# (Basic Arithmetic) Multiple number questions: 34 + 54 + 54.

Basic question here but I might aswell get it checked out. I've gone through the multiplication, division, subtraction and addition sections of Khan Academy but something he never went through were multiple number questions like so:

454 + 2324 + 4352
4773 - 3944 - 38482
3747 * 32848 * 27748
82794 / 23484 / 2394


We only did two number questions like 54 + 34. For the addition one I guess you just stack them up and add them as normal but for the others they don't seem to quite make sense for me. How do you go about doing them?

Addition and multiplication works both ways, as we see below: \begin{align*} \overbrace{454 + 2324}^\text{add these first} + 4352 &= 2778+4352 \\ &=7130 \\ 454 + \overbrace{2324 + 4352}^\text{add these first} &= 454+6676 \\ &=7130 \end{align*} and \begin{align*} \overbrace{3747 \times 32848}^\text{multiply these first} \times 27748 &= 123081456 \times 27748 \\ &= 3415264241088 \\ 3747 \times \overbrace{32848 \times 27748}^\text{multiply these first} &= 3747 \times 911466304 \\ &= 3415264241088. \end{align*} We see we get the same answer in both cases. Since this happens in general, both $+$ and $\times$ are called associative binary operations.
For division, we simply would not write $82794 / 23484 / 2394$, since it's ambiguous. We would add brackets in either case: \begin{align*} \overbrace{(82794 / 23484)}^\text{divide these first} / 2394 &= \tfrac{13799}{3914} / 2394 \\ &= \tfrac{13799}{9370116} \\ 82794 / \overbrace{(23484 / 2394)}^\text{divide these first} &= 82794 / \tfrac{206}{21} \\ &= \tfrac{869337}{103}. \end{align*}