Question

consider the following expression: -6 + 3 dot 5 ____ sqrt16 + 32 divided by 8

which operator can be inserted to make the statement true?

Answer 1

To evaluate the expression \(-6 + 3 \cdot 5 \_\_\_ \sqrt{16} + \frac{32}{8}\), we first simplify what we can.

1. Calculate \(\sqrt{16}\):
\[
\sqrt{16} = 4
\]

2. Calculate \(\frac{32}{8}\):
\[
\frac{32}{8} = 4
\]

Now, we substitute these values back into the expression:
\[
-6 + 3 \cdot 5 \_\_\_ 4 + 4
\]

3. Calculate \(3 \cdot 5\):
\[
3 \cdot 5 = 15
\]

This gives us:
\[
-6 + 15 \_\_\_ 4 + 4
\]

Now, we can rewrite the expression as:
\[
-6 + 15 \_\_\_ 4 + 4
\]

Next, we calculate \(-6 + 15 + 4\):
\[
-6 + 15 = 9
\]
\[
9 + 4 = 13
\]

So we now have:
\[
13 \_\_\_ 4
\]

To make the expression true, we need to find an operator that, when applied to \(13\) and \(4\), results in \(0\), since all operations should yield the original expression as true.

The only operator that can satisfy this in this context is:

\[
13 - 4 = 9 \quad \text{(incorrect)}
\]
\[
13 + 4 = 17 \quad \text{(incorrect)}
\]
\[
13 \div 4 \quad \text{(not an integer)}
\]
\[
13 \times 4 = 52 \quad \text{(incorrect)}
\]
The correct choice is subtraction:

\[
13 - 4 = 9 \quad \text{ which connects to all other } -6, + 15 etc.
\]

So the operation you can use is subtraction:
\[
\_ = - \implies -6 + 15 - 4 + 4
\]

So you can insert \( - \) to make the statement true.

Final answer:
Insert the subtraction operator (-).