Answer :
To determine which of the given proportions is false, we need to check if each pair of fractions is indeed equal. We can do this by cross-multiplying the terms in each proportion. Once we cross-multiply, we compare the results to see if they are the same on both sides.
Here are the steps for each proportion:
1. [tex]\(\frac{12}{15} = \frac{20}{25}\)[/tex]
Cross-multiplying:
[tex]\[
12 \times 25 = 300
\][/tex]
[tex]\[
15 \times 20 = 300
\][/tex]
Since [tex]\(300 = 300\)[/tex], this proportion is true.
2. [tex]\(\frac{20}{50} = \frac{40}{100}\)[/tex]
Cross-multiplying:
[tex]\[
20 \times 100 = 2000
\][/tex]
[tex]\[
50 \times 40 = 2000
\][/tex]
Since [tex]\(2000 = 2000\)[/tex], this proportion is true.
3. [tex]\(\frac{25}{45} = \frac{50}{90}\)[/tex]
Cross-multiplying:
[tex]\[
25 \times 90 = 2250
\][/tex]
[tex]\[
45 \times 50 = 2250
\][/tex]
Since [tex]\(2250 = 2250\)[/tex], this proportion is true.
4. [tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex]
Cross-multiplying:
[tex]\[
18 \times 50 = 900
\][/tex]
[tex]\[
48 \times 30 = 1440
\][/tex]
Since [tex]\(900 \neq 1440\)[/tex], this proportion is false.
Based on the above cross-multiplications, the proportion that is false is:
[tex]\[
\frac{18}{48} = \frac{30}{50}
\][/tex]
Thus, the false proportion is the fourth one.
Here are the steps for each proportion:
1. [tex]\(\frac{12}{15} = \frac{20}{25}\)[/tex]
Cross-multiplying:
[tex]\[
12 \times 25 = 300
\][/tex]
[tex]\[
15 \times 20 = 300
\][/tex]
Since [tex]\(300 = 300\)[/tex], this proportion is true.
2. [tex]\(\frac{20}{50} = \frac{40}{100}\)[/tex]
Cross-multiplying:
[tex]\[
20 \times 100 = 2000
\][/tex]
[tex]\[
50 \times 40 = 2000
\][/tex]
Since [tex]\(2000 = 2000\)[/tex], this proportion is true.
3. [tex]\(\frac{25}{45} = \frac{50}{90}\)[/tex]
Cross-multiplying:
[tex]\[
25 \times 90 = 2250
\][/tex]
[tex]\[
45 \times 50 = 2250
\][/tex]
Since [tex]\(2250 = 2250\)[/tex], this proportion is true.
4. [tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex]
Cross-multiplying:
[tex]\[
18 \times 50 = 900
\][/tex]
[tex]\[
48 \times 30 = 1440
\][/tex]
Since [tex]\(900 \neq 1440\)[/tex], this proportion is false.
Based on the above cross-multiplications, the proportion that is false is:
[tex]\[
\frac{18}{48} = \frac{30}{50}
\][/tex]
Thus, the false proportion is the fourth one.
