SUBTRACTION. 14 2. John bought an arithmetic and slate for 35 cents; he gave 10 for the slate-what did the arithmetic cost him? 3. Charles had 14 apples, he gave 6 of them to his brotherhow many had he left? 4. A man bought a cow for 16 dollars, and sold her again for 28 dollars—how many dollars did he gain? 5. James bought 15 marbles, and gave George 6 of them—how many had he left ? 6. A man gave his son 25 cents to buy toys on a holyday. He paid 8 cents for a picture-book, 4 cents for a top, and 7 cents for marbles-how many had he left? 8, 4, and 7, from 25, leaves how many? 7. Jane went to the store with 25 dollars. She bought a dress for 9 dollars, a shawl for 6 dollars, and a pair of shoes for 1 dollar. How many dollars had she left? 9, 6, and 1 from 25 leaves how many? 8. Peter bought a wagon for 35 cents, and sold it for 46 cents. How many cents did he gain by the bargain? 9. James had 18 marbles in his pocket, and lost 11 of them how many had he left? SUBTRACTION. Subtraction teaches to take a less number from a larger of the same kind, and show the difference (or remainder.) . (Subtraction is precisely the reverse of Addition.) RULE. Write the less number under the larger, placing units under units, &c.; draw a line underneath, begin with the units and subtract each figure in the lower number from the figure over it, and set down the remainder: when a figure in the upper number is smaller than the figure under it, add ten to the upper number, or consider the upper figure to be ten more than it is, and carry one to the next lower figure, or add to the upper figure what the lower figure lacks of ten, and carry one, and so proceed. NOTE.-Some arithmeticians call the larger number minuend, and the less subtrahend. PROOF. Add the remainder and less number together, and their sum will be equal to the larger number. Questions to be put to the Learner by the Teacher. What is Subtraction? How must the numbers or figures be placed in Subtraction? Where must you begin to subtract? Why do we begin at the right hand to subtract? (Ans. Because figures increase from right to left.). What is the answer in Subtraction ed? What is Subtraction the reverse of? How is Addition proved by Subtraction ? (Ans. Subtract, successively, from the whole sum the several numbers which were added to produce it, and if the work be right there will be no remainder.) How is Subtraction proved ? NOTE, To Teachers. The learner should be questioned as often as once in each day, respecting the principles upon which the rules are founded; and the Teacher should not permit him to commence a new rule until he is fully acquainted with the principles of the rule in which he has been working. EXAMPLES. 1. From 275 larger num., or minuend. Add 150 the less number. Take 150 less num., or subtrahend. And 125 the difference. Proof 2. From 275--125=150 the less number. 50 difference. Explanation of the second example.-Say 5 from 5 nothing; set down a cipher under the fives; then say 7 cannot be taken from 2, and therefore you must add 10 to the 2, which makes it 12, (conceive the 10 to be borrowed ;) you will then say 7 from 12 leaves 5, which set down under the 7; then carry 1 for the 10 you borrowed, and say I from I nothing remains, omitting ciphers on the left of whole numbers, you have the answer, or difference, 50. 3. From 54 4. 36 5. 194 6. 804 7. 258 8. 1111 Take 23 17 75 405 163 12 19. The Bible contains 2718100 letters, and the New Testament contains 833338 letters. Required the difference. 20. The Bible contains 592439 words, and the New Testament 181259. What is the difference ? 21. The Bible contains 23214 verses, and the New Testament contains 7959 verses. What is the difference? 22. The Old Testament contains 929 chapters, and the New Testament 260 chapters. What is the difference? 23. The Old Testament contains 39 books, and the New Testament 27. What is the difference? 24. What is the difference between 1000000 and 1000? 25. A boy who had 100 marbles, sold 65, gave away 15, and lost 19—how many had he left? 26. What is a man's age in 1833, who was born in 1784 ? 27. From 658342 28. 390251 29. 886644 Take 427689 264163 7755 16 SUBTRACTION. 30. A tree 86 feet high was broken off by the wind; the top part which fell was 68 feet long-how high was the stump which was left? 31. What is the difference between 6421857 and 467931 ? 32. A trader gave 78 dollars for a hogshead of sugar, and sold it for 86 dollars. How much did he gain ? 33. A certain apprentice will be 21 years old in 1842; in what year was he born? 34. A farmer who had 3625 bushels of grain, sold 2700 bushels; how much had he left? 35. A man borrowed 632 dollars, and paid 475 dollars; how many dollars did he then owe? 36. From 6006006 take 999999, and what will remain ? 37. What is the difference between 8650700 and 987654 ? 38. The sum of two numbers is 75, the less number is 25; what is the larger number? 39. The larger of two numbers is 64, and their difference is 16; what is the less number? 40. What number is that which taken from 600 leaves 175 ? 41. A man possessing an estate of 20000 dollars, gave 2675 dollars to each of his two daughters, and the remainder to his son; what was his son's share ? 42. How much must be added to 475 to make 1250 ? From the remarks and illustrations now given, we deduce the following: Prob. 2. Having the sum of two numbers (given,) and one of the numbers given, to find the other. RULE.-Subtract the given number from the given sum, and the difference will be the number required. Prob. 3. Having the larger of two numbers given, and the difference between that and the less, to find the less number. RULE.--Subtract the difference from the larger for the less number. 43. The sum of two numbers is 24, the larger is 18; what is the less ? 44. The larger of two numbers is 60, and their difference 15; what is the less number? 45. What number is that which taken from 4433 leaves 650 ? 46. The Arabian method of notation was first known in England about the year 1150; how many years since up to 1833 ? 47. From 9 5 8 6 2 071 3 48. From 24753 2001 Take 6 64488330 Take 69 7 2 3 5 9 6. 49. From 311002200 Take 188100111 50. From 102030401 Take 99887701 MULTIPLICATION. MULTIPLICATION teaches a short way of doing Addition. NOTE, T. Teachers. Before the learner is required to answer any ques tions, either mentally or by the use of the slate, he should thoroughly learı the following MULTIPLICATION TABLE. are 12 Twice 4 6. 4 8 10 12 14 8 16 9 18 10 20. 11 22 12 24 3 times are 3 9 15 18 7 21 8 24 27 10 30 11 33 12 36 4 times 8 16 20 6 24 28 8 32 9 36 10 40 11 44 12 48 5 times 1 are 5 2 10 3 15 4 20 5 25 6 30 35 8 40 9 45 10 50 11 55 12 60 6 times 24 5 30 36 7 42 8 48 9 54 10 60 11 66 12 72 7 times 1 are 7 2 14 3 21 28 5 35 6 42 7 49 56 9 63 10 70 11 77 12 84 8 times 1 are 8 2 16 3 24 32 5 40 6 48 7 56 64 9 10 80 11 88 12 96 9 times 1 are 9 2 18 3 27 36 45 54 7 63 8 9 81 10 90 11 99 12 108 10 times 1 are 10 2 20 3 30 4 40 50 6 60 7 70 80 9 10 100 11 110 12 120 11 times 1 are 11 2 22 3 33 4 44 55 6 66 7 77 8 88 9 99 10 110 11 121 12 132 12 times 1 2 24 3 36 4 48 60 6 72 7 84 8 96 9 108 10 120 11 132 12 144 Twice 13 are 26 14 28 15 30 16 32 34 18 36 19 38 20 40 21 42 22 44 23 46 24 72 90 48 B2 18 MULTIPLICATION. EXAMPLES. -For Mental Exercise. 1. IF 1 copy-book cost 6 cents, how many cents must I give for 2 copy-books ? How many cents for 4 copy-books ? 2. In 1 dollar there are 100 cents; how many cents in 3 dollars? How many in six dollars and a half ? 3. If you pay 6 dollars for 1 barrel of flour, how many dollars must you pay for 10 ? 4. If i bushel of apples cost 25 cents, how many cents must I give for 3 bushel ? 5. What will 2 pounds of coffee cost at 14 cents per pound ? 6. There were 5 boys, who gave a poor man 3 cents apiece; how many cents did the man receive? 7. How many dollars must I pay for 12 yards of cloth, that is worth 4 dollars a yard? 8. How much will a Jerseyman get for 25 melons, if he sells them at 5 cents apiece ? 9. A teacher had 8 classes in his school, and 7 scholars in each class; how many scholars had he in all ? 10. There are 24 hours in one day; how many hours in 3 days? 11. If 1 pound of honey is worth 12 cents, how many cents are 9 pounds worth 12. 14 and what number make 20 ? MULTIPLICATION. The (larger) number to be multiplied is called the Multiplicand. RULE. 1. Write down the multiplicand, under which write the multiplier, placing units under units, tens under tens, &c., and draw a line under them? 2. Begin at the right hand, multiply each figure in the multiplicand by each in the multiplier, placing the first figure of every line (directly) under its (respective) multiplier, and to the product of the next figure carry one for every ten, as in Addition. 3. Add the several products together, and their sum will be the (total) product required. 1. Multiply the multiplier by the multiplicand. 2. Take one from the multiplier, and multiply the multiplicand by the difference, or remainder, and add the multiplicand to the product. 3. Subtract the multiplicand from the product as often as there inits in the multiplier. PROOF. |