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

Question

which operator can be inserted to make the statement true?

GPT-4o mini · Answer

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 (-).