Question: Choose the property that justifies the following statement.
$$\sqrt{19} \left( \frac{1}{5} \times 5 + \pi \right) = \sqrt{19} \left( 5 \times \frac{1}{5} + \pi \right)$$
commutative property of addition
commutative property of multiplication
distributive property of multiplication over addition
identity property of multiplication
inverse property of multiplication
1. **State the problem:** We need to identify which property justifies the equality:
$$\sqrt{19} \left( \frac{1}{5} \times 5 + \pi \right) = \sqrt{19} \left( 5 \times \frac{1}{5} + \pi \right)$$
2. **Analyze the expression inside the parentheses:**
The expressions inside the parentheses are:
$$\frac{1}{5} \times 5 + \pi$$ and $$5 \times \frac{1}{5} + \pi$$
3. **Focus on the multiplication terms:**
Notice that $$\frac{1}{5} \times 5$$ and $$5 \times \frac{1}{5}$$ are switched in order.
4. **Recall the commutative property of multiplication:**
This property states that for any numbers $$a$$ and $$b$$,
$$a \times b = b \times a$$
5. **Apply the property:**
Since $$\frac{1}{5} \times 5 = 5 \times \frac{1}{5}$$, the expressions inside the parentheses are equal.
6. **Conclusion:**
The equality is justified by the **commutative property of multiplication** because the order of multiplication is switched but the product remains the same.
**Final answer:** commutative property of multiplication