## Video and Examples

Here are some very important things we have discovered so far:

 Important understandings of ADDITION Adding a positive number goes to the right. Adding a negative number goes to the left.
 Important understandings of SUBTRACTION Subtracting a positive number goes to the left.  Subtracting a negative number goes to the right.

Putting these understandings together we find that

• Subtracting a negative number is the same as adding a positive number.
• Subtracting a positive number is the same as adding a negative number.

Here are two examples showing that each subtraction problem has a related addition problem that gives the exact same answer.

 5 – (-8) = 13 5 + 8 = 13 5 – 2 = 3 5 + (-2) = 3 Let's practice a little:

 Change the subtraction expression into an addition expression. Then simplify. (-4) – (+6) (-4) – (+6) will result in the same answer as (-4) + (-6). (-4) – (+6) = (-4) + (-6) = -10 (-7) – (-9) (-7) – (-9) will result in the same answer as (-7) + (+9) (-7) – (-9) = (-7) + (+9) = +2 (+3) – (+5) (+3) – (+5) will result in the same answer as (+3) + (-5) (+3) – (+5) = (+3) + (-5) = -2 (+8) – (-2) (+8) – (-2) will result in the same answer as (+8) + (+2) (+8) – (-2) = (+8) + (+2) = +10

By looking at the four examples above, we can see a pattern that occurs in each of the examples:

• The first integer stays the same;
• The subtraction sign turns into an addition sign;
• The second integer turns into its opposite.

In fact, the rule for subtracting positives and negatives is:

 To subtract two integers: The first integer stays the same and add the opposite of the second integer

# Self-Check

 Question 1 Write the following expression using addition. Then simplify. (+8) – (-5) [show answer] (+8) – (-5) (+8) + (+5) = +13

 Question 2 Write the following expression using addition. Then simplify. (-3) – (-4) [show answer] (-3) – (-4) (-3) + (+4) = +1

 Question 3 Write the following expression using addition. Then simplify. (-6) – (+7) [show answer] (-6) – (+7) (-6) + (-7) = -13