6-1. Enrichment. inch. inch. inches. 3.5 cm to 4.5 cm milliliters to 22.5 milliliters pounds to pounds. Greatest Possible Error

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1 - Greatest Possible Error When you measure a quantity, your measurement is more precise when you use a smaller unit of measure. But no measurement is ever exact there is always some amount of error. The greatest possible error (GPE) of a measurement is one half the unit of measure. At the right, you see how the GPE for the ruler shown is calculated as inch. Since 3 8, the actual measure of the line segment may range anywhere from inches 7 to inches. INCHES length of line segment: 3 8 inches, to the nearest 8 inch unit of measure: 8 inch GPE: half of 8 inch, or inch Use the GPE to give a range for the measure of each line segment... INCHES 8 inch to 7 8 inch INCHES 4 inch to 3 4 inch 3. INCHES 7 inches to inches. Using this scale, the weight of a bag of potatoes is measured as 3 pounds. What is the range for the actual weight of the potatoes? 4. CM cm to 4. cm. Using this container, the amount of a liquid is measured as 0 milliliters. What is the range for the actual amount of the liquid? 3 0 pounds 7 8 pounds to 3 8 pounds 7. milliliters to. milliliters 0 ml 40 ml 30 ml 0 ml 0 ml Glencoe/McGraw-Hill 4 and Connections, Course

2 - Using as a Benchmark When you estimate sums of proper fractions, it often helps to use the number as a benchmark, like this. If two fractions are each less than, their sum is less than Two halves make a whole, so. If two fractions are each greater than, their sum is greater than. 8 7 Fill in each with or Fill in each with one of the given fractions Fill in each with or Glencoe/McGraw-Hill 43 and Connections, Course

3 -3 Mystic Hexagons A hexagon is a six sided figure. In a mystic hexagon, the sum of the numbers along each side is the same number. This number is called the mystic sum. For example, the mystic sum for the hexagon at the right is For each mystic hexagon, write the mystic sum in the blank in the middle. Then find the missing fractions along the sides... Complete each mystic hexagon. Be sure to express all your answers in simplest form Glencoe/McGraw-Hill 44 and Connections, Course

4 -4 Unit Fractions A unit fraction is a fraction whose numerator is and whose denominator is any counting number greater than. unit fractions 3 0 A curious fact about unit fractions is that each one can be expressed as a sum of two distinct unit fractions. (Distinct means that the two new fractions are different from one another.) Did you know? The Rhind Papyrus indicates that fractions were used in ancient Egypt nearly 4,000 years ago. If a fraction was not a unit fraction, the Egyptians wrote it as a sum of unit fractions. The only exception to this rule seems to be the fraction 3.. The three sums shown above follow a pattern. What is it? Let n be the denominator of the given fraction. The denominators of the distinct unit fractions are (n ) and n(n ).. Use the pattern you described in Exercise. Express each unit fraction as a sum of two distinct unit fractions. a. 4 b c. 3 d. Does it surprise you to know that other fractions, such as, can be expressed as sums of unit fractions? One way to do this is by using equivalent fractions. Here s how Express each fraction as a sum of two distinct unit fractions. 00 a. 3 b. 4 c. d Express 4 as the sum of three distinct unit fractions. 4. CHALLENGE Show two different ways to express as the sum of three distinct unit fractions ,00 Glencoe/McGraw-Hill 4 and Connections, Course

5 - Equations with Fractions and Decimals Sometimes an equation involves both fractions and decimals. To solve an equation like this, you probably want to work with numbers in the same form. One method of doing this is to start by expressing the decimals as fractions. The example at the right shows how you might solve the equation m = 3 = 0.. m 3 0. m 3 3 m 3 3 m 3 Write 0. as a fraction. the number that is a solution of the given equation.. z ; 8, 3 8,, b; 0, 4,, c 0. 4 ;, 3,, j 3 ; 3, 3,, 3. 4 r 0.7; 4,, 3 4,. d 0. 7 ; 0, 3, 4, 0 4 Solve each equation. If the solution is a fraction or a mixed number, be sure to express it in simplest form k 4 8. s n t g 8 4. y x 3 4. q w a 7. p k Glencoe/McGraw-Hill 4 and Connections, Course

6 - The Stock Market When you buy stock in a company, you become a part owner in that company. You buy stock in units called shares. The stock report that you see in a newspaper lists high and low prices per share of stock. The prices are given as whole dollars or as halves, fourths, or eighths of a dollar. Find the difference between the high and low prices for each stock listed. The difference for Avon is shown as an example. High Low Stock Difference 4 3 /8 3 /4 Avon 4 3/8 3 /4 7 / /4 /8 Caldor /8 3 /4 Gn Motr 3. 4 /4 3 / Hrshey 4. /4 3 /8 K mart /4 Kellogg s. 4 3 /8 McDonl /4 4 7 /8 QuakrO / /8 Sears. 3 3 /8 8 Walgrn /8 Xerox. What stock listed above had the greatest difference between high and low prices? the least difference?. What would be the price of a share of Quaker Oats stock if it rose / above its high? Glencoe/McGraw-Hill 47 and Connections, Course

7 -7 Fractions of Time Denise organized information about some of her activities into the chart you see at the right. Then she decided to estimate what fraction of the school day she spends studying. This is how she did it. 4:00 P.M. : P.M. h min 7:00 P.M. 8:00 P.M. h Total h min Then she rounded h min to h. breakfast classes lunch classes swimming studying dinner studying watching TV sleeping Denise estimated that she spends about 4, or, of her day studying. 7: A.M. 7:30 A.M. 8:0 A.M. :30 A.M. :30 A.M. :0 P.M. :0 P.M. : P.M. : P.M. 3:30 P.M. 4:00 P.M. : P.M. :30 P.M. :30 P.M. 7:00 P.M. 8:00 P.M. 8:00 P.M. : P.M. 0:30 P.M. :4 A.M. Use the chart above. Estimate what fraction of a school day Denise spends on each activity.. swimming about 4 3. classes about 4. sleeping about 3. watching TV about 4. eating about. at school (classes and lunch) about 4 7. Denise sleeps from :30 P.M. until 8:30 A.M. on Saturday and Sunday. About what fraction of the seven-day week does she spend sleeping? about 3 8. Denise goes to school 80 days of the year. About what fraction of the 3-day year does she spend in classes? about 0 8. Denise studies about 4 hours on Saturday and about hours on Sunday. About what fraction of the seven-day week does she spend studying? about 0 0. Denise tries to swim every day at the same time, Monday through Friday, all through the year. About what fraction of the year does she spend swimming? about 3 0 Glencoe/McGraw-Hill 48 and Connections, Course