>> Welcome to the Cypress College Math Review on Negative Numbers.
Negative numbers are numbers less than 0.
On the number line, the positive numbers are to the right of 0
and the negative numbers are to the left of 0.
In algebra, sometimes the same symbol has different meanings.
The minus sign symbol is used in 3 different ways.
If it used between 2 numbers, it means subtraction.
For example, 9 minus 4.
If the minus sign is in front of a number, it makes it a negative number.
For example, negative 6.
And if the minus sign is in front of a variable or a parenthesis,
it means the opposite of the number.
For example, minus x is the opposite of x. Minus negative 3 is the opposite of negative 3.
Objective 1, adding integers.
An integer is a positive or negative whole number or 0.
For positive numbers we just add as usual and the answer is positive.
For example, 2 plus 3 equals 5.
For negative numbers we add absolute values and make the answer negative.
Recall that the absolute value of a number is its distance from 0.
So this is always a positive quantity.
For example, negative 2 plus negative 3 equals negative 5.
This is because the absolute value of negative 2 is 2 and the absolute value
of negative 3 is 3 we add absolute values 2 plus 3 to get 5
and then we make the answer negative, negative 5.
When one number is 0, the sum is the other number.
For example, 4 plus 0 equals 4.
For a positive number and a negative number,
subtract the smaller absolute value from the greater absolute value.
Then if the positive number has the greater absolute value the answer is positive.
If the negative number has the greater absolute value, the answer is negative.
If the numbers have the same absolute value, the answer is 0.
Cases 1 and 3 in this list are pretty straightforward so now let's take a look
at some examples of Cases 2 and 4.
Example A, add negative 4 plus negative 7.
Since both numbers are negative, we add their absolute values to get 4 plus 7 equals 11
and keep the negative sign so the answer is negative 11.
Example B, 4 plus negative 7.
Since one number is positive and the other is negative, we subtract the smaller absolute value
from the greater absolute value; 7 minus 4 equals 3
but since the negative number has the greater absolute value the answer is negative 3.
Example C, negative 24 plus 24.
Both of these numbers have the same absolute value, 24.
When we subtract 24 minus 24, we get 0 and, therefore, the answer is 0.
Pause the video and try these problems.
Objective 2 is subtracting integers.
First, the opposite or additive inverse of a number A is written minus A. The opposite
of an opposite rule says for any real number A the opposite of minus A equals A.
To subtract 2 numbers we can use the following rule.
For any real numbers A and B, A minus B equals A plus the opposite of B. In other words,
the first number minus the second number is equal
to the first number plus the opposite of the second number.
An easy way to remember this is the KFC method.
K, keep the first number the same; F, flip the sign; and, C,
change the sign of the second number.
Now let's do some examples of subtraction.
Example A, 4 minus 13 is equal to 4 plus negative 13.
Using the KFC method, we keep the 4 the same, we flip the subtraction sign to addition,
and we change the second number 13 to its opposite negative 13.
Now we have changed the subtraction problem into an addition problem
and we can use the previous method for adding integers.
If you subtract absolute values, it would be 13 minus 4 which would be 9 but notice
that the negative number has the larger absolute value
and so that's why the answer is negative 9.
Example B. Zero minus negative 7.
Applying the KFC method we keep the 0 the same, the subtraction sign turns to addition
and the second number, negative 7, changes to its opposite
which is positive 7 then 0 plus 7 equals 7 and that is the answer.
Example C. Negative 8 minus negative 3.
Using the KFC process we keep the negative 8, we flip the subtraction sign to addition
and we change the sign of the second number making it positive 3.
And so we have rewritten the problem as negative 8 plus 3.
Now applying the rule for adding integers.
We subtract absolute values 8 minus 3 is 5
but because the negative number has the larger absolute value the answer is negative 5.
Pause the video and try these problems.
Objective 3 is multiplying and dividing integers.
Multiplying and dividing follow different rules than adding and subtracting.
To multiply or divide 2 non-zero numbers first using the absolute values we multiply
or divide as indicated.
Then if the signs are the same, the answer is positive;
if the signs are different, the answer is negative.
Example A, negative 3 times 7.
The absolute values are 3 and 7 and so we multiply 3 times 7 to get 21
and since the signs are different we have a negative 3 and a positive 7
that means the answer is going to be negative.
So the answer is negative 21.
Example B. Negative 3 times negative 6.
The absolute values of the numbers are 3 and 6 and 3 times 6 equals 18.
Since the signs of the 2 numbers are the same, both of them are negative,
the answer is going to be positive and so we get 18.
Example C. Negative 24 divided by 3.
We start by just dividing 24 divided by 3 equals 8
but since the signs are different the answer is going to be negative, negative 8.
Pause the video and try these problems.