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Answer :
To determine which proportion is false, we can check each pair by cross-multiplying and comparing the products. If the products are equal, the proportions are true; if not, they are false.
1. Proportion 1: [tex]\(\frac{25}{45} = \frac{75}{135}\)[/tex]
Cross-multiply:
[tex]\[
25 \times 135 = 3375
\][/tex]
[tex]\[
45 \times 75 = 3375
\][/tex]
Since both products are equal, this proportion is true.
2. Proportion 2: [tex]\(\frac{10}{25} = \frac{40}{100}\)[/tex]
Cross-multiply:
[tex]\[
10 \times 100 = 1000
\][/tex]
[tex]\[
25 \times 40 = 1000
\][/tex]
The products are equal, so this proportion is true.
3. Proportion 3: [tex]\(\frac{24}{30} = \frac{20}{25}\)[/tex]
Cross-multiply:
[tex]\[
24 \times 25 = 600
\][/tex]
[tex]\[
30 \times 20 = 600
\][/tex]
The products are equal, so this proportion is true.
4. Proportion 4: [tex]\(\frac{18}{48} = \frac{20}{50}\)[/tex]
Cross-multiply:
[tex]\[
18 \times 50 = 900
\][/tex]
[tex]\[
48 \times 20 = 960
\][/tex]
The products are not equal, so this proportion is false.
Therefore, the false proportion is the fourth one: [tex]\(\frac{18}{48} = \frac{20}{50}\)[/tex].
1. Proportion 1: [tex]\(\frac{25}{45} = \frac{75}{135}\)[/tex]
Cross-multiply:
[tex]\[
25 \times 135 = 3375
\][/tex]
[tex]\[
45 \times 75 = 3375
\][/tex]
Since both products are equal, this proportion is true.
2. Proportion 2: [tex]\(\frac{10}{25} = \frac{40}{100}\)[/tex]
Cross-multiply:
[tex]\[
10 \times 100 = 1000
\][/tex]
[tex]\[
25 \times 40 = 1000
\][/tex]
The products are equal, so this proportion is true.
3. Proportion 3: [tex]\(\frac{24}{30} = \frac{20}{25}\)[/tex]
Cross-multiply:
[tex]\[
24 \times 25 = 600
\][/tex]
[tex]\[
30 \times 20 = 600
\][/tex]
The products are equal, so this proportion is true.
4. Proportion 4: [tex]\(\frac{18}{48} = \frac{20}{50}\)[/tex]
Cross-multiply:
[tex]\[
18 \times 50 = 900
\][/tex]
[tex]\[
48 \times 20 = 960
\][/tex]
The products are not equal, so this proportion is false.
Therefore, the false proportion is the fourth one: [tex]\(\frac{18}{48} = \frac{20}{50}\)[/tex].
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