[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.00,0:00:00.66,Default,,0000,0000,0000,,
Dialogue: 0,0:00:00.66,0:00:04.75,Default,,0000,0000,0000,,We're asked to simplify 8 plus\N5 times 4 minus, and then in
Dialogue: 0,0:00:04.75,0:00:09.01,Default,,0000,0000,0000,,parentheses, 6 plus 10\Ndivided by 2 plus 44.
Dialogue: 0,0:00:09.01,0:00:12.12,Default,,0000,0000,0000,,Whenever you see some type of\Ncrazy expression like this
Dialogue: 0,0:00:12.12,0:00:15.36,Default,,0000,0000,0000,,where you have parentheses and\Naddition and subtraction and
Dialogue: 0,0:00:15.36,0:00:17.76,Default,,0000,0000,0000,,division, you always want\Nto keep the order of
Dialogue: 0,0:00:17.76,0:00:19.00,Default,,0000,0000,0000,,operations in mind.
Dialogue: 0,0:00:19.00,0:00:20.97,Default,,0000,0000,0000,,Let me write them\Ndown over here.
Dialogue: 0,0:00:20.97,0:00:23.42,Default,,0000,0000,0000,,So when you're doing order of\Noperations, or really when
Dialogue: 0,0:00:23.42,0:00:24.82,Default,,0000,0000,0000,,you're evaluating any\Nexpression, you should have
Dialogue: 0,0:00:24.82,0:00:29.52,Default,,0000,0000,0000,,this in the front of your brain\Nthat the top priority
Dialogue: 0,0:00:29.52,0:00:30.77,Default,,0000,0000,0000,,goes to parentheses.
Dialogue: 0,0:00:30.77,0:00:37.85,Default,,0000,0000,0000,,
Dialogue: 0,0:00:37.85,0:00:40.06,Default,,0000,0000,0000,,And those are these little\Nbrackets over here, or however
Dialogue: 0,0:00:40.06,0:00:40.67,Default,,0000,0000,0000,,you want to call them.
Dialogue: 0,0:00:40.67,0:00:42.32,Default,,0000,0000,0000,,Those are the parentheses\Nright there.
Dialogue: 0,0:00:42.32,0:00:44.03,Default,,0000,0000,0000,,That gets top priority.
Dialogue: 0,0:00:44.03,0:00:46.12,Default,,0000,0000,0000,,Then after that, you want to\Nworry about exponents.
Dialogue: 0,0:00:46.12,0:00:48.24,Default,,0000,0000,0000,,There are no exponents in this\Nexpression, but I'll just
Dialogue: 0,0:00:48.24,0:00:52.15,Default,,0000,0000,0000,,write it down just for future\Nreference: exponents.
Dialogue: 0,0:00:52.15,0:00:55.00,Default,,0000,0000,0000,,One way I like to think about it\Nis parentheses always takes
Dialogue: 0,0:00:55.00,0:00:58.73,Default,,0000,0000,0000,,top priority, but then after\Nthat, we go in descending
Dialogue: 0,0:00:58.73,0:01:01.61,Default,,0000,0000,0000,,order, or I guess we should\Nsay in-- well, yeah, in
Dialogue: 0,0:01:01.61,0:01:05.40,Default,,0000,0000,0000,,descending order of how fast\Nthat computation is.
Dialogue: 0,0:01:05.40,0:01:07.52,Default,,0000,0000,0000,,When I say fast, how\Nfast it grows.
Dialogue: 0,0:01:07.52,0:01:09.80,Default,,0000,0000,0000,,When I take something to an\Nexponent, when I'm taking
Dialogue: 0,0:01:09.80,0:01:13.27,Default,,0000,0000,0000,,something to a power, it grows\Nreally fast. Then it grows a
Dialogue: 0,0:01:13.27,0:01:15.73,Default,,0000,0000,0000,,little bit slower or shrinks\Na little bit slower if I
Dialogue: 0,0:01:15.73,0:01:17.76,Default,,0000,0000,0000,,multiply or divide,\Nso that comes
Dialogue: 0,0:01:17.76,0:01:21.80,Default,,0000,0000,0000,,next: multiply or divide.
Dialogue: 0,0:01:21.80,0:01:24.91,Default,,0000,0000,0000,,Multiplication and division\Ncomes next, and then last of
Dialogue: 0,0:01:24.91,0:01:27.55,Default,,0000,0000,0000,,all comes addition\Nand subtraction.
Dialogue: 0,0:01:27.55,0:01:29.95,Default,,0000,0000,0000,,So these are kind of the\Nslowest operations.
Dialogue: 0,0:01:29.95,0:01:31.45,Default,,0000,0000,0000,,This is a little bit faster.
Dialogue: 0,0:01:31.45,0:01:33.61,Default,,0000,0000,0000,,This is the fastest operation.
Dialogue: 0,0:01:33.61,0:01:35.29,Default,,0000,0000,0000,,And then the parentheses,\Njust no matter
Dialogue: 0,0:01:35.29,0:01:36.98,Default,,0000,0000,0000,,what, always take priority.
Dialogue: 0,0:01:36.98,0:01:38.18,Default,,0000,0000,0000,,So let's apply it over here.
Dialogue: 0,0:01:38.18,0:01:40.29,Default,,0000,0000,0000,,Let me rewrite this\Nwhole expression.
Dialogue: 0,0:01:40.29,0:01:47.96,Default,,0000,0000,0000,,So it's 8 plus 5 times 4 minus,\Nin parentheses, 6 plus
Dialogue: 0,0:01:47.96,0:01:53.15,Default,,0000,0000,0000,,10 divided by 2 plus 44.
Dialogue: 0,0:01:53.15,0:01:55.73,Default,,0000,0000,0000,,So we're going to want to do the\Nparentheses first. We have
Dialogue: 0,0:01:55.73,0:02:00.05,Default,,0000,0000,0000,,parentheses there and there.
Dialogue: 0,0:02:00.05,0:02:02.17,Default,,0000,0000,0000,,Now this parentheses is pretty\Nstraightforward.
Dialogue: 0,0:02:02.17,0:02:05.12,Default,,0000,0000,0000,,Well, inside the parentheses\Nis already evaluated, so we
Dialogue: 0,0:02:05.12,0:02:08.01,Default,,0000,0000,0000,,could really just view\Nthis as 5 times 4.
Dialogue: 0,0:02:08.01,0:02:11.00,Default,,0000,0000,0000,,So let's just evaluate that\Nright from the get go.
Dialogue: 0,0:02:11.00,0:02:14.94,Default,,0000,0000,0000,,So this is going to result in\N8 plus-- and really, when
Dialogue: 0,0:02:14.94,0:02:16.65,Default,,0000,0000,0000,,you're evaluating the\Nparentheses, if your evaluate
Dialogue: 0,0:02:16.65,0:02:18.98,Default,,0000,0000,0000,,this parentheses, you literally\Njust get 5, and you
Dialogue: 0,0:02:18.98,0:02:21.07,Default,,0000,0000,0000,,evaluate that parentheses, you\Nliterally just get 4, and then
Dialogue: 0,0:02:21.07,0:02:22.93,Default,,0000,0000,0000,,they're next to each other,\Nso you multiply them.
Dialogue: 0,0:02:22.93,0:02:28.17,Default,,0000,0000,0000,,So 5 times 4 is 20 minus--\Nlet me stay
Dialogue: 0,0:02:28.17,0:02:29.96,Default,,0000,0000,0000,,consistent with the colors.
Dialogue: 0,0:02:29.96,0:02:34.29,Default,,0000,0000,0000,,Now let me write the next\Nparenthesis right there, and
Dialogue: 0,0:02:34.29,0:02:38.05,Default,,0000,0000,0000,,then inside of it, we'd evaluate\Nthis first. Let me
Dialogue: 0,0:02:38.05,0:02:40.08,Default,,0000,0000,0000,,close the parenthesis\Nright there.
Dialogue: 0,0:02:40.08,0:02:43.28,Default,,0000,0000,0000,,And then we have plus 44.
Dialogue: 0,0:02:43.28,0:02:46.25,Default,,0000,0000,0000,,So what is this thing right here\Nevaluate to, this thing
Dialogue: 0,0:02:46.25,0:02:47.80,Default,,0000,0000,0000,,inside the parentheses?
Dialogue: 0,0:02:47.80,0:02:49.17,Default,,0000,0000,0000,,Well, you might be tempted\Nto say, well, let me
Dialogue: 0,0:02:49.17,0:02:50.16,Default,,0000,0000,0000,,just go left to right.
Dialogue: 0,0:02:50.16,0:02:53.77,Default,,0000,0000,0000,,6 plus 10 is 16 and then\Ndivide by 2 and
Dialogue: 0,0:02:53.77,0:02:54.78,Default,,0000,0000,0000,,you would get 8.
Dialogue: 0,0:02:54.78,0:02:57.08,Default,,0000,0000,0000,,But remember: order\Nof operations.
Dialogue: 0,0:02:57.08,0:03:01.76,Default,,0000,0000,0000,,Division takes priority over\Naddition, so you actually want
Dialogue: 0,0:03:01.76,0:03:04.85,Default,,0000,0000,0000,,to do the division first, and\Nwe could actually write it
Dialogue: 0,0:03:04.85,0:03:05.79,Default,,0000,0000,0000,,here like this.
Dialogue: 0,0:03:05.79,0:03:07.96,Default,,0000,0000,0000,,You could imagine putting\Nsome more parentheses.
Dialogue: 0,0:03:07.96,0:03:09.79,Default,,0000,0000,0000,,Let me do it in that\Nsame purple.
Dialogue: 0,0:03:09.79,0:03:13.20,Default,,0000,0000,0000,,You could imagine putting some\Nmore parentheses right here to
Dialogue: 0,0:03:13.20,0:03:16.11,Default,,0000,0000,0000,,really emphasize the fact that\Nyou're going to do the
Dialogue: 0,0:03:16.11,0:03:17.76,Default,,0000,0000,0000,,division first.
Dialogue: 0,0:03:17.76,0:03:24.74,Default,,0000,0000,0000,,So 10 divided by 2 is 5, so this\Nwill result in 6, plus 10
Dialogue: 0,0:03:24.74,0:03:27.56,Default,,0000,0000,0000,,divided by 2, is 5.
Dialogue: 0,0:03:27.56,0:03:28.73,Default,,0000,0000,0000,,6 plus 5.
Dialogue: 0,0:03:28.73,0:03:32.23,Default,,0000,0000,0000,,Well, we still have to evaluate\Nthis parentheses, so
Dialogue: 0,0:03:32.23,0:03:34.60,Default,,0000,0000,0000,,this results-- what's\N6 plus 5?
Dialogue: 0,0:03:34.60,0:03:36.05,Default,,0000,0000,0000,,Well, that's 11.
Dialogue: 0,0:03:36.05,0:03:38.63,Default,,0000,0000,0000,,So we're left with\Nthe 20-- let me
Dialogue: 0,0:03:38.63,0:03:39.63,Default,,0000,0000,0000,,write it all down again.
Dialogue: 0,0:03:39.63,0:03:44.05,Default,,0000,0000,0000,,We're left with 8 plus\N20 minus 6 plus 5,
Dialogue: 0,0:03:44.05,0:03:47.00,Default,,0000,0000,0000,,which is 11, plus 44.
Dialogue: 0,0:03:47.00,0:03:50.82,Default,,0000,0000,0000,,And now that we have everything\Nat this level of
Dialogue: 0,0:03:50.82,0:03:53.58,Default,,0000,0000,0000,,operations, we can just\Ngo left to right.
Dialogue: 0,0:03:53.58,0:03:58.77,Default,,0000,0000,0000,,So 8 plus 20 is 28, so you\Ncan view this as 28
Dialogue: 0,0:03:58.77,0:04:01.89,Default,,0000,0000,0000,,minus 11 plus 44.
Dialogue: 0,0:04:01.89,0:04:06.03,Default,,0000,0000,0000,,28 minus 11-- 28 minus 10\Nwould be 18, so this
Dialogue: 0,0:04:06.03,0:04:07.39,Default,,0000,0000,0000,,is going to be 17.
Dialogue: 0,0:04:07.39,0:04:10.63,Default,,0000,0000,0000,,It's going to be 17 plus 44.
Dialogue: 0,0:04:10.63,0:04:16.21,Default,,0000,0000,0000,,And then 17 plus 44-- I'll\Nscroll down a little bit.
Dialogue: 0,0:04:16.21,0:04:21.16,Default,,0000,0000,0000,,7 plus 44 would be 51, so\Nthis is going to be 61.
Dialogue: 0,0:04:21.16,0:04:24.94,Default,,0000,0000,0000,,So this is going to\Nbe equal to 61.
Dialogue: 0,0:04:24.94,0:04:26.46,Default,,0000,0000,0000,,And we're done!
Dialogue: 0,0:04:26.46,0:04:26.60,Default,,0000,0000,0000,,