Select the group of fractions in an ascending order:

Question

Accepted Answer

To determine the correct order of the fractions in ascending order, we need to compare the sizes of the fractions given in each option. The fractions in question are $\frac{1}{4}$, $\frac{1}{3}$, and $\frac{1}{2}$.

**Explanation for Option 1: $\frac{1}{4}$ < $\frac{1}{3}$ < $\frac{1}{2}$**

1. **Comparing $\frac{1}{4}$ and $\frac{1}{3}$:**
   - To compare these fractions, we can find a common denominator. The least common denominator for 4 and 3 is 12.
   - Converting $\frac{1}{4}$ to a denominator of 12 gives $\frac{3}{12}$.
   - Converting $\frac{1}{3}$ to a denominator of 12 gives $\frac{4}{12}$.
   - Since $\frac{3}{12}$ < $\frac{4}{12}$, it follows that $\frac{1}{4}$ < $\frac{1}{3}$.

2. **Comparing $\frac{1}{3}$ and $\frac{1}{2}$:**
   - Again, we find a common denominator. The least common denominator for 3 and 2 is 6.
   - Converting $\frac{1}{3}$ to a denominator of 6 gives $\frac{2}{6}$.
   - Converting $\frac{1}{2}$ to a denominator of 6 gives $\frac{3}{6}$.
   - Since $\frac{2}{6}$ < $\frac{3}{6}$, it follows that $\frac{1}{3}$ < $\frac{1}{2}$.

Therefore, the correct ascending order is $\frac{1}{4}$ < $\frac{1}{3}$ < $\frac{1}{2}$, which is exactly what Option 1 states.

**Explanation for why the other options are incorrect:**

- **Option 2: $\frac{1}{2}$ < $\frac{1}{4}$ < $\frac{1}{3}$**
  - This option incorrectly places $\frac{1}{2}$ as the smallest fraction. As shown above, $\frac{1}{2}$ is actually the largest of the three fractions.

- **Option 3: $\frac{1}{2}$ < $\frac{1}{3}$ < $\frac{1}{4}$**
  - This option also incorrectly places $\frac{1}{2}$ as the smallest fraction and $\frac{1}{4}$ as the largest. In reality, $\frac{1}{4}$ is the smallest, and $\frac{1}{2}$ is the largest.

- **Option 4: $\frac{1}{3}$ < $\frac{1}{4}$ < $\frac{1}{2}$**
  - This option incorrectly places $\frac{1}{3}$ as smaller than $\frac{1}{4}$. As demonstrated, $\frac{1}{4}$ is smaller than $\frac{1}{3}$.

In conclusion, Option 1 is the correct answer because it accurately reflects the ascending order of the fractions based on their sizes.