Question

What value correctly fills in the blank so that the expressions are equivalent? 42+70= ? (6+10)
10
7
6
20

Answer 1

To determine the value that correctly fills the blank so that the expressions are equivalent, we first evaluate the left and right sides of the equation as follows:

1. **Calculate the left side:**
\[
42 + 70 = 112
\]

2. **Calculate the right side expression:**
Assuming the blank represents an unknown value \(x\), we compute:
\[
x \cdot (6 + 10) = x \cdot 16
\]

3. **Set both sides equal:**
\[
112 = x \cdot 16
\]

4. **Solve for \(x\):**
To solve for \(x\), divide both sides by 16:
\[
x = \frac{112}{16} = 7
\]

Now that we have solved for \(x\), we can evaluate the choices:

- **10**: Not equal to \(7\).
- **7**: Correct because we found \(x = 7\).
- **6**: Not equal to \(7\).
- **20**: Not equal to \(7\).

Thus, the correct value that fills in the blank is:
\[
\boxed{7}
\]