5. If a ship sail 192 miles a day, how many miles will she sail in 56 days? Ans. 10752 miles. 6. A merchant bought 46 bales of cloth, each bale containing 35 pieces, and each piéce 28 yards; how many yards did he buy in all? 7. Multiply 35860205 by 365, 8. Multiply 2703682 by 8409, 9. Multiply 15569800 by 8300, Questions. 1. What does Simple Multiplication teach? What does it perform the work of? 2. What is the number to be multipli ed called? What is the number you multiply by, called? 3. What is the number found by the operation, called ? What are the multiplier and multiplicand called? 4. When the multiplier is not greater than 12, how do you multiply? 5. When the multiplier consists of several figures, how do you write it down? In multiplying, where do you place the Ans. 45080. Ans. 13088974825. Ans. 22735261938. Ans. 129229340000. first figure in the product? 6. What do you do with the several products? 7. How do you prove multiplication? 8. When there are ciphers on the right hand of the factors, how do you multiply? 9. How do you multiply by 10, 100, 1000, &c.? 10. What is a composite number? 11. When the multiplier is a compo site, number, how do you multiply? 12. What is the sign of multiplication! Let me see you write it down. DIVISION. 1. If you divide 15 apples equally among 3 boys, how many will each have? How many times 3 in 15? 2. If 15 apples be divided equally among 5 boys, how many will each have? 5 in 15, how many times? 3. James has 16 cents to buy pencils with; how many can be buy at 4 cents apiece? How many times is 4 cents contained in 16 cents? 4. How many oranges, at 6 cents apiece, can you buy for 36 cents? 6 in 36 how many times? 5. A man bought 9 lemons for 81 cents; how much did he give apiece? 9 in 81 how many times? 6. How many barrels of cider, at 3 dollars a barrel, can be bought for 27 dollars? 7. In an orchard there are 48 trees, standing in 8 rows; how many trees are there in a row? How many times is 8 contained in 48? 8. How many barrels of flour can you buy for 84 dollars, at 7 dollars a barrel ? 9. If 9 yards of cloth cost 27 dollars, what is 1 yard worth? 10. A man worked 8 days for 40 shillings; how much was that a day? 11. A man divided 72 cents equally among 18 poor boys; how many cents did he give to each ?-He divided them as follows, viz: sum is large, and would require a great many subtractions, the operation is more easily performed by the Rule called Division. SIMPLE DIVISION Teaches to find how many times one simple or whole number is contained in another, and also what remains Hence it performs the work of several subtractions in a concise manner. There are four principal parts in division, viz: 1. The Dividend, or number given to be divided. 2. The Divisor, or number given to divide by. 3. The Quotient, or answer to the question, which shows how many times the divisor is contained in the di vidend. 4. The Remainder, which is always less than the divisor, and of the same name of the dividend. SHORT DIVISION Is when the divisor does not exceed 12. RULE. 1. Find how many times the divisor is contained in the first left hand figure, or figures of the dividend; place the figure expressing the number of times under the dividend, and carry the remainder, as so many tens to the next figure and divide the sum it makes as before; and if the divisor is not contained in this sum, place a cipher under it, and carry the whole as so many tens to the next figure thus proceed till you have divided all the figures of the dividend. Proof-Multiply the divisor and quotient together, and add the remainder (if there be any) to the product; and if the work be right the sum will equal the dividend. EXAMPLES. 1. How many yards of cloth, at 3 dollars a yard, can be bought for 654 dollars? Operation. Divisor 3)6 5 4 Quotient 2 18 yds. Ans. We must find how many times 3 dollars is contained in 654 dola lars; that is, we must divide 654 by 3. We find that the diviser 3 is contained in 6, the first figure of the dividend, 2 times. Then 3 is contained in 5, the next figure of the dividend, 1 time and 2 remain. This remainder we carry to the next figure as so many tens; thus, 2 tens =20, which added to 4, the next figure, makes 24, and 3 is contained in 24, 8 times. In this example, observe, that the 6 which we first divide, means 6 hundred, and the 2 which we place under it means 2 hundred, showing that 3 is contained in 600, 200 times, and the 5 means 5 tens, and the 1 which we place under it means 1 ten, &c. Proof. If 3 contained in 654, 218 times, then it is evident that 218 times 3, or which is the same thing, 3 times 218, will just make 654; and by multiplying them together we find the product to be 654, the di vidend; therefore right. 2. A father left his 6 children 2436 dollars to be equally livided among them; how many dollars had each? Operation. Divisor 6) 2 4 3 6 Quotient 4 0 6 Ars. Here 6, the divisor, is not con tained in 2, the first figure of the dividend; therefore we join the 2 (thousands) to the 4 (hundreds) making 24 (hundreds ;) and 6 is contained in 24 (hundreds) 4 (hundred) times. Then 6 is not contained in 3, the tens of the dividend, therefore we put a cipher under, (that is, in the quotient,) and join the 3 (tens) to the 6 (units,) making 36; and 6 is contained in 36, 6 times. Ans. Each had $406 9. How many times is 6 contained in 7326? Ans. 1221: 10: How many times is 5 contained in 4565? Ans. 913: 11. How many times is 7 contained in 84637? Ans. 12091. 12. Divide the number 9784 into 8 equal parts. Quot. 1223. Quotient 30502. 13. Divide 366024 by 12. 14. If 7 dollars will buy 1 Barrel of flour, how many barFels of flour may be bought for $3822 ? Ans. 546. 15. A market man received 2943 cents for melons that he sold at 9 cents apiece; how many did he sell? Ans. 327. 16. How many times is 7 contained in 6680, and how many över? Ans. 954 times, and 2 over. 17. A merchant has $5122 to purchase flour with; how many barrels can he buy at 8 dollars a barrel, and how many dollars will he have left? Ans. 640 barrels and 2 dollars left. 18. A prize of 3825 dollars was divided equally among 4 men; how much was each man's part? Note. We divide the 3825 dollars among the 4 men, and find that each must have 956 dollars, and there is $1 left, which we must divide. Now if we divide 1 dollar into 4 equal parts, each part will be of a dollar. Ans. Each man must have 9561 dollars Had this remainder been 3 dollars, it is evident that each man would have had 3 times of a dollar, that is of a dollar, more; and in all cases where there is a remainder, we may obtain the true quotient by placing the divisor under the remainder, with a line between, as above. Thus Remainder 1 shows that the divisor 4 is contained 4 in the remainder one fourth of a time. 19. How many cwt. of rice, at 4 dollars a cwt., may be bought for 947 dollars? Ans. 236 cwt 20. How many cwt. of sugar, at 9 dollars per cwt., can be bought for 2944 dollars? Ans. 327. 21. How many barrels of pork, at 11 dollars a barrel, 'can be bought for 2478 dollars? Ans. 225 barrels. LONG DIVISION. When the divisor exceeds 12, we cannot conveniently perform the operation in the mind; we therefore set the quotient figures on the right hand of the dividend, and write down the whole computation at full length, and this is called long division. RULE. I. Find how many times the divisor is contained in the east number of the left hand figures of the dividend, that will contain it once, or more: place the figure expressing the number of times, to the right hand of the dividend for the first quotient figure. II. Multiply the divisor by this quotient figure, and place the product under that part of the dividend used, and subtract it therefrom. III. Bring down the next figure of the dividend to the right hand of the remainder, and divide this number as before. Thus proceed till you have brought down, and divided, all the figures of the dividend. Note. 1. If the product of the divisor by any quotient figure, be greater than that part of the dividend used, it shows that the quotient figure is too large, and must be diminished. If the remainder at any time be equal to or |