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SOLUTION Because the distance between a and b is given by ͉ a - b ͉ , the distance between -5 and 3 is ͉–5-3͉=͉–8͉=8. 9 The distance between - 5 and 3 is 8. 9 veriﬁes that there are 8 units between -5 and 3 on the real number line. We obtain the same distance if we reverse the order of the subtraction: ͉ 3 - (-5) ͉ = ͉ 8͉ = 8. ● ● ● Check Point 7 Find the distance between -4 and 5 on the real number line. ᕩ Identify properties of the real numbers. Properties of Real Numbers and Algebraic Expressions When you use your calculator to add two real numbers, you can enter them in any order.
Here are three examples. • Woman, without her man, is nothing. Woman, without her, man is nothing. • What’s the latest dope? What’s the latest, dope? • Population of Amsterdam broken down by age and sex Population of Amsterdam, broken down by age and sex Name Meaning Examples Commutative Property of Addition Changing order when adding does not affect the sum. a + b = b + a • 13 + 7 = 7 + 13 • 13x + 7 = 7 + 13x Commutative Property of Multiplication Changing order when multiplying does not affect the product.
119. 3 * 10-23 gram. Find the mass of 20,000 molecules of oxygen. Express the answer in scientiﬁc notation. 120. 67 * 10-24 gram. Find the mass of 80,000 hydrogen atoms. Express the answer in scientiﬁc notation. 121. 2 * 107 seconds in a year. According to the United States Department of Agriculture, Americans consume 127 chickens per second. How many chickens are eaten per year in the United States? Express the answer in scientiﬁc notation. 122. Convert 365 days (one year) to hours, to minutes, and, ﬁnally, to seconds, to determine how many seconds there are in a year.