FRACTIONS 1. Draw a line of convenient length; divide it as nearly as you can into 3 equal parts. 2. What fraction expresses the relation of one of these parts to the whole line? What fraction expresses the relation of 2 of these parts to the whole line? 3 of them? 3. When a quantity is divided into 3 equal parts what are the parts called? In the fractions and which number shows that the fractions express thirds? 4. Draw a square and divide it into 4 equal parts. 5. What fraction expresses the relation of one of these parts to the whole square? What fraction expresses the relation of 2 of these parts to the whole square? 3 of them? 4 of them? 2 6. When a quantity is divided into 4 equal parts, what are the parts called? Which number in the fractions, 4, shows that the fractions express fourths? The number that names the kind of parts expressed by the fraction is called the denominator of the fraction. 7. In the above fractions which number tells how many of these parts are expressed by the fractions? The number that tells how many parts are expressed by a fraction is called the numerator. The numerator and denominator are called the terms of the fraction. 8. In what is the numerator? The denominator? 6 20 9. Answer the same questions for 5, 8, 7, 28. 10. What takes the place of the denominator in .3? In .20? In .7? In .5? In .9? 1. Which is greater, 7 yd. or 5 yd.? 2. Which is greater, or ? or 4? or §? 3. If two unequal fractions have equal denominators, which fraction is the greater? 4. Which fraction is greater, or ?or? Why? 5. Which is less, or ? or 2? Why? 6. If two unequal fractions have equal numerators, which fraction is the greater? Arrange the numbers in each set according to size, placing the least at the top: 10 6 20 .9 II. The areas of Denmark, Venezuela, England, and Germany are respectively 18, 10, 18, 10 of that of the British Isles. Arrange the names of these countries in order according to their areas. 3 12. Of all the cotton goods produced in the United States in 1900, about was made in Massachusetts, in South Carolina, in Pennsylvania, in Georgia, in Rhode Island, in Connecticut, in North Carolina, and in 20 New Hampshire. Arrange the names of these states in order according to the amount of cotton goods produced. 1 9 13. Of all the boots and shoes made in the United States in 1900, 8 were made in New Hampshire, 2 in Massachusetts, and in New York. Arrange the names of these states in order according to the value of boots and shoes manufactured. 9 Oral. PROBLEMS-TIME 1. How many years are there from 1800 to 1900? 1900 to 2000? 1800 19 From 1900 2. 100 years are called a century. How many years are there in of a century? In ? In .8? 5 3. How many years are there from 1890 to 1900? From 1900 to 1910? 4. 10 years are called a decade. A decade is what part of a century? 2 decades are what part of a century? 5. How many decades are there in .3 of a century? In .6 of a century? In .9? In .7? 6. How many years are there in .5 of a decade? In of a decade? In .3? In .9? In .7? 7. How many days are there in .1 of a 30-day month? In of it? In .2? In .5? In 7? In .9? 10 8. How many minutes are there in of an hour? In .7 of an hour? In? In .4? 9. How many minutes are there in 1.2 hours? In 2.1 hours? In 5.6 hours? In 10.5 hours? Written. 7.1 hr., 5 hr., 6 10.9 hr., 1 hr. 10. Add 3.5 hr., II. A train in traveling between the cities A and B required 14 hr., between B and Chr., between C and D 22 hr., and between D and E hr. Express these periods of time decimally and find how long, exclusive of time for stops, it took the train to travel from A to E. A B C D E 12. How many hours and tenths of an hour are there from 6 A. M. to 7:12 A. M.? From 7:12 A. M. to 9 A. M.? From 9 A. M. to 11:30 P. M.? 20 Oral. REVIEW AND SUMMARY 1. Which swings the faster, a long or a short pendulum? 2. A large clock has a pendulum that swings once every second. How many times does it swing in 1 minute? In 1 hour? In 10 hours? 3. The sound of a whistle was heard 3 seconds after the steam was seen; taking the velocity of sound as 1,090 ft. per second, how far away was the whistle? 4. In writing numbers decimally, what is used to separate the whole number from the decimal part? 5. How many tenths are expressed by .2? .3? .9? 1.9? 2.9? 3.0? 20.1? 6. How does multiplying a decimal by 10 change the position of the decimal point? 7. State where the decimal point will be when each of the following is multiplied by 10: 2.8; 3.7; .5; 20.2; 62.0; 207.2; 2.00. 8. How does dividing a number by 10 change the position of the decimal point? 9. State where the decimal point will be when each of the following is divided by 10: 2.7; 2.0; 2; 16.5. FORM STUDY Perpendiculars 1. The angles of a square are called right angles. What kind of angles do the adjacent sides of a rectangle form with one another? 2. Two straight lines which are sides of a right angle are said to be perpendicular to each other. Desig nate the lines in the picture that are A perpendicular to each other. 3. What kind of an angle is formed by the top and one side of a door? 4. The adjacent edges of a book are perpendicular to each other. Point out in the school-room lines that are perpendicular to each other. 5. Right angles may be constructed by using an object which has one of its corners a right angle. Construct a right angle with the aid of your book-cover. In drawing, a triangle or square is used, as shown in the picture. Carpenters also use the square. 6. Draw a line 4 in. long. At each end and on the same side of this line draw a line as long and perpendicular to it. Connect the end points of the perpendiculars. What is the area of the figure? |