Question

Consider the following expressions:
-6 + 3 * 5 ___ √16 + 32 ÷ 8.
Which operator can be inserted to make the statement true?

Answer 1

Let's evaluate both sides of the expression to see how we can make them equal.

First, we'll calculate the left side of the expression:

\[
-6 + 3 * 5
\]
According to the order of operations, we first multiply \(3\) and \(5\):
\[
3 * 5 = 15
\]
Now we can add:
\[
-6 + 15 = 9
\]

Next, let's calculate the right side of the expression:

\[
\sqrt{16} + 32 ÷ 8
\]
First, calculate \(\sqrt{16}\):
\[
\sqrt{16} = 4
\]
Now calculate \(32 ÷ 8\):
\[
32 ÷ 8 = 4
\]
Now we add these results together:
\[
4 + 4 = 8
\]

Now we can compare the values:
\[
9 \quad \text{(left side)} \quad \text{and} \quad 8 \quad \text{(right side)}
\]

To insert an operator that would make the left side equal to 8, we can take an operator like \(<, \leq, >, \geq, =\) or \( \neq \).

Currently, we have:
\[
9 \quad \text{and} \quad 8
\]

We can conclude:
\[
9 > 8
\]

Thus, we can insert the \(>\) operator to complete the expression as:
\[
-6 + 3 * 5 > \sqrt{16} + 32 ÷ 8
\]

Therefore, the operator that can be inserted is **greater than (>)**.