Examples. 144. DRILL TABLE No. 4. A 1. $18.40 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. $100.02 24. $444.44 25. $100.10 $83.22 $36.41 $30.05 $204.75 $9.208 $5.632 $876. $100.35 $15.207 $1.36 $20.95 $0.402 $19.005 $ 63.072 $7.645 $419.28 $0.625 $ 500.57 $268.06 $29.70 $11.005 United States Money. B Twelve dollars, twenty-five cents. One hundred thirty dollars, six cents. Forty-nine dollars, twenty-four cents. Seventeen cents, eight mills. Thirty-eight dollars, five mills. 89 dollars, fifty cents, three mills. Fifty-four dollars, nine cents. Four dollars, forty-four cents, four mills. Nine dollars, nine cents, nine mills. 145. Exercises on Table No. 4. 103. Read as dollars, cents, and mills, the numbers expressed in A. § 104. Read decimally the numbers expressed in A. 105. Write in figures the numbers expressed in B. 106. Disregarding the mills, change the numbers expressed in A to cents. 107. Change the numbers expressed in B to mills. 108. Add the numbers from 1 to 8* in A to each number expressed in B. 109. Add the numbers expressed in A and B, (1st) from 1 to 4*; (3d) from 3 to 6, etc. 114. Ax9= ? 115.† A÷ 10 = ? 116.t B11=? (2d) from 2 to 5; 110. $900- A = ? 111. A-B=? 118. A÷7=? 119. A÷$0.25 =? 120.1 A$0.16 = ? 121. B$0.005 = ? 112. A×6= ? 113. Bx7 = ? 117.t B÷12 = ? 122. If a person saves a sum equal to A in one month, how much wil! he save in 13 months? 146. Questions for Review. What are the units of United States money? How are dollars, cents, and mills expressed by figures? sidered the principal unit? Give the sign for dollars. change dollars to cents? dollars to mills? cents to mills? lars? cents to dollars? 123. How many pounds of sugar, at 8 cents a pound, can be bought for each sum of money expressed in A?‡ Give the table. What is conHow do you mills to dol * Inclusive. † See page 66, note. § See page 57, for Explanation of the Use of the Drill Tables. How do you add numbers in United States money? How do you subtract? When you multiply, where do you put the decimal point in the product? Divide $185 by 7, continue the division to mills, and explain. What is necessary in order to divide one sum of money by another? Divide $900 by 36 cents. What are coins? Why is paper money sometimes used in place of coins? Name the gold coins; the silver coins. How is a What is a creditor? a debtor? an account? a bill? bill receipted? Reject mills. 147. Miscellaneous Examples. 27. A girl bought a pair of boots for $2.37, another pair for $1.65, slippers for $1.25, and shoes for 82. What was the whole cost? 28. I bought a horse for $95.00, a wagon for $ 63.00, and a harness for $15.00; kept them a week, paying $2.50 for board of the horse, then sold them for $175.00. Did I gain or lose, and how much? 29. What should I pay for 2 dozen pigeons at 85o peɩ dozen, 2 dozen at $1.10 per dozen, and 1 dozen for 90%. 30. There were sold in one week 8874 sheep at $4.13 pe head. What did they bring? 31. There were sold 4778 beeves, averaging 874 pound apiece, at 7 per pound. What was received for them? 32. What did I gain by buying 2 pieces of cambric, each containing 62 yards, for $39.68, and selling them for 40 cents per yard? 33. A man paid $16.25 for 13 days' work. What was that a day? 34. Among how many boys must $12 be distributed, that each may receive 75 cents? 35. I sold 35 barrels Pippins at $1.75 per barrel, 17 barrels Pome Royals at $1.80 per barrel, 13 barrels Golden Sweets at $1.25 per barrel, and 25 of Russets at $2.25 per barrel. Paid 17 cents a barrel for picking, and $12.00 for freight. What remained after my expenses were paid? 36. Paid $3.00 for 1 dozen apple-trees, $3.36 for 1 dozen peach-trees, $3.30 for half a dozen pear-trees. What did I pay for the whole, and how much apiece for each kind? 37. A carpenter paid for stock and work for a barn, $ 450.75; for mason's work, $38.25; for digging and stoning cellar, $47.18; for painting, $ 40.00; to the plumber, $8.12. He then sold the barn, and lost, in so doing, $ 14.30; how much did he sell it for? SECTION VIII. FACTORS. 148. What numbers multiplied together will produce 10? Answer, 2 and 5; also 1 and 10; thus, 2 x 510 and 1 × 10 = 10. A number that may be used as multiplicand or as multiplier to make another number is a factor of that number. Name two factors of 15; of 16; of 18; of 24; of 36; of 45. NOTE I. The word factor will be used in this Arithmetic to denote only such factors as are not fractional. NOTE II. If a number be divided by any of its factors there will be no remainder. Hence a factor of a number is also called a divisor or a measure of that number. 149. Name some factors of 12 besides the number itself and 1. Has the number 13 factors besides itself and 1? Has the number 14? 15? 17? 18? 19? A number that has other factors besides itself and one is a composite number. Which of the numbers 12, 13, 14, 15, 17, 18, 19 are composite numbers? 150. A number that has no other factors besides itself and one is a prime number. Which of the numbers 12, 13, 14, 15, 17, 18, 19 are prime numbers? Name the composite numbers from 1 to 40. Name the prime numbers from 1 to 40. NOTE. In speaking of the factors of a number, we do not usually include the number itself and one. Thus, we frequently say that a prime number has no factors. 151. Name the factors of 12 that are prime numbers. Name those that are not prime numbers. A factor that is a prime number is a prime factor. 152. Oral Exercises. a. What are the prime factors of 6? 8? 14? 24? 27? b. What are the prime factors of 22? 36? 28? 20? 35? c. What are the prime factors of 16? 21? 15? 33? 26? 153. In seeking for the factors of a number we may use certain tests, the more convenient of which are the following: 1. A number whose units' figure is 0, 2, 4, 6, or 8, is divisible by 2. NOTE. A number that is divisible by 2 is an even number; a number that is not divisible by 2 is an odd number. 2. A number is divisible by 3 if the sum of its digits* is divisible by 3. Thus, 285 is divisible by 3, for 2+8+5 = 15 is divisible by 3. 3. A number is divisible by 4 if its tens and units together are divisible by 4. Thus, 6724 is divisible by 4, while 6731 is not. 4. A number is divisible by 5 if the units' figure is either 0 or 5. 5. A number is divisible by 6 if it is an even number and divisible by 3.. 6. A number is divisible by 8 if its hundreds, tens, and units are divisible by 8. Thus, 6728 is divisible by 8, while 6724 is not. 7. A number is divisible by 9 if the sum of its digits is divisible by 9. 8. A number is divisible by 11 if the sums of its alternate digits are equal, or if their difference is divisible by 11. Thus, 1782 and 1859 are divisible by 11, while 4987 is not. 9. A number is divisible by a composite number, if it is divisible by all the factors of the composite number. Thus 3555 is divisible by 15, for it is divisible by 3 and by 5. NOTE. For the reasons of these tests, see Appendix, page 303. * A digit here means the number denoted by a figure without regard to its place. |