Choose the expression(s) that is (are) equivalent to the given rational number. 20 A. B. C..5 A..67 B..6 C. 30 D. E. 1 4 D. 4 E.

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1 . EXERCISES Choose the expression(s) that is (are) equivalent to the given rational number... 0 A. B. C.. A.. B.. C. 0 D..0 E.. D.. E.... A.. B.. C.. A.. B.. C D. E. D. E. 00 Use the fundamental property of rational numbers to write each of the following in lowest terms..... Use the fundamental property to write each of the following in three other ways For each of the following, write a fraction in lowest terms that represents the portion of the figure that is in color. (a) (b) (c) (d). For each of the following, write a fraction in lowest terms that represents the region described. (a) the dots in the rectangle as a part of the dots in the entire figure (b) the dots in the triangle as a part of the dots in the entire figure (c) the dots in the rectangle as a part of the dots in the union of the triangle and the rectangle (d) the dots in the intersection of the triangle and the rectangle as a part of the dots in the union of the triangle and the rectangle. Refer to the figure for Exercise and write a description of the region that is represented by the fraction.. Batting Averages In a softball league, the first six games produced the following results: Greg Tobin got hits in 0 at-bats, and Jason Jordan got hits in 0 at-bats. Which player (if either) had the higher batting average?

2 0 CHAPTER The Real Numbers and Their Representations. Batting Averages After ten games, the following batting statistics were obtained. Player At-bats Hits Home Runs Anne Kelly 0 Christine O Brien Brenda Bravener Otis Taylor 0 Carol Britz 0 0 Answer each of the following, using estimation skills as necessary. (a) Which player got a hit in exactly of his or her at-bats? (b) Which player got a hit in just less than of his or her at-bats? (c) Which player got a home run in just less than 0 of his or her at-bats? (d) Which player got a hit in just less than of his or her at-bats? (e) Which two players got hits in exactly the same fractional parts of their at-bats? What was the fractional part, reduced to lowest terms?. Refer to the margin note discussing the use of common fractions on early U.S. copper coinage. The photo on the right here shows an error near the bottom that occurred on certain early cents. Discuss the error and how it represents a mathematical impossibility Recipe for Grits The following chart appears on a package of Quaker Quick Grits. Microwave Stove Top Servings Water cup cup cups cups Grits Tbsp Tbsp cup cup Salt (optional) dash dash tsp tsp (a) How many cups of water would be needed for microwave servings? (b) How many cups of grits would be needed for stove-top servings? (Hint: is halfway between and.). U.S. Immigrants More than million immigrants were admitted to the United States between 0 and. The pie chart gives the fractional number from each region of birth for these immigrants. U.S. IMMIGRANTS BY REGION OF BIRTH Perform the indicated operations and express answers in lowest terms. Use the order of operations as necessary Asia 0 Europe 00 Other Source: U. S. Bureau of the Census. Latin America (a) What fractional part of the immigrants were from Other regions? (b) What fractional part of the immigrants were from Latin America or Asia? (c) How many (in millions) were from Europe?

3 . Rational Numbers and Decimal Representation The mixed number represents the sum. We can convert to a fraction as follows:. The fraction can be converted back to a mixed number by dividing into. The quotient is, the remainder is, and the divisor is. Convert each mixed number in the following exercises to a fraction, and convert each fraction to a mixed number It is possible to add mixed numbers by first converting them to fractions, adding, and then converting the sum back to a mixed number. For example, The other operations with mixed numbers may be performed in a similar manner. Perform each operation and express your answer as a mixed number..... Solve each problem. 0.. Socket Wrench Meaurements A hardware store sells a 0-piece socket wrench set. The measure of the largest socket is in., while the measure of the smallest socket is in. What is the difference between these measures? 0. Swiss Cheese Hole Sizes Under existing standards, most of the holes in Swiss cheese must have diameters between and in. To accommodate new high-speed slicing machines, the USDA wants to reduce the minimum size to in. How much smaller is in. than in.? (Source: U.S. Department of Agriculture.) A quotient of quantities containing fractions (with denominator not zero) is called a complex fraction. There are two methods that are used to simplify a complex fraction. Method : Method : Simplify the numerator and denominator separately. Then rewrite as a division problem, and proceed as you would when dividing fractions. Multiply both the numerator and denominator by the least common denominator of all the fractions found within the complex fraction. (This is, in effect, multiplying the fraction by, which does not change its value.) Apply the distributive property, if necessary, and simplify. Use one of the methods above to simplify each of the following complex fractions

4 CHAPTER The Real Numbers and Their Representations The expressions in Exercises and are called continued fractions. Write each of the following continued fractions in the form p q, reduced to lowest terms. (Hint: Start at the bottom and work upward.).. Find the rational number halfway between the two given rational numbers ,,,,,,. Hourly Earnings in Private Industry The table shows average hourly earnings of various fields in private industry for a recent year. Find the average of these amounts. Private Industry Group Hourly Earnings Mining $.0 Construction.0 Manufacturing. Transportation, public utilities. Wholesale trade. Retail trade. Finance, insurance, real estate. Service. Source: U.S. Bureau of Labor Statistics.. Average Housing Costs The table shows the annual average housing costs in selected cities in. Find the average of these amounts. (The annual rental housing costs are based on a U.S. expatriate family of two earning $,000 and residing in a four- to six-room unit. Utilities and renter s insurance are included.) City Housing Cost (Dollars) Bombay, India $, Dusseldorf, Germany, Hong Kong, China, London, England, Madrid, Spain 0, New York, NY, Paris, France, San Francisco, CA 0, Singapore, Sydney, Australia,0 Tokyo, Japan, Source: Runzheimer International. In the March issue of The Mathematics Teacher there appeared an article by Laurence Sherzer, an eighth-grade mathematics teacher, that immortalized one of his students, Robert McKay. The class was studying the density property and Sherzer was explaining how to find a rational number between two given positive rational numbers by finding the average. McKay pointed out that there was no need to go to all that trouble. To find a number (not necessarily their average) between two positive rational numbers a b and c d, he claimed, simply add the tops and add the bottoms. Much to Sherzer s surprise, this method really does work. For example, to find a rational number between and, add to get the numerator and to get the denominator. Therefore, by McKay s theorem, is between and. Sherzer provided a proof of this method in the article. Use McKay s theorem to find a rational number between the two given rational numbers. 0. and. and. and 0. and. and. and. Apply McKay s theorem to any pair of consecutive integers, and make a conjecture about what happens in this case.. Explain in your own words how to find the rational number that is one-fourth of the way between two different rational numbers. Convert each rational number into either a repeating or a terminating decimal. Use a calculator if your instructor so allows

5 . Irrational Numbers and Decimal Representation Convert each terminating decimal into a quotient of integers. Write each in lowest terms Use the method of Example to decide whether each of the following rational numbers would yield a repeating or a terminating decimal. (Hint: Write in lowest terms before trying to decide.) Follow through on each part of this exercise in order. margin note on terminating and repeating decimals in this section, which refers to this idea. (a) Find the decimal for. (b) Find the decimal for.. It is a fact that... Multiply both sides of (c) By adding the decimal expressions obtained in this equation by. Does your answer bother you? parts (a) and (b), obtain a decimal expression for See the margin note on terminating and repeating. decimals in this section. (d) Does your result seem bothersome? Read the.