2.3 Subtracting Real Numbers Objectives: Define subtraction in terms of addition. Subtract numbers with like & unlike signs. Standards Addressed: 2.1.8.F:

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Presentation transcript:

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

Ex. 1

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

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.

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

Ex. 3 a.

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

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 = 6 or = 3 The sums are all whole numbers.

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