Question

Which of the following pair(s) of fractions is/are equivalent.

• A. $\frac{1}{3}$ and $\frac{3}{6}$
• B. $\frac{1}{4}$ and $\frac{2}{10}$
• C. $\frac{1}{3}$ and $\frac{3}{9}$
• D. $\frac{1}{4}$ and $\frac{2}{8}$

Answer 1

Answer: (C), (D)

$\frac{1}{4}$ and $\frac{2}{8}$

Equivalent fractions can be defined as fractions that may have different numerators and denominators but they represent the same value.

Let's simplify the each fraction
Option 1: $\frac{1}{3}$ and $\frac{3}{6}:$

$\frac{1}{3}$ is in its simplest form because 1 and 3 have no common factors except 1.
and
$\frac{3}{6}=\frac{1\times 3}{2\times 3}=\frac{1}{2}\ne \frac{1}{3}$
$\therefore \frac{1}{3}$ and $\frac{3}{6}$ are not equivalent.

Option 2: $\frac{1}{4}$ and $\frac{2}{10}:$

$\frac{1}{4}$ is in its simplest form because 1 and 4 have no common factors except 1.
and
$\frac{2}{10}=\frac{1\times 2}{2\times 5}=\frac{1}{5}\ne \frac{1}{4}$
$\therefore \frac{1}{4}$ and $\frac{2}{10}$ are not equivalent.

Option 3: $\frac{1}{3}$ and $\frac{3}{9}:$

$\frac{1}{3}$ is in its simplest form because 1 and 3 have no common factors except 1.
and
$\frac{3}{9}=\frac{1\times 3}{3\times 3}=\frac{1}{3}$
$\therefore \frac{1}{3}$ and $\frac{3}{9}$ are equivalent.

Option 4: $\frac{1}{4}$ and $\frac{2}{8}:$

$\frac{1}{4}$ is in its simplest form since 1 and 4 have no common factors except 1.
$\frac{2}{8}=\frac{1\times 2}{2\times 4}=\frac{1}{4}$
$\therefore \frac{1}{4}$ and $\frac{2}{8}$ are equivalent.