Answer :
To determine which of the given proportions is false, let's evaluate each proportion one by one. The goal is to check if the fractions on either side of the equal sign are equivalent. Two fractions are equivalent if their cross products are equal, meaning if [tex]\(\frac{a}{b} = \frac{c}{d}\)[/tex], then [tex]\(a \times d\)[/tex] should equal [tex]\(b \times c\)[/tex].
Let's go through each proportion:
1. For [tex]\(\frac{10}{25} = \frac{40}{100}\)[/tex]:
Cross multiply the fractions:
[tex]\[
10 \times 100 = 1000
\][/tex]
[tex]\[
25 \times 40 = 1000
\][/tex]
Both products are equal, so this proportion is true.
2. For [tex]\(\frac{24}{30} = \frac{20}{25}\)[/tex]:
Cross multiply the fractions:
[tex]\[
24 \times 25 = 600
\][/tex]
[tex]\[
30 \times 20 = 600
\][/tex]
Both products are equal, so this proportion is true.
3. For [tex]\(\frac{25}{45} = \frac{75}{135}\)[/tex]:
Cross multiply the fractions:
[tex]\[
25 \times 135 = 3375
\][/tex]
[tex]\[
45 \times 75 = 3375
\][/tex]
Both products are equal, so this proportion is true.
4. For [tex]\(\frac{18}{48} = \frac{20}{50}\)[/tex]:
Cross multiply the fractions:
[tex]\[
18 \times 50 = 900
\][/tex]
[tex]\[
48 \times 20 = 960
\][/tex]
These products are not equal, indicating that this proportion is false.
Based on this check, the proportion [tex]\(\frac{18}{48} = \frac{20}{50}\)[/tex] is false.
Let's go through each proportion:
1. For [tex]\(\frac{10}{25} = \frac{40}{100}\)[/tex]:
Cross multiply the fractions:
[tex]\[
10 \times 100 = 1000
\][/tex]
[tex]\[
25 \times 40 = 1000
\][/tex]
Both products are equal, so this proportion is true.
2. For [tex]\(\frac{24}{30} = \frac{20}{25}\)[/tex]:
Cross multiply the fractions:
[tex]\[
24 \times 25 = 600
\][/tex]
[tex]\[
30 \times 20 = 600
\][/tex]
Both products are equal, so this proportion is true.
3. For [tex]\(\frac{25}{45} = \frac{75}{135}\)[/tex]:
Cross multiply the fractions:
[tex]\[
25 \times 135 = 3375
\][/tex]
[tex]\[
45 \times 75 = 3375
\][/tex]
Both products are equal, so this proportion is true.
4. For [tex]\(\frac{18}{48} = \frac{20}{50}\)[/tex]:
Cross multiply the fractions:
[tex]\[
18 \times 50 = 900
\][/tex]
[tex]\[
48 \times 20 = 960
\][/tex]
These products are not equal, indicating that this proportion is false.
Based on this check, the proportion [tex]\(\frac{18}{48} = \frac{20}{50}\)[/tex] is false.
