College

Which of the following proportions is false?

A. [tex]\frac{20}{50}=\frac{40}{100}[/tex]

B. [tex]\frac{25}{45}=\frac{50}{90}[/tex]

C. [tex]\frac{12}{15}=\frac{20}{25}[/tex]

D. [tex]\frac{18}{48}=\frac{30}{50}[/tex]

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].