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------------------------------------------------ Which fraction pairs are equivalent?

A. \(\frac{15}{25}\) and \(\frac{24}{30}\)
B. \(\frac{14}{21}\) and \(\frac{8}{20}\)
C. \(\frac{12}{35}\) and \(\frac{14}{35}\)
D. \(\frac{18}{45}\) and \(\frac{14}{35}\)

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]