WEBVTT
00:00:00.750 --> 00:00:06.450
Calculate 75 minus 12.66 all in parentheses times five.
00:00:06.840 --> 00:00:12.880
So notice in our question, we have subtraction, we have multiplication, and we have parentheses.
00:00:12.910 --> 00:00:14.020
So where do we begin?
00:00:14.560 --> 00:00:24.570
We need to follow the order of operations, sometimes called PEMDAS because we begin with P, the parentheses, sometimes called brackets.
00:00:25.120 --> 00:00:28.430
Then, we have exponents also known as powers.
00:00:28.810 --> 00:00:35.810
Then after we take care of the parentheses and the exponents, we move to multiplication and division.
00:00:36.190 --> 00:00:38.910
And this is whichever comes first, left to right.
00:00:39.760 --> 00:00:45.740
And lastly, we have addition and subtraction, following the same pattern: whichever comes first, left to right.
00:00:46.410 --> 00:00:47.750
So we go through this list.
00:00:47.750 --> 00:00:49.010
We begin with parentheses.
00:00:49.070 --> 00:00:50.470
Do we have any parentheses?
00:00:50.790 --> 00:00:51.590
Yes, we do.
00:00:51.930 --> 00:00:55.570
So this means we must work inside of the parentheses first.
00:00:56.140 --> 00:00:58.090
And we have subtraction inside of here.
00:00:58.130 --> 00:01:01.930
So we need to take 75 and subtract 12.66.
00:01:02.300 --> 00:01:10.140
And to do so, we need to line up our decimal points and add two zeros at the end where it’s needed of this 75.
00:01:10.640 --> 00:01:14.640
So we begin on the right with zero minus six which we can’t do.
00:01:15.090 --> 00:01:18.450
So we need to borrow, which we can’t take anything from zero.
00:01:18.630 --> 00:01:19.980
So we have to move to the left.
00:01:20.310 --> 00:01:21.690
We can borrow from the five.
00:01:21.890 --> 00:01:24.240
So if we borrow from the five, it becomes a four.
00:01:24.720 --> 00:01:30.610
Now if we borrowed one from five, we can bring the one over here to making the zero a 10.
00:01:31.430 --> 00:01:40.130
So now that this number is a 10 and not a zero, we can borrow one from 10 making it nine and making our original zero a 10.
00:01:40.380 --> 00:01:43.070
So 10 minus six is four.
00:01:43.730 --> 00:01:47.830
Now, in the next column, we have nine minus six which is three.
00:01:48.170 --> 00:01:49.360
Bring down our decimal point.
00:01:49.860 --> 00:01:52.320
And then four minus two is two.
00:01:52.370 --> 00:01:55.810
And then lastly, seven minus one is six.
00:01:56.200 --> 00:02:01.700
So, so far, we’ve worked inside the parentheses and we took 75 minus 12.66.
00:02:02.160 --> 00:02:08.030
So now, we have 62.34 times five after we’ve subtracted.
00:02:08.620 --> 00:02:11.260
So that means we only have multiplication left.
00:02:11.660 --> 00:02:13.560
There aren’t exponents we need to work with.
00:02:14.080 --> 00:02:15.440
But there is multiplication.
00:02:15.850 --> 00:02:19.070
So we need to take 62.34 times five.
00:02:19.370 --> 00:02:22.210
So we take five times four which is 20.
00:02:22.360 --> 00:02:28.120
So we carry the two and then we take five times three which is 15 but then add two.
00:02:28.630 --> 00:02:29.730
And we get 17.
00:02:30.140 --> 00:02:32.420
Then, we take five times two which is 10.
00:02:32.520 --> 00:02:34.900
But then, we add one, so 11.
00:02:34.900 --> 00:02:35.830
We carry the one.
00:02:36.200 --> 00:02:40.890
And then five times six which is 30 plus one, so 31.
00:02:41.290 --> 00:02:44.730
Now notice that 62.34 is a decimal.
00:02:44.730 --> 00:02:45.870
So we have a decimal point.
00:02:46.410 --> 00:02:51.950
And since we have 62.34, there are two places after the decimal point.
00:02:51.980 --> 00:03:01.790
So we need that here in our answer, so 311.70, which we could write as 311.7.
00:03:01.830 --> 00:03:03.400
We don’t need the zero at the end.
00:03:03.790 --> 00:03:05.070
But either way would be correct.
00:03:05.650 --> 00:03:11.510
Now, let’s show one more way that we could have multiplied 62.34 and five together.
00:03:11.990 --> 00:03:23.180
For 62.34 times five, we could have taken 62 times five and our decimal portion times five 0.34 times five and then added those together.
00:03:23.290 --> 00:03:26.690
And that would have given us 311.70.
00:03:27.150 --> 00:03:32.480
So looking at that, 62 times five: five times two is 10.
00:03:32.480 --> 00:03:33.340
So we carry the one.
00:03:33.910 --> 00:03:35.420
Five times six is 30.
00:03:35.420 --> 00:03:37.630
And 30 plus one is 31.
00:03:38.140 --> 00:03:40.950
So 62 times five gives us 310.
00:03:41.490 --> 00:03:43.810
And now, 0.34 times five.
00:03:43.810 --> 00:03:46.300
We take five times four which is 20.
00:03:46.300 --> 00:03:47.230
So we carry the two.
00:03:47.260 --> 00:03:51.360
And then, five times three is 15 plus two is 17.
00:03:51.720 --> 00:03:52.770
So we carry the one.
00:03:53.280 --> 00:03:55.630
And five times zero is zero.
00:03:55.690 --> 00:03:57.700
But zero plus one is one.
00:03:57.900 --> 00:04:00.310
And then, we have our decimal point with two spaces.
00:04:00.540 --> 00:04:03.760
So we do the same for our answer, 1.70.
00:04:04.360 --> 00:04:14.710
So 310 plus 1.70 would give us an answer of 311.70 or 311.7.
00:04:15.050 --> 00:04:21.690
So once again, our final answer will be 311.70 or 311.7.