Transcript Combining Signed Numbers

Combining Signed Numbers
Adding and subtracting signed numbers
Step 1: Collapse signs
Sometimes you’ll see two signs in a row:
5 + ( -2 )
or
7 – ( -5 )
Collapse them into a single sign using the rule:
if the signs are the same, make a single +
if the signs are different, make a single –
5 + ( -2 ) = 5 - 2
and
7–(-5)=7+5
Step 2: Combine the numbers
Once each number has only one sign, combine them
using the following rules:
if the signs are the same, ADD
if the signs are different, SUBTRACT
Step 3: Determine the sign of the answer
The sign of the larger number
(just the ‘number’ part – forget the signs for a second)
goes on the answer
BIG sign wins!
A rule to remember
If the first number is positive, it doesn’t
have to show its sign. All of the other
numbers do have to show their signs.
5–2+3
5 is positive ~ 2 is negative ~ 3 is positive
Example 1:
5+(+2)
Collapse the 2 signs in a row:
5+(+2)
5+2
Signs are the same therefore +
Example 1:
Really
5+(+2)
5+2
+5+2
The signs are the same, ADD the number parts
5 plus 2 = 7
Example 1:
5+(+2)
+5+2
5 plus 2 = 7
BIG sign wins!
Sign of the 5 goes on the answer: + 7
Example 2:
5+(-2)
Collapse the 2 signs in a row:
5+(-2)= 5-2
The signs are different, therefore -
Example 2:
Really
5+(-2)
5-2
+5-2
Signs different, SUBTRACT the number parts
5 minus 2 = 3
Example 2:
5+(-2)
+5-2
5 minus 2 = 3
BIG sign wins!
Sign of the 5 goes on the answer: + 3
Example 3:
-5+(+2)
Collapse the 2 signs in a row:
-5+(+2)= 5+2
The signs are the same, therefore +
Example 3:
-5+(+2)
-5+2
Signs different, SUBTRACT the number parts
5 minus 2 = 3
Example 3:
-5+(+2)
-5+2
5 minus 2 = 3
BIG sign wins!
Sign of the 5 goes on the answer: - 3
REMEMBER THE RULES
Collapse your signs
same +
different -
Decide whether to add or subtract
same +
different -
Sign of the larger goes on the answer
(BIG sign wins)