Question

Mrs. Adenan sold 63 bracelets at one craft fair and 36 bracelets at a second craft fair. Which expression correctly applies the distributive property to show equivalent expressions for the total number of bracelets she sold?
63 + 36 = (3) (21) + (9) (4)
63 + 36 = (7) (9) + (12) (3)
63 + 36 = 9 (7 + 4)
63 + 36 = 3 (21 + 9)

Answer 1

To find which expression correctly applies the distributive property to show equivalent expressions for the total number of bracelets Mrs. Adenan sold (which is \(63 + 36\)), we need to check if the right-hand side of each expression correctly equals \(99\) (the sum of \(63\) and \(36\)) and if the distributive property is being applied correctly.

1. **Checking \(63 + 36 = (3)(21) + (9)(4)\)**:
\[
(3)(21) = 63 \quad \text{and} \quad (9)(4) = 36 \quad \Rightarrow \quad 63 + 36 = 63 + 36 \, \text{(True)}
\]

2. **Checking \(63 + 36 = (7)(9) + (12)(3)\)**:
\[
(7)(9) = 63 \quad \text{and} \quad (12)(3) = 36 \quad \Rightarrow \quad 63 + 36 = 63 + 36 \, \text{(True)}
\]

3. **Checking \(63 + 36 = 9(7 + 4)\)**:
\[
7 + 4 = 11 \quad \Rightarrow \quad 9(11) = 99 \, \text{(False)}
\]

4. **Checking \(63 + 36 = 3(21 + 9)\)**:
\[
21 + 9 = 30 \quad \Rightarrow \quad 3(30) = 90 \, \text{(False)}
\]

Based on this analysis, the expressions that correctly apply the distributive property and show equivalent expressions for the total number of bracelets sold are:

- \(63 + 36 = (3)(21) + (9)(4)\)
- \(63 + 36 = (7)(9) + (12)(3)\)

Therefore, both the first and second expressions are correct. The preferred simplest representation that shows the distributive property of the total is:

**\(63 + 36 = (3)(21) + (9)(4)\)** or **\(63 + 36 = (7)(9) + (12)(3)\)**.