# What is 3x4x(10-7)divided by 2?

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#### Explanation

Explain in detail...

#### Explanation:

I want someone to double check my answer

2
Feb 16, 2017

Insert your own parentheses when confused

#### Explanation:

With a problem like this, we want to group terms together.

Let's write this as

$\frac{3 \cdot 4 \cdot \left(10 - 7\right)}{2}$

Now, we want to do the innermost parentheses first.

$\frac{3 \cdot 4 \cdot \left(3\right)}{2}$

A term with no operations needs no parentheses, so let's remove them.

$\frac{3 \cdot 4 \cdot 3}{2}$

Now, we work on the other parentheses $3 \cdot 4 \cdot 3 = 36$.

Our problem is now $\frac{36}{2}$

Again, terms with no operations need no parentheses, so let's remove them. We have $\frac{36}{2}$, which is 18.

Except, maybe we didn't do it in the right order. Maybe it's a trick question. Let's try it differently.

$3 \cdot 4 \cdot \left(\frac{10 - 7}{2}\right)$

We evaluate the numerator:

$3 \cdot 4 \cdot \left(\frac{3}{2}\right)$

And multiply it out:

$12 \cdot \left(\frac{3}{2}\right) = \frac{36}{2} = 18$

So, as long as we evaluate the parentheses before doing anything else, it works out.

How about we write the problem differently a third time?

$3 \cdot 4 \cdot \left(10 - 7\right) \cdot \left(\frac{1}{2}\right)$

We can now multiply the 3 and 4:

$12 \cdot \left(10 - 7\right) \cdot \left(\frac{1}{2}\right)$

Now, we'll multiply the 12 to both terms in the parentheses.

$\left(120 - 84\right) \cdot \left(\frac{1}{2}\right)$

Evaluate the parentheses:

$36 \cdot \left(\frac{1}{2}\right) = \frac{36}{2} = 18$

So, you can approach it many ways, but make sure that you follow the order of operations.

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