Answer :
To find which proportion is false, we'll examine the given fractions one by one to see if they are equal:
1. Proportion 1: [tex]\(\frac{18}{48} = \frac{20}{50}\)[/tex]
To check if these fractions are equal, we can cross-multiply and compare the products:
- Multiply 18 by 50: [tex]\(18 \times 50 = 900\)[/tex]
- Multiply 48 by 20: [tex]\(48 \times 20 = 960\)[/tex]
Since [tex]\(900 \neq 960\)[/tex], this proportion is false.
2. Proportion 2: [tex]\(\frac{10}{25} = \frac{40}{100}\)[/tex]
Check if these fractions are equal by cross-multiplying:
- Multiply 10 by 100: [tex]\(10 \times 100 = 1000\)[/tex]
- Multiply 25 by 40: [tex]\(25 \times 40 = 1000\)[/tex]
Since [tex]\(1000 = 1000\)[/tex], this proportion is true.
3. Proportion 3: [tex]\(\frac{24}{30} = \frac{20}{25}\)[/tex]
Check if these fractions are equal by cross-multiplying:
- Multiply 24 by 25: [tex]\(24 \times 25 = 600\)[/tex]
- Multiply 30 by 20: [tex]\(30 \times 20 = 600\)[/tex]
Since [tex]\(600 = 600\)[/tex], this proportion is true.
4. Proportion 4: [tex]\(\frac{25}{45} = \frac{75}{135}\)[/tex]
Check if these fractions are equal by cross-multiplying:
- Multiply 25 by 135: [tex]\(25 \times 135 = 3375\)[/tex]
- Multiply 45 by 75: [tex]\(45 \times 75 = 3375\)[/tex]
Since [tex]\(3375 = 3375\)[/tex], this proportion is true.
From these steps, we found that the first proportion, [tex]\(\frac{18}{48} = \frac{20}{50}\)[/tex], is false.
1. Proportion 1: [tex]\(\frac{18}{48} = \frac{20}{50}\)[/tex]
To check if these fractions are equal, we can cross-multiply and compare the products:
- Multiply 18 by 50: [tex]\(18 \times 50 = 900\)[/tex]
- Multiply 48 by 20: [tex]\(48 \times 20 = 960\)[/tex]
Since [tex]\(900 \neq 960\)[/tex], this proportion is false.
2. Proportion 2: [tex]\(\frac{10}{25} = \frac{40}{100}\)[/tex]
Check if these fractions are equal by cross-multiplying:
- Multiply 10 by 100: [tex]\(10 \times 100 = 1000\)[/tex]
- Multiply 25 by 40: [tex]\(25 \times 40 = 1000\)[/tex]
Since [tex]\(1000 = 1000\)[/tex], this proportion is true.
3. Proportion 3: [tex]\(\frac{24}{30} = \frac{20}{25}\)[/tex]
Check if these fractions are equal by cross-multiplying:
- Multiply 24 by 25: [tex]\(24 \times 25 = 600\)[/tex]
- Multiply 30 by 20: [tex]\(30 \times 20 = 600\)[/tex]
Since [tex]\(600 = 600\)[/tex], this proportion is true.
4. Proportion 4: [tex]\(\frac{25}{45} = \frac{75}{135}\)[/tex]
Check if these fractions are equal by cross-multiplying:
- Multiply 25 by 135: [tex]\(25 \times 135 = 3375\)[/tex]
- Multiply 45 by 75: [tex]\(45 \times 75 = 3375\)[/tex]
Since [tex]\(3375 = 3375\)[/tex], this proportion is true.
From these steps, we found that the first proportion, [tex]\(\frac{18}{48} = \frac{20}{50}\)[/tex], is false.
