Download Negative Numbers, Opposites and Additive Inverses

Negative Numbers,
Opposites and Additive
Inverses
Additive Inverse
In the History of Numbers presentation we talked about
Brahmagupta who showed that subtracting a number from
itself results in zero. We call that number the additive
inverse.
The additive inverse is the opposite or negative of a
number and the sum of a number and its additive inverse is
zero.
Examples: 2+-2 = 0
-3+3 = 0
Negative Integers
We know that each positive integer has a corresponding
negative integer. These corresponding integers are called
opposites. They are also called additive inverses.
Examples: -2 is the opposite of 2 and -2 + 2 = 0
15 is the opposite of -15 and 15 + -15 = 0
We may say that 2 is the opposite of -2, -15 is the opposite
of 15 and so on. They are opposites of each other.
The words opposite, additive inverse, negative and minus
are often used in the same sense.
Example: -2 may
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Other examples?
be read in any of the following ways:
“negative 2”
“minus 2”
“the opposite of 2”
“the additive inverse of 2”
Uhhhh, so why do we care…….
We care, because now we are going to be doing some
work with positive and negative numbers and we need
some rules.
Three
1.
2.
3.
rules we need are:
Same-sign rule
Mixed-sign rule
Neighbor-sign rule
Same-sign rule
When you are combining numbers with the same sign, keep the
sign and add the numbers.
Again, we start with the number line……
Let’s add two positive numbers:
3 + 2 = + 3 + 2= +(3 + 2) = 5
Let’s add two negative numbers:
-3 + -2 = -(3 + 2) = -5
Examples?
Steps to the same-sign rule
1. Ask yourself: Is the sign of the numbers positive or
negative?
2. Whichever sign the numbers have, put down that sign
followed by a set of parentheses.
3. Inside the parentheses, place the numbers and stick a plus
sign between them.
4. Add the numbers, take away the parentheses and there is
your answer.
Examples:
1. 18 + 20
2. - 15 - 5
3. 7 + 51
4. 100 + 256
5. - 18 - 5
6. - 8 - 9
Real life example!
When working out this rule with positive numbers, imagine that
you receive money from different people.
Example: Suppose you receive $2 from one person and $3
from another person. Altogether you have $5, so the answer is
+5
When working with negative numbers, imagine that you owe
money to different people.
Example: Suppose you owe $3 to one friend and you also
owe $2 to another friend. Altogether you owe $5, so the
answer is -5. Owing money is a pain, so it’s negative!
Mixed-sign rule
When you are combining numbers with mixed signs, ignore
the signs and see which number is bigger. Take the sign of
the bigger number and write it down in front of a set of
parenthesis. Then, inside the parenthesis, subtract the
smaller number from the larger number.
Example: 5 - 9 = -(9 - 5) = -4
-3 + 10 = +(10 - 3) = +7
Examples?
Steps to the Mixed-sign rule
1. Ignore the signs, and see which number is bigger.
2. Take the sign in front of that larger number and place it in
front of a set of parentheses.
3. Inside the parentheses and still ignoring the signs, place the
larger number first and subtract the smaller number from it.
4. Subtract the numbers, take away the parenthesis and there
is your answer.
Examples:
1. 18 - 2
2. -15 + 8
3. 22 - 24
4. -88 + 10
5. -9 + 15
6. -10 + 17
Neighbor-Sign Rule
You use the neighbor-sign rule when two signs stand next to
each other with no number between them.
You might see it like this: 2 - (+3) or 2 - +3.
The two signs merge to become one.
Here is the pattern: + + turns into +
+ - turns into - + turns into - - turns into +
Steps to the Neighbor-sign rule
1. Look at the two neighboring signs.
2. Using the patterns, determine which sign the two signs
will become.
3. Change the signs into one sign.
4. Work out your answer using either the same-sign rule or
the mixed-sign rule.
Note: The Neighbor-sign rule has no bearing on what the
final sign of the answer will be.
Examples:
1. 13 - (-4)
2. 15 + (-3)
3. -5 + (+2)
4. -7 - (+4)
5. -10 - (+8)
6. 12 + (-9)