Question

Consider the following expressions:

−6+3⋅5 ______ 16−−√+32÷8 .

Which operator can be inserted to make the statement true?

Answer 1

To solve the problem, we need to evaluate both sides of the expression and determine which operator can be used to make them equal.

Let's simplify both sides.

1. Calculate the left side:
\[ -6 + 3 \cdot 5 \]
\[ = -6 + 15 \]
\[ = 9 \]

2. Calculate the right side:
\[ 16 - \sqrt{16} + 32 \div 8 \]
First, calculate \( \sqrt{16} \):
\[ \sqrt{16} = 4 \]
Now substitute it back into the expression:
\[ 16 - 4 + 32 \div 8 \]
Now calculate \( 32 \div 8 \):
\[ 32 \div 8 = 4 \]
Now we can simplify the right side:
\[ 16 - 4 + 4 \]
\[ = 16 - 4 + 4 \]
\[ = 16 \]

Now we have:
\[ 9 \ \_\_\_ \ 16 \]

Next, we can find the operator that can be inserted between the numbers for the statement to be true.

For this case:
- If we insert "less than," it would be 9 < 16, which is true.
- If we insert "equal to," it would be 9 = 16, which is false.
- If we insert "greater than," it would be 9 > 16, which is also false.

Thus, the valid operator to insert is:
**<** (less than).

So, the complete expression would be:
\[ -6 + 3 \cdot 5 < 16 - \sqrt{16} + 32 \div 8 \]

This is true since \( 9 < 16 \).