Simplifying $3^2 + (-8\div2)$

Question

Simplify $3^2 + (-8\div2)$.

I know its not possible to divide $-8$ into $2$, so is there a way to make the 8 positive before working the problem?

Given the recent frequency of topics with the acronym "STEM" in them, educators apparently have decided that the problem with math education is that it needed a new, trendy name. — Emily, Mar 12 '13 at 23:27
You can divide $-8$ into $2$ (depending upon the number system you are working in), the result is $\frac {-1}4$. But that is not relevant to this question. — Ross Millikan, Mar 12 '13 at 23:28
A Google search suggests that the word "into" in this case is ambiguous and thus should be avoided. — Tanner Swett, Mar 12 '13 at 23:28
Er...what is STEM? Something "Secundary...Education Mathematics"...or what? — DonAntonio, Mar 12 '13 at 23:51

score 1 · Answer 1 · answered Mar 12 '13 at 23:17

1

Hint: $(-8)\div2=-(8\div2)$. In fact, you should do division first before considering the minus sign.

answered Mar 12 '13 at 23:17

NECing

4,095

Thank you...that's the way I orginally worked the problem but wasn't sure.. – Deriah Mar 12 '13 at 23:30

score 1 · Answer 2 · answered Mar 12 '13 at 23:24

1

On the contrary, it is possible to divide $-8$ by $2$. The definition of division is that $x \div y = z$ if and only if $x = z \cdot y$ and $y \neq 0$. We know that $-8 = -4 \cdot 2$; therefore, $-8 \div 2 = -4$.

answered Mar 12 '13 at 23:24

Tanner Swett

10,624

score 1 · Answer 3 · answered Mar 12 '13 at 23:46

From http://en.wikipedia.org/wiki/Order_of_operations, the order of operations are as:

exponents and roots
multiplication and division
addition and subtraction.

So, if you come across a problem like this, you should follow the steps above in order, from 1 to 3.

Now to address your question, for $3^2 + (-8÷2)$, we do the exponents first:

$$3^2 + (-8\div2)=3\times3+(-8\div2),$$ Then we can take the minus sign out of $8$ and multiply $3\times3$, so

$$3\times3+(-8\div2)=9+((-1)\times 8\div2).$$

Now, we can operate $8 \div 2$,

$$9+((-1)\times 8\div2)=9+((-1)\times 4).$$

Next, any number $\alpha$ multiplied by $(-1)$ will become $-\alpha$. So, if we have $\alpha$, then $\alpha\times(-1)=-\alpha$. For example if we have $\alpha=5$, then $5\times(-1)=-5$

So, we have $$9+((-1)\times 4)=9+(-4),$$

since here $\alpha=4$, so $4\times(-1)=(-1)\times 4=-4$.

Now, $$9+(-4)=9-4=5,$$

where we subtracted.

Hope this helps.

Simplifying $3^2 + (-8\div2)$

3 Answers3