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)