7. Allie worked for $$ \frac{1}{2} $$ hour on Saturday and $$ \frac{2}{5} $$ hour on Sunday. What is a common denominator for the fractions? Write the fractions with the common denominator. $$ \frac{1}{2}=\frac{2}{5}=\square $$

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UpStudy AI · Accepted Answer

To solve the problem of finding a common denominator for the fractions $$ \frac{1}{2} $$ and $$ \frac{2}{5} $$, and then rewriting the fractions with that common denominator, follow these steps:

### 1. Find a Common Denominator

The denominators of the given fractions are 2 and 5. To find a common denominator, you can determine the **Least Common Multiple (LCM)** of these two numbers.

- **Factors of 2:** 2
- **Factors of 5:** 5

Since 2 and 5 are both prime numbers, their LCM is simply their product:
$$ \text{LCM}(2, 5) = 2 \times 5 = 10 $$

So, the common denominator is **10**.

### 2. Rewrite the Fractions with the Common Denominator

Now, convert each fraction to an equivalent fraction with the denominator of 10.

- **For $$ \frac{1}{2} $$:**
  $$
  \frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10}
  $$

- **For $$ \frac{2}{5} $$:**
  $$
  \frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10}
  $$

### 3. Final Answer

Putting it all together:

- **Common Denominator:** 10
- **Equivalent Fractions:**
  $$
  \frac{1}{2} = \frac{5}{10} \quad \text{and} \quad \frac{2}{5} = \frac{4}{10}
  $$

$$
\boxed{
\begin{align*}
\text{Common denominator} &= 10 \
\frac{1}{2} &= \frac{5}{10} \
\frac{2}{5} &= \frac{4}{10}
\end{align*}
}
$$
The common denominator is 10. $$ \frac{1}{2} = \frac{5}{10} \quad \text{and} \quad \frac{2}{5} = \frac{4}{10} $$

7. Allie worked for \( \frac{1}{2} \) hour on Saturday and \( \frac{2}{5} \) hour on Sunday. What is a common denominator for the fractions? Write the fractions with the common denominator. \( \frac{1}{2}=\frac{2}{5}=\square \)

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