Question

Complete the following stepped-out solution to show that 5/11*w*11/5+3 is equivalent to w+3.
5/11* *w+3 Commutative Property of Multiplication
*w+3 Inverse Property of Multiplication
w+3 Identity Property of Multiplication

Answer 1

Let's complete the stepped-out solution to demonstrate that \( \frac{5}{11} \cdot w \cdot \frac{11}{5} + 3 \) is equivalent to \( w + 3 \).

### Step 1: Write the Expression
Starting with the expression:
\[
\frac{5}{11} \cdot w \cdot \frac{11}{5} + 3
\]

### Step 2: Apply the Commutative Property of Multiplication
We can rearrange the multiplication using the Commutative Property. This allows us to change the order of factors:
\[
\left(\frac{5}{11} \cdot \frac{11}{5}\right) \cdot w + 3
\]

### Step 3: Simplify Using the Inverse Property of Multiplication
Now, we simplify \( \frac{5}{11} \cdot \frac{11}{5} \). According to the Inverse Property of Multiplication, these two fractions are inverses of each other:
\[
\frac{5}{11} \cdot \frac{11}{5} = 1
\]
Thus, we have:
\[
1 \cdot w + 3
\]

### Step 4: Apply the Identity Property of Multiplication
Using the Identity Property of Multiplication, which states that multiplying by 1 does not change the value:
\[
w + 3
\]

### Conclusion
Now, we can conclude that:
\[
\frac{5}{11} \cdot w \cdot \frac{11}{5} + 3 = w + 3
\]

Thus, the complete stepped-out solution is:

1. \( \frac{5}{11} \cdot w \cdot \frac{11}{5} + 3 \)
2. Rearranging: \( \left(\frac{5}{11} \cdot \frac{11}{5}\right) \cdot w + 3 \) (Commutative Property of Multiplication)
3. Simplifying: \( 1 \cdot w + 3 \) (Inverse Property of Multiplication)
4. Applying Identity: \( w + 3 \) (Identity Property of Multiplication)

Finally:
\[
\frac{5}{11}w \cdot \frac{11}{5} + 3 \equiv w + 3
\]