chain for 15 dollars, and a seal for 8 dollars; and then sold the whole for 80 dollars: did he make or lose, and how much? 33. Four boys bought a foot-ball for 75 cents. John paid 20 cents, James 33 cents, and William 18 cents: how much did Reuben pay? 34. A grocer bought a hogshead of sugar for 65 dollars, and a hogshead of molasses for 55 dollars; he sold them both for 125: did he make or lose, and how much? 35. A farmer bought 4 sheep for 15 dollars, and 6 lambs for 10 dollars; he sold the whole for 30 dol lars: did he make or lose, and how much? 36. A tailor has a piece of cloth containing 25 yards, and a second piece containing 35 yards; he cut 8 yards from the first piece, and 12 from the second: how many yards of cloth has he left? 37. A merchant has a piece of cloth, for which he paid 36 dollars; he wishes to sell it so as to make a profit of 12 dollars: what must he ask for it? 38. A farmer has 150 sheep in three fields. In the first he has 45, in the second 55: how many has he in the third? 39. There is an orchard with ten full rows of trees and 7 trees in each row; besides which there are 3 broken rows with 4 trees in each row: how many trees are there in the orchard? How many more in the whole than in the broken rows? 40. An orchard contains 20 apple trees, 10 cherry trees, and 15 plum trees: how many more apple and cherry trees than plum trees? 41. James worked 4 days in a week for 12 cents a day, and William 2 days for 4 cents a day: how much more did James earn than William ? 42. A butcher bought 16 sheep of one man, 14 of another, and 25 of a third; he then killed 9, afterwards he killed 21: how many had he left ? 43. A man earned 16 dollars a month for 6 months and his son James 7 dollars a month for the same time: how much more did the father earn than the son? LESSON VI Factoring Numbers. 1. Four are how many times 2? factors of 4?* 2. Six are how many times 3? 2? What are the factors of 6? What are the How many times 3. Eight are how many times 4? times 2? What are the factors of 8? How many 4. Nine are how many times 3? What are the factors of 9? 5. Ten are how many times 5? How many times 2? What are the factors of 10? 6. Twelve are how many times 6? times 2? How many times 4? How How many many times How many How many 3 ? What are the factors of 12? 7. Fourteen are how many times 7? times 2? What are the factors of 14? 8. Fifteen are how many times 5? times 3? What are the factors of 15? 9. Sixteen are how many times 8? times 2? How many times 4? What are the fac tors of 16? How many 10. Eighteen are how many times 9? How many times 2 ? How many times 6? How many times 3 8 ? What are the factors of 18? *SUGGESTION.- --In each of the following questions, two numbers are named, and it is required to find a third which multiplied bỷ the second, will give a product equal to the first. The second and third numbers are called FACTORS of the first. Let the pupil point out the factors in every example. 11. Twenty are how many times 2? How many times 10? How many times 5? How many times What are the factors of 20 ? 4 ? 12. Twenty-two are how many times 11? How many times 2? 13. Twenty-four are how many times 12? How many times 2? How many times 8? How many times 3 ? How 14. Twenty-six are how many times 2? How many times 13? What are the factors of 26? 15. Twenty-seven are how many times 9? many times 3? What are the factors of 27 ? 16. Twenty-eight are how many times 14? How many times 2? What are the factors of 28? 17. Thirty are how many times 15? How many times 2? How many times 10? How many times 3? What are the factors of 30? 18. Thirty-three are how many times 11? How many times 3? 19. Thirty-four are how many times 2? How many y times 17? 20. Thirty-six are how many times 18? How many times 12? How many times 9? How many times 6? How many times 4? How many times 3 ? How many times 2? What are the factors of 36 ? 21. Thirty-eight are how many times 19? How many times 2? What are the factors of 38 ? 22. Forty are how many times 20? How many imes 10? How many times 8? How many times 5 ? ? How many times 4? How many times 2? 23. Forty-two are how many times 21? How many times 2? How many times 6? How many times 7? What are the factors of 42 ? 24. Forty-four are how many times 22? How many times 2? How many times 11? How many times 4? What are the factors of 44? 25. Forty-six are how many times 23? many times 2? What are the factors of 46 ? How 26. Forty-eight are how many times 24? How many times 16? How many times 12? How many times 8? How many times 6? How many times 4? How many times 3? How many times 2? What are the factors of 48? 27. Forty-nine are how many times 7? What are the factors of 49? 28. Fifty are how many times 25? How many times 10? How many times 5? What are the factors of 50? 29. Fifty-four are how many times 9 ? How many times 6? How many times 27 the factors of 54 ? What are How many What are the 30. Fifty-six are how many times 7? How many times 28? times 8? factors? 31. Sixty are how many times 10? How many times 12? How many times 5? What are the factors? 32. Sixty-four are how many times S? How many times 16? How many times 4? What are the factors? 33. Seventy are how many times 7? How many times 10? What are the factors? 34. Seventy-two are how many times 8? How many times 9? What are the factors? 35. Eighty-four are how many times 12? How many times 7? What are the factors? 36. Ninety-six are how many times 12? How many times 8? What are the factors? SECTION FOURTH. LESSON I. In which Divisors are used from 1. How many 2's are there in 2. in 2, how many times? 2. How many 2's are there in 4? many times? 3. How many 2's are there in 6? mary times? 4. How many 2's are there in 8? many times? 5. How many 2's are there in 10? many times? 2 to 5.* 2 is contained 2 in 4, how 2 in 6, how 2 in 8, how 2 in 10, how 6. How many 2's are there in 12? 2 in 12; how many times? 7. How many 3's are there in 3? 3 is contained in 3, how many times? 8. How many 3's are there in 6? many times? 9. How many 3's are there in 9? many? 10. How many 3's are there in 12? many? 11. How many 3's are there in 15? many times? 3 in 6, how 3 in 9, how 3 in 12, how 3 in 15, how * DIVISION is the process of finding how many times one num ber contains another. The number to be divided is called the dividend. The number by which we divide is called the divisor. The number expressing how many times the dividend contains the divisor is called the quotient. In case there is a number left, it is called the remainder. The divisor and quotient are factors of the dividend. |