WEBVTT
00:00:01.840 --> 00:00:09.880
You are given three expressions: negative π₯ plus π¦, π₯π¦, and π₯ divided by π¦.
00:00:09.880 --> 00:00:18.840
When π₯ equals negative three and π¦ equals negative seven, which expression has the largest value?
00:00:19.800 --> 00:00:21.200
You must show your working.
00:00:23.200 --> 00:00:25.920
Weβre told that π₯ is equal to negative three.
00:00:26.520 --> 00:00:28.720
And π¦ is equal to negative seven.
00:00:30.000 --> 00:00:38.640
Before starting this question, it is worth remembering that when multiplying or dividing two negative numbers, we get a positive answer.
00:00:39.800 --> 00:00:47.320
Also when two negative signs are touching or weβre subtracting a negative number, our answer becomes positive.
00:00:49.120 --> 00:00:54.320
We will now substitute our values of π₯ and π¦ into the three expressions.
00:00:55.640 --> 00:00:58.880
The first expression is negative π₯ plus π¦.
00:00:59.960 --> 00:01:06.280
Substituting in our values gives us negative negative three plus negative seven.
00:01:07.520 --> 00:01:10.200
Adding a negative number is the same as subtracting.
00:01:10.800 --> 00:01:15.120
So in the bracket, we need to subtract seven from negative three.
00:01:16.600 --> 00:01:18.600
This is equal to negative 10.
00:01:20.080 --> 00:01:26.720
If we consider a number line, subtracting seven from negative three takes us down to negative 10.
00:01:28.440 --> 00:01:35.160
As mentioned earlier, subtracting a negative number or two negatives touching each other turns into a positive.
00:01:36.720 --> 00:01:40.640
This means that negative of negative 10 is equal to 10.
00:01:42.040 --> 00:01:51.560
The first expression, negative π₯ plus π¦, gives us an answer of 10 when π₯ equals negative three and π¦ equals negative seven.
00:01:53.360 --> 00:01:57.960
The second expression, π₯π¦, means π₯ multiplied by π¦.
00:01:58.680 --> 00:02:02.600
In this case, we need to multiply negative three by negative seven.
00:02:03.880 --> 00:02:07.640
Two negative numbers multiplied together make a positive number.
00:02:08.160 --> 00:02:11.360
And three multiplied by seven is equal to 21.
00:02:12.280 --> 00:02:17.640
Therefore, negative three multiplied by negative seven is also equal to 21.
00:02:19.320 --> 00:02:23.000
Finally, we have π₯ divided by π¦.
00:02:23.000 --> 00:02:25.960
This is equal to negative three divided by negative seven.
00:02:27.840 --> 00:02:31.920
When dividing two negative numbers, the answer is also positive.
00:02:33.280 --> 00:02:38.920
This means that negative three divided by negative seven is equal to three-sevenths.
00:02:40.960 --> 00:02:47.120
We now have three values for our expressions, 10, 21, and three-sevenths.
00:02:48.440 --> 00:02:49.680
All three are positive.
00:02:50.040 --> 00:02:52.200
And the largest number is 21.
00:02:52.800 --> 00:02:55.400
And the smallest number is three-sevenths.
00:02:56.880 --> 00:03:07.280
We can therefore conclude that when π₯ is equal to negative three and π¦ is equal to negative seven, the expression which has the largest value is π₯π¦.