STAAR Review Adding / subtracting integers

Getting the idea  

Example 1 Add -3 + 5 Strategy: Use a number line to add the integers. Step 1: Begin at 0 on the number line. Move 3 units in the negative direction to locate -3. Step 2: From -3, move 5 units in the positive direction Step 3: Locate the point on the number line that represents the sum. The result is a point at +2. Solution: -3 + 5 = 2

Rules For Adding Signs Rule Both Positive  You can also use the signs of integers to help you add them. The table shows the rules for adding integers based on their signs. Rules for Adding Integers Signs Rule Both Positive  Add the numbers. The sum is positive.  Both Negative  Add the absolute values. The sum is negative.  One Positive , one Negative  Subtract the smaller absolute value from the larger absolute value. The sum has the sign of the integer with the larger absolute value.  OR 

EXAMPLE 2 Add -83 + 57 Strategy: Use rules for adding integers. Step 1: Examine the signs of the numbers. (The signs have different signs.) Step 2: Find the absolute values of the integers. |-83| = 83, |57| = 57 Step 3: Subtract the smaller absolute value from the larger absolute value. (83 - 57 = 26) Step 4: Take the sign of the integer with the larger absolute value. 83> 57, so -83 has a larger absolute value compared to 57. The sign of the sum is negative. Solution: -83 + 57 = -26

EXAMPLE 3 Strategy: Use rules for adding integers to find -64 + (-25) The table shows the changes in Michael’s checking account after two transitions. What is the net change in his checking account balance? Strategy: Use rules for adding integers to find -64 + (-25) Step 1: Examine the signs of the numbers. (The integers have the same sign. They are both negative.) Step 2: Find the absolute values of the integers. |-64| = 64, |-25| = 25 Step 3: Add the absolute values. (64 + 25 = 89) Step 4: Place a negative sign in front of the sum. -64 + (-25) = -89 Solution: The net change in Michael’s checking account balance is -89 dollars. Date Transaction Debit / Credit ($) 4/12 Check # 221 -64 4/16 ATM withdrawal -25

EXAMPLE 4 The Greyhounds football team lost 7 yards on their first series of plays and gained 34 yards on their second series. What were the net yards gained or lost after the first two series of plays? Strategy: Use rules for adding integers to find -7 + 34 Step 1: Examine the signs of the numbers. (The integers have different signs.) Step 2: Find the absolute values of the integers. |-7| = 7, |34| = 34 Step 3: Subtract the smaller absolute value from the larger absolute value. (34 – 7 = 27) Step 4: Take the sign of the integer with the larger absolute value. 34> 7, so 34 has a larger absolute value compared to -7. The sign of the sum is positive. Solution: The net change in yards for the first 2 series was positive 27 yards.

Subtracting integers Rule for subtracting integers: To subtract an integer, add it’s opposite. Then follow rules for adding integers. Example: Subtract 4 – 6 Strategy: Use integer rules to subtract integers. Step 1: Rewrite the problem by adding the opposite. (add a line and change the sign) 4 – 6 = 4 + (-6) Step 2: Examine the signs of the numbers. (The integers have different signs.) Step 3: Find the absolute values of the integers. |4| = 4, |-6| = 6 Step 4: Subtract the smaller absolute value from the larger absolute value. (6 - 4 = 2) Step 5: Take the sign of the integer with the larger absolute value. 6> 4, so -6 has a larger absolute value compared to 4. The sign of the sum is negative. Solution: 4 – 6 = -2.