$$ \frac{21}{6} $$ or $$ 3 \frac{1}{3} ? $$

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UpStudy AI · Accepted Answer

To compare $$ \frac{21}{6} $$ and $$ 3 \frac{1}{3} $$, we can convert both expressions to improper fractions or decimals.

1. **Convert $$ 3 \frac{1}{3} $$ to an improper fraction:**
   $$
   3 \frac{1}{3} = 3 + \frac{1}{3} = \frac{3 \times 3 + 1}{3} = \frac{9 + 1}{3} = \frac{10}{3}
   $$

2. **Now we have:**
   - $$ \frac{21}{6} $$
   - $$ \frac{10}{3} $$

3. **Next, we can convert $$ \frac{10}{3} $$ to have a common denominator with $$ \frac{21}{6} $$:**
   - The denominator of $$ \frac{21}{6} $$ is 6. To convert $$ \frac{10}{3} $$ to a fraction with a denominator of 6, we multiply the numerator and denominator by 2:
   $$
   \frac{10}{3} = \frac{10 \times 2}{3 \times 2} = \frac{20}{6}
   $$

4. **Now we can compare:**
   - $$ \frac{21}{6} $$ and $$ \frac{20}{6} $$

Since $$ \frac{21}{6} > \frac{20}{6} $$, we conclude that:

$$
\frac{21}{6} > 3 \frac{1}{3}
$$

Thus, $$ \frac{21}{6} $$ is greater than $$ 3 \frac{1}{3} $$.
$$ \frac{21}{6} $$ is greater than $$ 3 \frac{1}{3} $$.

\( \frac{21}{6} \) or \( 3 \frac{1}{3} ? \)

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