Download Arithmetic of Signed Numbers

Arithmetic of Signed Numbers
Addition: There are 2 cases, like signs and different signs.
Like Signs
1. Add the numbers.
2. Keep the sign.
Example: -3 + 5
Different Signs
1. Subtract the numbers.
2. Take the sign of the larger (absolute value).
Decide which rule applies.
This problem has numbers to add which have different signs.
We will subtract the numbers. The sign will come from the 5
because it is farther from 0. (It has the larger absolute value.)
-3 + 5 = 2
Example: -3 + (-4)
Decide which rule applies. Look at the signs.
This problem has numbers which have the same kind of sign.
Add the numbers and keep the negative sign.
-3 + (-4) = -7
Subtraction: Subtracting a positive number is the same as adding a negative number.
5 - 3 is the same as 5 + (-3). Since we have such nice clear rules for
addition, we can use them instead of thinking of subtraction. Just take
the subtraction sign as the sign of the number which follows and think
about the addition rules. So for 5 - 3 , we are thinking +5 and -3. These
are numbers with different signs. We should subtract and take the sign
of the larger. We get +2.
Example: -2 - 4
Think: -2 + (-4).
-2 -4
It is not necessary to write this step. Just slide the sign between the
numbers over to the number which follows.
These are numbers with like signs. We will add the numbers and
keep the sign.
-2 - 4 = -6
We have one situation where we need to be careful.
5 - (-3)
Slide the sign between the numbers to the number which follows.
5 -(-3) We want to add 5 and the opposite of -3. We can simplify the
second number. The opposite of -3 is +3.
5 + 3 =8
Example: -1 - (-7)
-1 -(-7)
-1 + 7
Slide the sign between the numbers to the number which follows.
Simplify. The opposite of -7 is +7.
Now you have numbers with different signs. Follow the different
signs rule. Subtract the numbers and take the sign of the larger.
-1 + 7 = 6
Multiplication and Division:
1. Perform regular multiplication or division.
2. Count the number of negative signs.
An odd number of negatives gives a negative answer.
An even number of negatives gives a positive answer.
Example: (-2)(3)(-1)(-4)
24
-24
Multiply. (Remember parentheses side by side means to
multiply.) Count the number of negative signs. There are 3
negatives. 3 is an odd number so the sign is negative.
Example: (-3)(-5)
= 15
You have 2 negative signs. 2 is even so the sign is positive.
Example: -12 ÷ -4 = 3
You have an even number of negatives.
Example:
−8
= -2
4
Example:
−2 1
=
−4 2
Reduce because it is a fraction. The sign is positive
because there are 2 (an even number) negatives.