16. If 1 monitor can mend 2 pens in a minute, how long will it take 3 monitors to mend 28 pens ? 17. It is worth as much to pasture 1 cow, as 5 sheep. If I pay 1 dollar a month for pasturing a cow, what must I pay for pasturing 35 sheep, 7 months? 18. If 3 horses eat 1 ton of hay in I month, how long will 5 tons last 4 horses? 19. A drover sold a cow for 20 dollars, and, in so doing, he gained a sum equal to of what he had paid for the cow. How much had he paid for her? and a 20. Suppose a man can dig a trench in 4 days, boy in 6 days;- what part of it can each dig in 1 day? What part of it can both together dig in 1 day? In what time can they both finish it? 21. Suppose a cistern has one tap that will discharge it in 5 hours, and another in 7 hours,-in what time will they both discharge it? 22. If 1 man can perform a piece of work in 35 days, in what time can 6 men perform it? 23. If 4 men drink a barrel of cider in 20 days, in what time will 9 men drink the same quantity ? 24. If 9 men can do a piece of work in 5 days, in how many days will 7 men do the same work? 25. A farmer kept his sheep in four pastures-In the first pasture he had of his flock; in the second, ; in the third,; and in the fourth he had 32 sheep. How many sheep had he? 26. There is a school, in which of the scholars read in the Classical Reader, read in the National Reader, read in Pierpont's Introduction, and 36 little boys read in the Young Reader. How How many scholars are there in the school? 27. If a post 4 feet high cast a shadow 3 feet, at noonday, what is the height of a steeple, that casts a shadow 90 feet, at the same time. 23. A and B are laborers- A earns 10 dollars a month, and B 9; but A gives of his earnings to B. What will each lay up in 3 months? 29. If 12 men can perform a piece of work in 6 days, in what time would 10 men perform the work? 30. How many men must be employed, to dig a trench in 3 days, that 6 men can dig in 4 days? 31. Suppose two men start from the same place, and travel in opposite directions, one at the rate of 5 miles an hour and the other as fast;- how far apart will they be in 11 hours? 32. A fox has 35 rods the start of a greyhound, but the hound runs 10 rods while the fox runs 7. How many rods must the hound run to catch the fox? 33. A started on a journey, and travelled 5 miles an hour-B started on the same journey, 2 hours after, and travelled 71⁄2 miles an hour. In how many hours Idid B overtake A? 34. A jockey paid 9 times as much for his horse as he did for his saddle; he paid 3 times as much for his saddle as he did for his bridle; and for his bridle he paid 5 dollars. What did the whole cost? 35. Suppose a man can reap of a field of wheat in a day, and his son can reap of it in a day; what part of it can they both reap in a day? In what time can they both reap the whole? 36. A boy being asked, how much money he had, replied-' If I had as much more, and as much more, and as much more as I really have, I should then have 70 cents.' How much must he have had? 37. A gentleman paid 85 dollars for 5 weeks' board of himself, his son, and one servant, at a hotel- His own board cost twice as much as his son's, and his son's cost three times as much as the servant's. the expense of each, per week? What was with him Come with but do not say ess first what swer thave C 88 NOTE TO TEACHERS. The teacher should now be provided with "A KEY TO THE NORTH AMERICAN ARITHMETIC," otherwise he must lose much time in examining operations. The KEY is a small book designed exclusively for teachers, and contains answers to all the examples in the Written Arithmetic. If the KEY cannot be obtained at every place where the Arithmetic is for sale, it may still be obtained from the publishers of the Arithmetic, and from the principal book-stores in the larger cities and towns. A variety of expedient methods may be pursued, in examining written operations in arithmetic; and perhaps no one system can be adopted, from which it will not be found advantageous, occasionally, to depart. My own practice for several years, with occasional variation, has been as follows. A certain number of examples having been assigned for a lesson the day previous, each scholar is supposed to be prepared with the solutions upon his slate, and the class are paraded for recitation. Every scholar passes his slate into the hands of the scholar next above him, except the head scholar, who hands his to the foot scholar. The first scholar then reads from the slate he holds, the answer to the first example; and the teacher, holding the key, declares the answer to be right, or wrong. When the answer has been pronounced right, it is the duty of every scholar who finds a different answer upon the slate he holds, to signify it, and the error is noted against the owner of the slate. The first example being disposed of, the answer to the second example is read by the second scholar, and disposed of in like manner. Thus the reading of answers goes through the class, and each scholar detects the errors of his neighbour. Individual scholars are occasionally called upon to explain their work in a particular example, and to give their reasons for the operation adopted. By this mode of examination, the work of a large class is particularly inspected, in nearly the same time that would be required to inspect the work of one scholar. Besides the advantage of despatch in this mode of examination, the exercise itself is beneficial to the pupils. Each scholar acts the part of an inspector-he is interested to be critical-he acquires a facility in deciphering the work of others and thus his perceptive powers are cultivated, and a habit of alertness is attained. Before the learners attempt to perform operations by figures, they should be able to write figures with facility, and to arrange them regularly. To attain this object, the arrangement of figures below, may be repeatedly copied upon the slate, until a good degree of despatch and accuracy is acquired. 1 2 3 4 5 6 7 8 9 0 1 2 345678 901234 567890 1 2 3 4 5 6 7 8 9 0 1 2 345678 123456 1 2 3 4 5 6 789012 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 90 123456 789012 3 4 5 6 7 8 345678 89 WRITTEN ARITHMETIC. CHAPTER 1. NUMERATION. SECTION 1. THE UNIT, which is the first thing to be considered in numeration, signifies One. The figure 1 stands for one unit; 2, for two units; 3, for three units; 4, for four units; 5, for five units; 6, for six units; 7, for seven units; 8, for eight units; 9, for nine units. The TEN is a number which is made up of ten units. One ten is expressed thus, 10; two tens, thus, 20; three tens, thus, 30; four tens, thus, 40; &c. The HUNDRED is a number which is made up of ten tens. One hundred is expressed thus, 100; two hundreds, thus, 200; three hundreds, thus, 300; &c. Suppose the balls below, which are arranged in three places, to represent 8 units, 3 tens, and 1 hundred. Learn from the figures above, that the first or right hand figure expresses units, the second figure expresses tens, and the third figure expresses hundreds. H* number, which is made up of ten The THOUSAND is hundreds. One thousand is expressed thus, 1000; two thousand, thus, 2000; three thousand, thus, 3000; &c Observe, that a figure expresses thousands, when it stands in the fourth place from the right; therefore ten thousand is expressed thus, 10 000; and a hundred thousand, thus, 100 000. Examine the following Numeration Table. Begin at the right hand, and observe, that every three figures may be viewed by themselves; the first three express so many units, tens and hundreds; the second three, so many Thousands; the third three, so many Millions the fourth three, Billions; the fifth three, Trillions.* To read the line of figures in this table, begin with the left hand figure, and proceed as follows. 472 156 795 841 526 This character, 0, called nought, or cipher, expresses nothing of itself-it stands only to occupy a place, where there is none of the denomination belonging to that place to be expressed. For example, in the number 240, there are no units; therefore a cipher stands in the units' place. In the number 407, there are no tens; therefore a cipher stands in the tens' place. *The old method of embracing siz figures in a period, is of late abandoned |