Write down in figures the following numbers: Ten. Twenty-one. Four hundred and sixty-seven, Two thousand three hundred and eighty-nine. sand three hundred and twenty-nine. Fifty-eight millions seven hundred and thir ty-two thousand one hundred and five. Eight hundred and ten millions nine hun-) 10 21 35 467 2389 34570 6034000 7804329 58732105 dred and two thousand five hundred 810902512 and twelve. Three thousand two hundred and three) millions six hundred and eight thou- 3203608999 sand nine hundred and ninety-nine.) Question 1. What is Arithmetick? 2. What are the ten digits by which numbers are expressed? 3. What is an integer? 4. What is a fraction? 5. What are the principal rules by which the operations in Arithmetick are conducted? 6. What does Numeration teach ? SIMPLE ADDITION. Simple Addition teaches to put together numbers of the same denomination, into one sum; as 5 dollars, 4 dollars, and 3 dollars, make 12 dollars. Before the pupil enters upon Addition in the usual way, with figures, it would be useful for him to learn to perform easy operations in his mind. For this purpose let him be exercised in the following questions, or in others which are similar. 1. If you have two cents in one hand and two in the other, how many have you in both ? 2. If you have three cents in one hand, and two in the other, how many have you in both ? 3. If you have five cents in one hand, and two in the other, how many have you in both? 4. John has six cents, and Robert has three; how many have they both together? 5. Charles gave five cents for an orange, and two for in apple; how many did he give for both? 6. Dick had four nuts, John had three, and David had two; how many had they all together? 7. Henry had five peaches, Joseph had three, and Tom had two, and they put them all into a basket how many were there in the basket? 8. Three boys, Peter John and Oliver, gave some money to a beggar. Peter gave seven cents, John four, and Oliver three. How many did they all give him? 9. A man bought a sheep for eight dollars, and a calf for seven dollars; what did he give for both? 10. A boy gave to one of his companions eight peaches; to another six ; to another four; and kept two himself; how many had he at first? 11. How many are two and three ?-two and five ?— three and seven ?-four and five ? · 12. How many are two and four and one? 13. How many are three and two and one? 14. How many are four and three and two? 15. How many are five and four and three ? 16. How many are four and five and two? 17. How many are seven and three and one? 18. How many are eight and four and two? 19. How many are nine and five and one? 20. How many are five and six and seven ? 21. How many are four and three and two and one? 22. How many are two and three and one and four? 23. How many are five and three and two and one ?* *It is expected that many of these questions will be varied by the teacher, and rendered harder, or easier, or others substituted as the capacity of the pupil may require. RULE. Place the figures to be added, one under another, so that units will stand under units, tens under tens, hundreds under hundreds, &c. Draw a horizontal line under them, and beginning at the bottom of the first column, on the right hand side, that is, at units, add together the figures in that column, proceeding from the bot tom to the top. Consider how many tens are contained in their sum, and how many remain besides the even number of tens; place the amount under the column of units, and carry so many as you have tens to the next column. Proceed in the same manner through every column, setting down under the last column its full amount. PROOF. Begin at the top of the sum and add the several rows of figures downwards as they were added upwards, and it the additions in both cases be correct, the sums will agree. 1. A boy owed one of his companions 6 cents; he owed another 8, another 5, and another 9. How much did he owe in all ? Ans. 28 cents. 2. A man received of one of his friends 7 dollars, of another 10, of another 19, and of another 50. many dollars did he receive? How Ans. 86 dollars. 3. A person bought of one merchant ten barrels of flour, and paid 40 dollars; of another 20 barrels of cider, for which he paid 60 dollars, and 20 barrels of sugar at 450 dollars; and of another 95 barrels of salt at 570. How many barrels did he buy, and how much money did he pay for the whole ? Ans. 145 barrels, and paid 1120 dollars. 4. A had 250 dollars; B had 375; C had 5423; D, 64320; E, 287432, and F, 4321567. How much would it all make, if put together? Ans. $4679367. Question. 1. What does Simple Addition teach? 2. How do you place the numbers to be added? Where do you begin the Addition? How do you prove a sum in Addition? 13 SIMPLE SUBTRACTION. Simple Subtraction teaches to take a less number from a greater of the same denomination, and thus to Ifind the difference between them. Questions to prepare the learner for this rule. 1. If you have seven cents, and give away two; how jmany will you have left? 2. If you have eight cents, and lose four of them; how many will you have left? 3. A boy having ten cents, gave away four of them; how many had he left? 4. A man owing twelve dollars, paid four of it; how much did he then owe? 5. A man bought a firkin of butter for fifteen dollars, and sold it again for ten dollars; how much did he lose? 6. If a horse is worth ten dollars, and a cow is worth four; how much more is the horse worth than the cow? 7. A boy had eleven apples in a basket, and took out five; how many were left? 8. Susan had fourteen cherries, and ate four of them; how many had she left? 9. Thomas had twenty cents, and paid away five of them for some plums; how many had he left? 10. George is twelve years old, and William is seven how much older is George than William? 11. Take four from eight; how many will remain? 12. Take three from nine; how many will remain? 13. Take five from ten; how many will remain? 14. Take six from ten; how many will remain? 15. Take six from eleven; how many will remain? 16. Take five from twelve; how many will remain? 17. Take four from thirteen; how many will remain? 18. Take six from fourteen; how many will remain? 19. Take six from fifteen; how many will remain? 20. Take eight from sixteen; how many will remain? 21. Take nine from twelve; how many will remain? 22. Take nine from fourteen; how many will remain? 23. Take three from thirteen; how many will remain? 2 |