Answer :
Out of the given pairs:
- [tex]\( \frac{12}{35} \)[/tex] and [tex]\( \frac{14}{35} \)[/tex] are equivalent.
- [tex]\( \frac{18}{45} \)[/tex] and [tex]\( \frac{14}{35} \)[/tex] are equivalent.
To determine if two fractions are equivalent, you can simplify them to their lowest terms and then compare them. Let's simplify each fraction pair:
1. [tex]\( \frac{15}{25} \)[/tex]and [tex]\( \frac{24}{30} \)[/tex]:
[tex]\( \frac{15}{25} = \frac{3}{5} \) \\ \( \frac{24}{30} = \frac{4}{5} \)[/tex]
These fractions are not equivalent because [tex]\( \frac{3}{5} \)[/tex] is not equal to [tex]\( \frac{4}{5} \).[/tex]
2. [tex]\( \frac{14}{21} \)[/tex] and [tex]\( \frac{8}{20} \)[/tex]:
[tex]\( \frac{14}{21} = \frac{2}{3} \)\\ \( \frac{8}{20} = \frac{2}{5} \)[/tex]
These fractions are not equivalent because [tex]\( \frac{2}{3} \)[/tex] is not equal to [tex]\( \frac{2}{5} \).[/tex]
3. [tex]\( \frac{12}{35} \)[/tex] and [tex]\( \frac{14}{35} \)[/tex]:
Both fractions are already in their simplest form, and they have the same denominator. Therefore, they are equivalent.
4. [tex]\( \frac{18}{45} \)[/tex] and [tex]\( \frac{14}{35} \)[/tex]:
[tex]\( \frac{18}{45} = \frac{2}{5} \)\\ \( \frac{14}{35} = \frac{2}{5} \)[/tex]
These fractions are equivalent because they both simplify to [tex]\( \frac{2}{5} \).[/tex]
The equivalent fraction pairs are [tex]\( \frac{15}{25} \) and \( \frac{24}{30} \), and \( \frac{18}{45} \) and \( \frac{14}{35} \).[/tex]
To determine which fraction pairs are equivalent, we need to simplify each fraction to its simplest form and then compare them.
1. For [tex]\( \frac{15}{25} \) and \( \frac{24}{30} \)[/tex]:
Both fractions can be simplified to [tex]\( \frac{3}{5} \)[/tex], so they are equivalent.
2. For[tex]\( \frac{14}{21} \) and \( \frac{8}{20} \)[/tex]:
[tex]\( \frac{14}{21} \)[/tex] simplifies to[tex]\( \frac{2}{3} \) and \( \frac{8}{20} \)[/tex] simplifies to [tex]\( \frac{2}{5} \)[/tex].
These fractions are not equivalent.
3. For [tex]\( \frac{12}{35} \) and \( \frac{14}{35} \)[/tex]:
Both fractions have the same denominator of 35. Since the numerators are different, these fractions are not equivalent.
4. For [tex]\( \frac{18}{45} \) and \( \frac{14}{35} \)[/tex]:
[tex]\( \frac{18}{45} \)[/tex] simplifies to [tex]\( \frac{2}{5} \) and \( \frac{14}{35} \)[/tex] simplifies to [tex]\( \frac{2}{5} \)[/tex].
These fractions are equivalent.
Therefore, the equivalent fraction pairs are [tex]\( \frac{15}{25} \) and \( \frac{24}{30} \), and \( \frac{18}{45} \) and \( \frac{14}{35} \).[/tex]
