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PROCESS.

16. Divide 423.68 by 100.

ANALYSIS.—Since each removal of a figure 100) 423.68 one place to the right decreases its value ten

fold, the removal of the decimal point one place 4.2368

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.

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Divide:

Divide:
17. 48.26 by 100. 20. 4.897 by 100.
18. 382.457 by 1000. 21. 06045 by 1000.

19. 13.8542 by 1000. 22. 3845.63 by 10000.
23. At $8.25 per ton, how much hay can be bought for
$29.35?
24. At $ .18 per dozen,

how many

dozen eggs can be bought for $32.40 ?

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 ?

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11.

216. Many methods have been devised for abbreviating the processes of computation, among which the following are of much practical value:

12.

CASE I.

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217. To multiply by a number a little less than a unit of the next higher order.

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1. How much less than 10 is 9? Than 100 is 99? Than 1000 is 999? Than 100 is 98? Than 100 is 97? Than 100 is 96 ?

2. How much less than 10 times a number is 9 times the number? Than 100 times is 99 times? Than 1000 times is 999 times? Than 100 times is 97 times? Than 1000 times is 997 times?

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WRITTEN EXERCISES.

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1. Multiply 4685 by 97. PROCESS.

ANALYSIS.—Ninety-seven 46 8500 -100 times 4685

times a number is 100 times 14055

the number minus 3 times 3 times 4685

the number. We annex two 45 4445 = 97 times 4 6 8 5 ciphers to the multiplicand,

thus multiplying by 100, and then subtract from the product three times the multiplicand, leaving 97 times the multiplicand.

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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.

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1. Multiply 4 by 8; 4 by 8 tens; 4 by 16 tens.
2. Multiply 7 by 6; 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?

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PROCESS.

1. Multiply 3684 by 124.

ANALYSIS.—The multiplier may be regarded as 3684 composed of 12 tens and 4 units, or 3 times as 124 many tens as units.

We therefore first multiply by 4 units; and since there are 3 times as many 14736

tens as nnits, we multiply this product by 3, and 44208

write the result as tens by placing it one place to 456816 the left of units.

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Multiply:

2. 3825 by 63.
3. 5973 by 93.
4. 8126 by 123.
5. 6924 by 213.
6. 14273 by 246.
7. 28653 by 328.
8. 68435 by 217.

Multiply:

9. 3692 by 357. 10. 6384 by 248. 11. 4239 by 369. 12. 12783 by 189. 13. 36412 by 279. 14. 36485 by 2408. 15. 29753 by 3609.

CASE III.

PR

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219. To multiply by a number which is an aliquot part of some higher unit.

1. What part of 10 is 2? Is 5? Is 21? Is 31?

2. What part of 100 is 10? Is 20 ? Is 25? Is 50 ? Is 121? Is 331?

3. What part of a dollar are 50 cents? 25 cents? 20 cents? 10 cents? 121 cents ?

4. What part of a dollar are 33} cents? 16 cents ?

220. An Aliquot Part of a number is such a part as will exactly divide the number.

Thus, 5, 10, 123, etc., are aliquot parts of 100.
The aliquot parts of 10, commonly used, are:
5=
= } of 10.

| 3} = 1 of 10. | 21= 4 of 10.
The aliquot parts of 100, commonly used, are:
50 = 1 of 100. 33} = of 100, 10=1 of 100.
25= 1 of 100. 163 = 1 of 100.

81=1 of 100. 20 } of 100. 12}=} of 100.

61=1 of 100. Other parts of 100 are: 40 == of 100. 37;=j of 100. | 663 = s of 100. 60 of 100.

621= of 100. 75 of 100. 80 =- 4 of 100. 871={ of 100. 433 = of 100.

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II' RITTEN

EXERCISES.

1. Multiply 434 by 25.

PROCESS.

4) 43400

10850

ANALYSIS.—Since 25 is of 100, we may multiply by 25 by first multiplying by 100, and then taking of the product.

2. What will 85 yards of cloth cost at $.33} per yard ?

PROCESS.

3) 85

ANALYSIS.—At $1 per yard, the cloth would cost $85; and at $.33}, or } of a dollar, it will cost } of $85, or $28.333.

28.33}

Multiply:

3. 688 by 127.
4. 402 by 163
5. 5056 by 25.
6. 75630 by 331.

Multiply:

7. 8404 by 50. 8. 2160 by 371. 9. 4236 by 663. 10. 7288 by 75.

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11. What will be the cost of 27 yards of cloth at $.25 per

yard?

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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 374 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 $1.371 per

bushel ?

CASE IV.

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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 many times 100 is 250? 275? 280? 285? 4. How many times 1000 is 3000? 3500? 3750? 4585?

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