)[/tex]
- Calculate: [tex]\(24 \times 25 = 600\)[/tex] and [tex]\(30 \times 20 = 600\)[/tex]
- Since [tex]\(600 = 600\)[/tex], this proportion is true.
3. Proportion: [tex]\(\frac{25}{45} = \frac{75}{135}\)[/tex]
- Cross multiply: [tex]\(25 \times 135\)[/tex] and [tex]\(45 \times 75\)[/tex]
- Calculate: [tex]\(25 \times 135 = 3375\)[/tex] and [tex]\(45 \times 75 = 3375\)[/tex]
- Since [tex]\(3375 = 3375\)[/tex], this proportion is true.
4. Proportion: [tex]\(\frac{10}{25} = \frac{40}{100}\)[/tex]
- Cross multiply: [tex]\(10 \times 100\)[/tex] and [tex]\(25 \times 40\)[/tex]
- Calculate: [tex]\(10 \times 100 = 1000\)[/tex] and [tex]\(25 \times 40 = 1000\)[/tex]
- Since [tex]\(1000 = 1000\)[/tex], this proportion is true.
After cross checking each proportion, we see that the first proportion, [tex]\(\frac{18}{48} = \frac{20}{50}\)[/tex], is false.
