SECTION 4. ABBREVIATIONS. When there are ciphers standing between figures, in the multiplier, they may be disregarded. 1. What is the product of 12318 multiplied by 7004? 12318 7004 49272 86226 86275272 2. What is the product of 9651 multiplied by 304 ? 3. How many are 1001 times 57 906? 4. How many are 905 times 820 437 ? Ciphers on the right hand of the multiplier or multi plicand may be disregarded till the multiplication is per formed, and then placed on the right hand of the product 5. What is the product of 5763 multiplied by 3600 ? 5763 3600 34578 17289 20746800 6. What is the product of 158 multiplied by 350 ? 7. How many are 800 times 369 ? 8. How many are 40 times 4728 ? Ciphers on the right hand of the multiplier and mul tiplicand both, may all be disregarded in multiplying, and finally placed on the right hand of the product. 9. What is the product of 46000 multiplied by 340. 46000 340 134 138 1564000C 10. What is the product of 8370 multiplied by 240? 11. How many are 90 times 761000? 12. How many are 5700 times 6800? When the multiplier is 10, 100, 1000, &c. merely place the ciphers of the multiplier on the right hand of. the multiplicand, and it becomes the product. 13. What is the product of 5 multiplied by 10? 14. What is the product of 17 multiplied by 100? 15. What is the product of 49 multiplied by 1000 › 16. In 1 dollar there are 100 cents. How many cents are there in 6 dollars? 17. How many cents are there in 25 dollars? 18. If 1 box of lemons cost 7 dollars, how many cents will it take to pay for 10 boxes? When the multiplier is a number, that can be produced by multiplying two smaller numbers together, multiply the multiplicand first by one of the smaller numbers, and the product thence arising by the other. 19. Find the price of 32 horses, at 96 dollars apiece. 96 price of 1 horse. 8 768 price of 8 horses. 4 3072 price of 4 times 8 horses, or 32 horses Observe in the above example, that 32 can be produced by multiplying 4 and 8 together. The 4 and the 8 are called the factors of 32. 20. A merchant bought 24 hogsheads of molasses at 19 dollars a hogshead. What did the whole cost? In this example we consider 24 to be the multiplier. For 24, we can find several different sets of factors; viz. 3, 8; also, 4, 6; also, 2, 3, 4; also, 2, 2, 6. Either set of these factors may be used. 21. If a ship sail at the rate of 129 miles a day, how many miles will she sail in 72 days? 22. If 1 man can dig 41 bushels of potatoes in a day.. how many bushels can 28 men dig? 23. Multiply 425 by 36, using the factors of 36. 24. How many are 63 times 540 ? 25. How many are 45 times 2807 ? Questions to be answered Orally. (1) What is meant by multiplicand? what by multiplier?-ana what by product? (2) When we say, 5 times 8 are 40, which of these numbers is the multiplicand?which the multiplier ? and which the product? (3) Can you obtain the product of any two numbers, by means of addition? (4) Recite the rule for multiplication. (5) When there are ciphers between figures in the multiplier, what may be done? (6) When there are ciphers on the right of the multiplier, or multiplicand, or right of both, what may be done with them? (7) In what inanner can you multiply by 10, by 100, by 1000, &c.? (8) What is meant by the factors of a number? (9) Name two factors of 24. (10) Name three factors of 24. (11) Name two factors of 36. (12) Name three factors of 36. on the Perform the following examples by either of the foregoing methods, which may be found convenient. 26. What is the value of a farm consisting of 200 acres of land, at 40 dollars an acre? 27. Suppose a book to contain 235 pages, 45 lines in each page, and 50 letters in each line;- how many letters are there in the book? 28. Suppose an orchard to consist of 109 rows, 126 trees in a row, and 1007 apples on a tree;- how many trees, and how many apples are there? 29. Suppose a crew of fifty men have provision for 30 days, allowing each man 20 ounces a day;- how many days would it last, if each man ate 1 ounce a day? 30. Suppose a crew of fifty men have provision for 30 days, allowing each man 20 ounces a day;-how many men would it serve for the same time, if each man ate one ounce a day? 31. How many fishes would be caught by 14 boats, employed for 30 days, each boat drawing a net 15 times a day, and taking 13 fishes each draught? 32 What is the product of 90042 multiolied by 9009 ? CHAP. V. DIVISION. SECTION 1. 1. How many yards of cloth, at 3 dollars a yard, can be bought for 396 dollars? Here we must find how many times 3 dollars there are in 396 dollars: that is, we must divide 396 by 3. 3)396 We first divide the 3 hundreds, then the 132 9 tens, and then the 6 units; thus, 3 in 3, once; 3 in 9, 3 times; 3 in 6, 2 times. Observe in the above example, that the 3 which we first divide, means 3 hundred; and the 1 which we place under it means 1 hundred, showing that 3 is contained in 300, 100 times. The 9 means 9 tens, and the 3 which we place under it means 3 tens, showing, that 3 Is contained in 90, 30 times. A Dividend is a number which is to be divided; such is the number 396 in the above example. A Divisor is a number by which we divide; such is the number 3 in the above example. The Quotient is the number of times which the divisor is contained in the dividend; such is the number 132 in the above example. Find the quotient in each of the following examples. (2). 4)8 (5). 4)4884 (3). 2)46 (4). 3)936 6. A man laid out 69 dollars for sheep, paying 3 dollars a head for them. How many did he buy? 7. If 4 bushels of wheat will pay for 1 barrel of flour, how many barrels will 848 bushels pay for? SECTION 2. 1. How many times is 4 contained in 3684 ? 4)3684 921 In this example we find that 4 is not contained in 3, therefore we join the 3 with the 6, and say, 4 in 36, 9 times 2. How many times is 7 contained in 56? 3. How many times is 9 contained in 639? 4. How many times is 5 contained in 405? 5. How many times is 4 contained in 3248? 6. How times is 3 contained in 1569? 7. If 4 horses are required to draw 1 wagon, many wagons might be drawn by 168 horses? many how 8. How many yards of broad-cloth, that is sold at 6 dollars a yard, can be bought for 492 dollars? 9. If a man can travel 5 miles an hour, how many hours will it take him to travel 205 miles? 10. Suppose 69 to be a dividend, and 3 a divisor; what is the quotient? 11. Suppose 128 to be a dividend, and 4 a divisor, what is the quotient? 12. Suppose 486 to be a dividend, and 6 a divisor; what is the quotient? 13. How many times is 4 contained in 872? 4)872 218 4 in 8, 2 times; 4 in 7, 1 time, and there is 3 over; (we join this 3 with the 2, making 32,) then 4 in 32, 8 times. 14. How many times is 6 contained in 726? 15. How many times is 8 contained in 896? 16. How many times is 5 contained in 1605? 17. How many times is 7 contained in 924? 18. How many times is 4 contained in 6732? 19. Suppose 1585 to be a dividend and 5 the divisor; what is the quotient? 20. Suppose 4518 to be a dividend and 6 the divisor; what is the quotient? 21. How many times is 7 contained in 742? 7)742 106 The divisor not being contained once in the ten's place of the dividend we write a O in the ten's place of the quotient. 22. How many times is 3 contained in 609? 23. How many times is 8 contained in 1624? 24. How many times is 5 contained in 4015? 25. How many times is 9 contained in 2880? 26. How many times is 7 contained in 10500? K |