Adding Integers. Adding Integers.notebook. September 22, Symbols. Addition: A walk on the number line. Let's do on the number line.

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1 Symbols Adding Integers We will use "+" to indicate addition and " " for subtraction. Parentheses will also be used to show things more clearly. For instance, if we want to add 3 to 4 we will write: 4 + ( 3), which is clearer than Or if we want to subtract 4 from we will write: ( 4), which is clearer than Addition: A walk on the number line. While this section is titled "Addition" we're going to learn here how to both add and subtract using the number line. Addition and subtraction are inverse operations (they have the opposite effect). If you add a number and then subtract the same number you haven't changed anything. Addition undoes subtraction, and vice versa. Addition: A walk on the number line. Here's how it works. 3. Walk the number of steps given by the second number. Rules for directions Go in the opposite direction when subtracting, rather than adding, the second number Subtracting a negative number means you move to the right: since that's the opposite of moving to the left

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3 You can always add using the number line. But if we study our results, we can see how to get the same answers without having to draw the number line. We'll get the same answers, but more easily = ( ) = To add integers with the same sign. Add the absolute value of the integers. 2. The sign stays the same. (Same sign, find the sum) + ( 7) = = = 7; both signs are positive; so = 7 We can see some patterns here that allow us to create rules to get these answers without drawing. 4 + ( ) = = 9; both signs are negative; so 4 + ( ) = Interpreting the Absolute Value Approach The reason the absolute value approach works, if the signs of the integers are the same, is: The absolute value is the distance you travel in a direction, positive or negative. If both numbers have the same sign, the distances will add together, since they're both asking you to travel in the same direction. To add integers with different signs. Find the difference of the absolute values of the integers. 2. Keep the sign of the integer with the greater absolute value. + ( 7) = 2 (Different signs, find the difference) = 2; 7 > and 9 is negative; so + ( 7) = 2 If you walk one mile west and then two miles west, you'll be three miles west of where you started

4 Interpreting the Absolute Value Approach Adding Rational Numbers: If the signs of the integers are the different: For the 2 nd leg of your trip you're traveling in the opposite direction of the st leg, undoing some of your original travel. The total distance you are from your starting point will be the difference between the two distances. The sign of the answer must be the same as that of the larger number (in absolute value), since that's the direction you traveled farther. If you walk one mile west and then two miles east, you'll be one mile east of where you started. To add integers with the same sign. Add the absolute value of the integers. 2. The sign stays the same. (Same sign, find the sum) To add integers with different signs. Find the difference of the absolute values of the integers. 2. Keep the sign of the integer with the greater absolute value. (Different signs, find the difference) ( 4) = ( 4) = ( 20) = 4 + ( 30) =

5 + 0 = Try these. a) + ( 8) b) 4 + ( 60) c) d) 4 + ( 4) e) The temperature in North Dakota was C at 4 A.M. It had fallen 3 C since 3 A.M. What was the temperature at 3 A.M.? Use integer addition to find the starting temperature. 02 Oct 0:6 AM The teacher used the number line shown to simplify a numerical expression. What expression is shown? Write three addition problems that have a sum of zero. a b. 8 + ( 3) c. + ( 3) d. 3 + Sep 7 0:03 AM Oct 2 6:2 PM Sep 22 7:30 AM