Integers

Subtracting Integers

Subtract integers using Keep-Change-Flip: keep the first integer, change subtraction to addition, flip the sign of the second integer.

Example

Rewrite subtraction as adding the opposite, then use integer addition rules.

highlighted = computed this step

Step 1 — Set up

Set up the expression.

−3−(−5)-3 - ( -5 )
Start with -3 - (-5).move left 30-3The first number -3 puts the start point left of 0.

Step 2 — Add the opposite

Flip the second number: the opposite of -5 is 5.

−(−5)=5-( -5 )= \hl{5}
The opposite of -5 is 5.-505So subtracting -5 becomes adding 5.

Step 3 — Rewrite as addition

Rewrite subtraction as addition: -3 + 5.

−3+5-3 + \hl{5}
Rewrite subtraction as -3 + 5.move left 30-3move right 52Adding positive 5 means moving right.

Step 4 — Apply sign rule

Different signs: 5 - 3 = 2.

different signs5−3=2\text{different signs} \quad 5 - 3 = \hl{2}
Add the opposite: move right 5.move left 30-3move right 52From -3, moving right 5 lands at 2.

Step 5 — Result

Read the final result.

22
-3 - (-5) = 2.move left 30-3move right 52The final point is 2.
subtract-integers To subtract integers: a - b = a + (-b). - Keep the first integer as-is. - Change the subtraction sign to addition. - Flip (negate) the second integer. Then apply integer addition rules.