PROCESS. 100) 423.68 4.2368 .014532 by .0692. 14. 71.142 by .0071. 15. .027538 by .0326. ANALYSIS.—Since each removal of a figure one place to the right decreases its value tenfold, the removal of the decimal point one place to the left divides by 10, and the removal of the decimal point two places to the left divides by 100. Hence, RULE. To divide by 1 with any number of ciphers annexed, remove the decimal point as many places to the left as there are ciphers annexed. 23. At $8.25 per ton, how much hay can be bought for $29.35? 24. At $.18 per dozen, how many bought for $32.40? dozen eggs can be 25. If I pay $106.40 for 35 hats, how much do they each cost me? 26. How many hogsheads of molasses, at $57.38 each, can be purchased for $1319.74? 27. How many stoves, at $21.35 each, can be bought for $789.95? SHORT PROCESSES. 216. Many methods have been devised for abbreviating the processes of computation, among which the following are of much practical value: CASE I. 217. To multiply by a number a little less than a unit of the next higher order. 1. How much less than 10 is 9? 1000 is 999? Than 100 is 98? 100 is 96? Than 100 is 99? Than Than 100 is 97? Than 2. How much less than 10 times a number is 9 times the number? Than 100 times is 99 times? 999 times? Than 100 times is 97 times? is 997 times? Than 1000 times is Than 1000 times then subtract from the product three times the multiplicand, leaving 97 times the multiplicand. Multiply: 2. 3856 by 99. 4. 48567 by 999. Multiply: 6. 346725 by 997. 10. What will be the cost of 385 bushels of corn at $.97 per bushel? 11. How much must be paid for 1373 pounds of tea at $.96 per pound? 12. At $97 per acre, what will a farm of 139 acres cost? CASE II. 218. To multiply when one part of the multiplier is a factor of another part. 1. Multiply 4 by 8; 2. Multiply 7 by 6; 4 by 8 tens; 4 by 16 tens. 7 by 6 tens; 7 by 18 tens. 3. When 7 times a number is known, how may 21 times a number be found? 21 tens times? 21 hundreds times? 124 14736 44208 456816 WRITTEN EXERCISES. 1. Multiply 3684 by 124. PROCESS. 3684 ANALYSIS.-The multiplier may be regarded as composed of 12 tens and 4 units, or 3 times as many tens as units. We therefore first multiply by 4 units; and since there are 3 times as many and tens as nnits, we multiply this product by 3, write the result as tens by placing it one place to the left of units. CASE III. 219. To multiply by a number which is an aliquot 3. What part of a dollar are 50 cents? 25 cents? 20 cents? 10 cents? 12 cents? 4. What part of a dollar are 33 cents? 163 cents? 220. An Aliquot Part of a number is such a part as will exactly divide the number. Thus, 5, 10, 121, etc., are aliquot parts of 100. The aliquot parts of 10, commonly used, are: The aliquot parts of 100, commonly used, are: PROCESS. 4)43400 10850 EXERCISES. ANALYSIS.-Since 25 is of 100, we may multiply by 25 by first multiplying by 100, and then taking of the product. PROCESS. 3)85 28.33 2. What will 85 yards of cloth cost at $.33 per yard? ANALYSIS.-At $1 per yard, the cloth would cost $85; and at $.33, or of a dollar, it will cost of $85, or $28.33}. 11. What will be the cost of 27 yards of cloth at $.25 per yard? 12. When butter is worth 33 cents a pound, what will 824 pounds be worth? 13. What will be the cost of 216 pounds of tea at $.75 per pound? 14. What will 287 bushels of oats cost at 37 cents per bushel? 15. What will 394 bushels of potatoes cost at 62 cents per bushel? 16. What is the value of 319 bushels of wheat at $1.37 per bushel? CASE IV. 221. To find the cost when the quantity and the price of 100 or 1000 are given. 1. When the cost of 100 articles is known, how can the cost of 500 be found? 600? 800? 900? 2. When the cost of 100 articles is given, how can the cost of 250 be found? 350? 750? 850? 950? 3. How 4. How many times 100 is 250? 275? 280? 285? many times 1000 is 3000? 3500? 3750? 4585? |