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Answer :
We can verify each proportion by cross multiplying the fractions. Recall that for two fractions, [tex]$\frac{a}{b}$[/tex] and [tex]$\frac{c}{d}$[/tex], the proportions are equivalent if and only if
[tex]$$
a \times d = c \times b.
$$[/tex]
Let’s check each option:
1. For the proportion
[tex]$$
\frac{18}{48} = \frac{30}{50},
$$[/tex]
we check by cross multiplication:
[tex]$$
18 \times 50 = 900 \quad \text{and} \quad 30 \times 48 = 1440.
$$[/tex]
Since [tex]$900 \neq 1440$[/tex], this proportion is false.
2. For the proportion
[tex]$$
\frac{25}{45} = \frac{50}{90},
$$[/tex]
we cross multiply:
[tex]$$
25 \times 90 = 2250 \quad \text{and} \quad 50 \times 45 = 2250.
$$[/tex]
Since the products are equal, this proportion is true.
3. For the proportion
[tex]$$
\frac{12}{15} = \frac{20}{25},
$$[/tex]
we have:
[tex]$$
12 \times 25 = 300 \quad \text{and} \quad 20 \times 15 = 300.
$$[/tex]
Both products are equal, so this proportion is true.
4. For the proportion
[tex]$$
\frac{20}{50} = \frac{40}{100},
$$[/tex]
we perform the cross multiplication:
[tex]$$
20 \times 100 = 2000 \quad \text{and} \quad 40 \times 50 = 2000.
$$[/tex]
Since both products are equal, this proportion is true.
Since only the first option gave different products in the cross multiplication step, the false proportion is:
[tex]$$
\frac{18}{48} = \frac{30}{50}.
$$[/tex]
[tex]$$
a \times d = c \times b.
$$[/tex]
Let’s check each option:
1. For the proportion
[tex]$$
\frac{18}{48} = \frac{30}{50},
$$[/tex]
we check by cross multiplication:
[tex]$$
18 \times 50 = 900 \quad \text{and} \quad 30 \times 48 = 1440.
$$[/tex]
Since [tex]$900 \neq 1440$[/tex], this proportion is false.
2. For the proportion
[tex]$$
\frac{25}{45} = \frac{50}{90},
$$[/tex]
we cross multiply:
[tex]$$
25 \times 90 = 2250 \quad \text{and} \quad 50 \times 45 = 2250.
$$[/tex]
Since the products are equal, this proportion is true.
3. For the proportion
[tex]$$
\frac{12}{15} = \frac{20}{25},
$$[/tex]
we have:
[tex]$$
12 \times 25 = 300 \quad \text{and} \quad 20 \times 15 = 300.
$$[/tex]
Both products are equal, so this proportion is true.
4. For the proportion
[tex]$$
\frac{20}{50} = \frac{40}{100},
$$[/tex]
we perform the cross multiplication:
[tex]$$
20 \times 100 = 2000 \quad \text{and} \quad 40 \times 50 = 2000.
$$[/tex]
Since both products are equal, this proportion is true.
Since only the first option gave different products in the cross multiplication step, the false proportion is:
[tex]$$
\frac{18}{48} = \frac{30}{50}.
$$[/tex]
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