Tip:
Highlight text to annotate it
X
1.2b: Operations with Integers –
Multiply and Divide with Different Signs
There is a pattern to multiplying
and recognizing this pattern can help assist you in doing the problem.
When we have 2 x 2, we get the answer of 4;
2 x 1 is 2, 2 x 0 would be 0.
Therefore, if you see that I have been decreasing by 2 each time,
2 x -1 would therefore results in a -2.
The pattern here is that we decrease by 2.
Multiplying and dividing with a negative and a positive
or a positive and a negative
results in an answer that is always negative.
There are a couple easy methods to remembering this.
To remember, you can think of the idea
that when good or positive things happen to bad or negative people,
it is a bad thing or in otherwise if positive times a negative,
you will result in a negative.
To remember the opposite of this, you can think that
when bad or negative things happen to good or positive people,
it is a bad thing or a negative times a positive is a negative.
This also applies with division.
It follows the same rules
and that when you have a positive divided by a negative,
you get a negative answer or a negative divided by a positive,
you will result in a negative answer.
Let us look at example 1.
In example 1, we are asking -54 ÷ 9.
First, assess what the number will be by just asking what is 54 ÷ 9,
the answer to that is 6.
Now that we have the number answer, we must determine the sign on that answer.
We look at the signs in the problem.
There is a negative on the 54.
There is no symbol on the 9.
When no symbol is written, it is assumed that the number is positive.
We therefore have a negative divided by a positive.
When we have a negative divided by a positive,
we can remember this with the idea that when bad things happen to good people,
it is a bad thing or results in a negative.
Therefore, -54 ÷ 9 results in -6.
In the next example, we apply the same concept to a multiplication problem.
We have 3 x -8.
Remember that if there is no symbol between a number and the parenthesis,
it is assumed that this is multiplication.
This problem is not asking 3 minus 8.
We start by doing the number portion of this problem
and assessing what 3 x 8 is.
3 x 8 is 24.
We write down that answer
and then decide what the sign on this number should be.
We look at the 3, since no sign is given, we assume that it is a positive.
We then look at the 8 and see that it is a negative.
So, we have a positive times a negative.
When we have a positive times a negative, it then results in a negative answer.
Remember, you can always think of the saying
when good things happen to bad people, that is a bad thing.
The answer is therefore -24.
Remember, when multiplying and dividing with different signs
that a positive and a negative is a negative
and a negative and a positive results in a negative.