Answer :
We need to check whether the fractions in each pair are equivalent. Two fractions, [tex]$\frac{a}{b}$[/tex] and [tex]$\frac{c}{d}$[/tex], are equivalent if and only if
[tex]$$
a \cdot d = c \cdot b.
$$[/tex]
Let's check each pair:
1. For the pair [tex]$\frac{12}{35}$[/tex] and [tex]$\frac{14}{35}$[/tex], we compute:
[tex]$$
12 \times 35 = 420 \quad \text{and} \quad 14 \times 35 = 490.
$$[/tex]
Since [tex]$420 \neq 490$[/tex], these fractions are not equivalent.
2. For the pair [tex]$\frac{14}{21}$[/tex] and [tex]$\frac{8}{20}$[/tex], we compute:
[tex]$$
14 \times 20 = 280 \quad \text{and} \quad 8 \times 21 = 168.
$$[/tex]
Since [tex]$280 \neq 168$[/tex], these fractions are not equivalent.
3. For the pair [tex]$\frac{15}{25}$[/tex] and [tex]$\frac{24}{30}$[/tex], we compute:
[tex]$$
15 \times 30 = 450 \quad \text{and} \quad 24 \times 25 = 600.
$$[/tex]
Since [tex]$450 \neq 600$[/tex], these fractions are not equivalent.
4. For the pair [tex]$\frac{18}{45}$[/tex] and [tex]$\frac{14}{35}$[/tex], we compute:
[tex]$$
18 \times 35 = 630 \quad \text{and} \quad 14 \times 45 = 630.
$$[/tex]
Since [tex]$630 = 630$[/tex], these fractions are equivalent.
Thus, the only equivalent fraction pair is the fourth one: [tex]$\frac{18}{45}$[/tex] and [tex]$\frac{14}{35}$[/tex].
The final answer is choice 4.
[tex]$$
a \cdot d = c \cdot b.
$$[/tex]
Let's check each pair:
1. For the pair [tex]$\frac{12}{35}$[/tex] and [tex]$\frac{14}{35}$[/tex], we compute:
[tex]$$
12 \times 35 = 420 \quad \text{and} \quad 14 \times 35 = 490.
$$[/tex]
Since [tex]$420 \neq 490$[/tex], these fractions are not equivalent.
2. For the pair [tex]$\frac{14}{21}$[/tex] and [tex]$\frac{8}{20}$[/tex], we compute:
[tex]$$
14 \times 20 = 280 \quad \text{and} \quad 8 \times 21 = 168.
$$[/tex]
Since [tex]$280 \neq 168$[/tex], these fractions are not equivalent.
3. For the pair [tex]$\frac{15}{25}$[/tex] and [tex]$\frac{24}{30}$[/tex], we compute:
[tex]$$
15 \times 30 = 450 \quad \text{and} \quad 24 \times 25 = 600.
$$[/tex]
Since [tex]$450 \neq 600$[/tex], these fractions are not equivalent.
4. For the pair [tex]$\frac{18}{45}$[/tex] and [tex]$\frac{14}{35}$[/tex], we compute:
[tex]$$
18 \times 35 = 630 \quad \text{and} \quad 14 \times 45 = 630.
$$[/tex]
Since [tex]$630 = 630$[/tex], these fractions are equivalent.
Thus, the only equivalent fraction pair is the fourth one: [tex]$\frac{18}{45}$[/tex] and [tex]$\frac{14}{35}$[/tex].
The final answer is choice 4.
