1. 2.3 Subtracting Real Numbers Objectives: Define subtraction in terms of addition. Subtract numbers with like & unlike signs. Standards Addressed: 2.1.8.F: Use the number line model to demonstrate integers and their applications. 2.1.3.K: Describe the inverse relationship between addition and subtraction.

3. Ex. 1

4. Ex. 2 Use the definition of subtraction to find each difference. -11 – (-5.5) _________________________ -2.7 – 5.3 _________________________ 2 – 5 _________________________ 8.2 – 6 _________________________ -11 + 5.5= -5.5 -2.7 + - 5.3 = -8 2 + -5 + -3 8.2 + -6 = 2.2

5. Measuring Distance on a Number Line Sometimes you will need to determine the distance between points on a number line. One method of doing this uses absolute value. To find the distance between points A, - 4, and B, 2, subtract the values, and then find the absolute value of the difference. The distance between -4 and 2 is |2 – (-4)| = |6| = 6, or |(-4) – 2| = |-6| = 6.

6. In general, if you let a represent the value for point A and let b represent the value for point B, the distance between points A and B on a number line is

7. Ex. 3 a.

8. Ex. 3 b. Find the distance between -2 and 13 on a number line. | -2 – 13 | = | -15 | = 15

9. Closure Under Addition The sum of any 2 real numbers is a real number. To mathematicians, this means that the set of real numbers is closed under addition. I.E. 2 + 4 = 6 or 3 + 0 = 3 The sums are all whole numbers.

10. NOT SUBTRACTION The set of whole number is closed under addition, but NOT subtraction. I.E. 4 – 8 = -4 Not a whole number