LESSON 65 The relation of one number to another is ascertained by division. When we wish to find what part a smaller number is of a larger number, we divide the smaller by the larger. What part of 12 is 4? 4+12=2, or 3. Therefore 4 is of 12. But when we wish to find how many times a smaller number equals a larger, we divide the larger by the smaller. 12 is how many times 4? 12 ÷ 4 = 3. Therefore 12 is 3 times 4. 1. What part of 16 is 4? MODEL. 4 ÷ 16 = f, or. Therefore 4 is of 16. 12. What is the relation of 126 to 84? 132 to 22? 72 to 108? 84 to 56? 13. If 56 buggies cost $4200, find the cost of 84. SUGGESTION. 84 = , or of 56. 14. How much will 120 head of cattle cost, if 15 cost $525? 15. If 39 pocket knives cost $33.15, how much will 26 cost? 16. What is the relation of 20 to 35? 123 to 25¢? 8 to 25? 331 to $1? $2 to 25? $3 to 75¢? LESSON 66 1. What is the relation of 1 foot to a yard? What is the relation of a yard to a foot? 2. What is the relation of an inch to a foot? What is the relation of a foot to an inch? 3. If 17 bu. of wheat cost $10, how many bushels can you buy for $25 ? SUGGESTION. $258, or 1⁄2 of $10. 4. If 8 men can do a piece of work in 3 days, how long will it take 2 men to do of the work? 5. What is the relation of 3 of 18 to 3 of 36? 6. 331% of 27 is what part of 81? 7. What is the relation of a mile to 108? 120 rods? 8. What is the relation of 81% to 163 % ? 9. What per cent of a quantity is of it? of it? 10. What is the relation of 2 bushels to 6 pecks? 11. If 2 bushels of corn are worth $1.60, how much are 6 pecks worth? 12. What part of a day is 10 hr.? What is the relation of a day to 10 hr.? 13. What part of a mile is 40 rd. What per cent of a mile is 40 rd. ? 14. There are 60 pupils in a school, and 45% of them are boys. How many are girls ? 15. 623 +9 = ? 80? 80? 75÷11 = ? 16. If 36 doz. oranges cost $10.80, how much will 48 doz. cost? 17. What is the relation of the G. C. D. of 18, 24, and 36 to the L. C. M. of 12, 20, 30? DECIMALS LESSON 67 In decimals, as in whole numbers, the value of a figure depends upon its position. Thus, in .555, the second 5 is of the value of the first 5, and the third 5 is of the value of the second 5, and of the value of the first 5. Or, the first 5 is 10 times the value of the second 5, and 100 times the value of the third 5. 1. In the number 55.55, the first 5 at the left of the decimal point represents how many units? The second 5 at the left represents how many units? How many tens? The second 5 at the left of the point is how many times the value of the first 5 at the left? 2. The first 5 at the right of the point in the number 5.55 is what part of the value of the first 5 at the left of the point? The second 5 at the right of the point is what part of the value of the first 5 at the right? 3. In $543.27, the 5 represents five times how many dollars? The 4 represents four times how many dollars? The 3 represents three times how many dollars? The 2 represents two times what part of a dollar? The 7 represents seven times what part of a dollar? 4. In 4.56 rods, what does the 4 stand for? What does the 5 stand for? The 6? 5. Compare the values of the 3's in 33, 3.3, .33, .333. 6. In the number 555.555, state the value of each figure as compared with the others, commencing at the left. 7. State the number of tenths, hundredths, and thousandths in each of the following: .538, .608, .004, .400. Annexing ciphers to the right of a decimal does not change the value of the decimal. Thus, 50 = .5= .50 = 5; .500 = 50% = $. 1000 1. Change .35 to a common fraction in its lowest 12. Change 8.05 to a mixed number in its simplest form. 21. Change .4 to a common fraction in its lowest terms. = 10 10 10 25 32. Change 9.83 to a mixed number in its simplest form. = 7 hundredths and 4 hundredths remaining. 4 hundredths = 40 thousandths, of 40 thousandths 5 thousandths. Hence, when reduced to the decimal form, = 3 tenths + 7 hundredths + 5 thousandths, or .375. Frequently the division will not terminate, and the common fraction cannot be exactly expressed decimally. |