[br][b]Understanding the Concepts & Rules[/b]Based on the video and your notes, let's summarize the key ideas for adding and subtracting integers.[br][b]A. The Number Line as a Movement Tool (for both addition and subtraction)[/b]Think of the number line as your map:[br][list][*][b]Positive Numbers:[/b] Move to the [b]right[/b].[br][/*][*][b]Negative Numbers:[/b] Move to the [b]left[/b].[br][/*][*][b]Starting Point:[/b] Always begin at the first number in your problem.[br][/*][/list][b]B. Rules for Adding Integers[/b][list=1][*][b]Adding Numbers with the SAME Sign:[/b][br][list][*][b]Rule:[/b] Add their "plain" values (their [b]absolute values[/b]).[br][/*][*][b]Keep[/b] the original sign.[br][/*][*][b]Example:[/b][br][list][*]5+3=8 (Both positive, so add 5 and 3, keep positive)[br][/*][*]−5+(−3)=−8 (Both negative, so add 5 and 3, keep negative)[br][/*][/list][/*][/list][/*][*][b]Adding Numbers with DIFFERENT Signs:[/b][br][list][*][b]Rule:[/b] [b]Subtract[/b] the smaller "plain" value (absolute value) from the larger "plain" value.[br][/*][*]The sign of your answer will be the sign of the number that had the [b]larger absolute value[/b] (the number "further from zero").[br][/*][*][b]Example:[/b][br][list][*]5+(−3)=2 (Subtract 3 from 5, which is 2. The 5 is larger and positive, so the answer is positive.)[br][/*][*]−5+3=−2 (Subtract 3 from 5, which is 2. The 5 is larger and negative, so the answer is negative.)[br][/*][/list][/*][/list][/*][/list][b]C. Rule for Subtracting Integers: The "Keep, Change, Change" Trick![/b]Subtraction can be tricky, but there's a simple rule to turn it into an addition problem:[br][list][*][b]Rule:[/b] To subtract an integer, [b]add its opposite[/b].[br][list][*]This is often remembered as "[b]Keep, Change, Change[/b]" (KCC):[br][list=1][*][b]Keep[/b] the first number exactly the same.[br][/*][*][b]Change[/b] the subtraction sign ( ) to an addition sign (+ ).[br][/*][*][b]Change[/b] the sign of the second number to its [b]opposite[/b]. (If it was positive, make it negative. If it was negative, make it positive).[br][/*][/list][/*][/list][/*][/list][*][b]Example:[/b][br][list][*]3−7=?[list][*]Keep 3, Change − to +, Change 7 to −7[/*][*]Becomes: 3+(−7) (Now use addition rule for different signs)[br][/*][*]Solution: −4[/*][/list][/*][*]−5−2=?[list][*]Keep −5, Change − to +, Change 2 to −2[/*][*]Becomes: −5+(−2) (Now use addition rule for same signs)[br][/*][*]Solution: −7[/*][/list][/*][*]4−(−3)=?[list][*]Keep 4, Change − to +, Change −3 to +3[/*][*]Becomes: 4+3 (Now use addition rule for same signs)[br][/*][*]Solution: 7[br][/*][/list][/*][/list][/*]