More on Adding and Subtracting Integers

In the examples below, look at how the symbols for add, subtract, negative and positive are combined.

 1 Add a positive number to zero looks like this $0 + (+3)$ we say  ‘zero add positive 3’ 2 Add a negative number to zero looks like this $0 + (-3)$ we say ‘zero add negative 3’ 3 Subtract a positive number from zero looks like this $0 - (+3)$ we say ‘zero subtract positive 3’ 4 Subtract a negative number from zero looks like this $0 - (-3)$ we say ‘zero subtract negative 3’

Did you notice that the brackets around the numbers include the sign of the number?

The sign belongs to the number because it tells us which side of zero the number is on.

Including brackets around the number and its sign means the symbols refer to negative and/or positive.

When the symbols (either $+ / -$ ) refers to the operation (add or subtract), we don’t use brackets.

Summary: Operating with integers $(+, -)$

Question Equivalent toResult Notice the pattern
$3+({\color{red}{+}}5)$ $3+5$ $8$ 1. Adding a positive number is the same as just adding
$3+({\color{dodgerblue}{-}}5)$ $3-5$ $-2$ 2. Adding a negative number is the same as just subtracting
$3-({\color{red}{+}}5)$ $3-5$ $-2$ 3. Subtracting a positive number is the same as just subtracting
$3-({\color{dodgerblue}{-}}5)$ $3+5$ $8$ 4. Subtracting a negative number is the same as just adding

Now try these questions:

Question Equivalent to Result Notice the pattern
${\color{dodgerblue}{-}}3+({\color{red}{+}}5)$ ${\color{dodgerblue}{-}}3+5$

${\color{dodgerblue}{-}}3+({\color{dodgerblue}{-}}5)$ ${\color{dodgerblue}{-}}3-5$

${\color{dodgerblue}{-}}3-({\color{red}{+}}5)$ ${\color{dodgerblue}{-}}3-5$

${\color{dodgerblue}{-}}3-({\color{dodgerblue}{-}}5)$ ${\color{dodgerblue}{-}}3+5$