Combining Signed Numbers Adding and subtracting signed numbers
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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: 5 + ( + 2 )
5 + 2 Really + 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: 5 + ( - 2 )
5 - 2 Really + 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)
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