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an unit to express 1 part each time the quantity is . divided, will become less in value in the same proportion. -

Reduction, is changing a number from one denomination to another, without altering its value.

When a number in one denomination is to be chang- ed to a less denomination.

RULE,

Multiply the given number by as many as it takes of that denomination to which it is to be reduced, to make 1 in the given denomination.

Question 1. In 3 had. of rum, how many gallons ! - . .

Operation 1. . Operation 2.
- 3 . . 63
, 63 * - 63
— * 63.
189 ... --
189

Illustration.—It was proved, pages 43, 44, 45, that we place the multiplier in the product, once for each unit in the multiplicand, consequently, multiplying a greater denomination by as many as it takes of a less to make one in the greater, we place the value of each unit of the greater in the product. The product is equal to the multiplicand, for we place the multiplier, which is equal to an unit in the multiplicand, once in the product for each unit in the multiplicand. The product is of the same denomination as the multiplier, for it is the same number that we should obtain, were we to set down the multiplier as many times as there are units in the multiplicand, and add them together, the sum of several numbers always being of the same denomination as the numbers themselves; or the product is of the

same denomination as the multiplier, because it is as much larger than the multiplicand as the multiplier is larger than one.

In the 2d operation of the last question, by setting down the number of gallons in one hogshead, as many times as there are hinds. and adding them together, we obtain a number expressing all the gallons in the 3 hlids. but by multiplying the number of hbds. by 63, the number of gallons contained in 1 hlid., we obtain the same number. The product being equal to the multiplicand, 189 gal. express the same quantity of liquor as the 3 hbds., but in a less denomination.

2. In 25 £. how many shillings? Ans. 500, 3. In 500 s. how many pence 2 Ans. 6000. 4. In 6000 d. how many farthings 2 - Ans. 24000. 5. In 10 lb. Troy weight, how many ounces ! * Ans. 120. 6. In 120 oz. how many pennyweights? - Ans. 2400. 7. How many drams in 7 oz. Apothecaries' weight? Ans. 56. 8. In 14 T. how many hundreds 2 Ans. 280. 9. In 280 cwt. how many quarters ? Ans. 1120. 10. In 1120 qr, how many pounds? Ans. 31360. 11. In 1120 qr, how many pounds, Neat weight? - Ans. 28000.

JNote 1. When the given number consists of two denominations, the greater denomination must be reduced as directed by the rule, and if the less denomination be of the same name as the multiplier, it must be added to the product. The sum will express the value of the two given denominations, for the product is equal to the number in the greater denomination, and being of the same denomination as the multiplier, and the number in the less denomination being of the same denomination, by adding it to the product, we obtain both of the given numbers in the sum.

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9 6 7 number of furlongs in 120 M. 7 fur.

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In 15 yd. 3 q1... how many quarters?
Ans. 63.
How many quarters in 15 E. Fl. 2 qr. ?
Ans. 47:
In 15 E. E. 2 qr, how many quarters?
Ans. 77:
How many quarters in 15 E. Fr. 1 qr. ?
Ans. 91.
In 16 Y. 3 mo, how many months?
- Ans. 211.
In 125 square M. 6 A. how many acres?
- Ans. 80006.

a number is to be reduced to any less denomination.

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Multiply the highest denomination by as many as it takes of the next less to equal one in the greater; multiply the product by as many as it takes of the next less denomination to make one in that product.

Multiply each succeeding product in the same manner until the given number is reduced to the denomination required, and add to each product the given number of the same denomination.

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1 2 0 number of hundreds in 6 T.
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1 9 2 4 0 0 the number of ounces in 6 T. 1 qr. 1 0 the given ounces added.

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Illustration of the last rule.—By the last illustration, each product expresses the same value as the multiplicand which precedes it, and as we add the several numbers in the less denominations to products of the same name, the last product with the number added to it, (if there be any given of that denomination,) will express the same value as all the numbers given of the several denominations. See operation of the last question.

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20. In 21+, 15 s. 11 d. 3 qr., how many farthings? Ans. 20927. 21. In 51 C. 127 ft., how many solid feet of wood 2 Ans. 6655. 22. In 16 lb. 17 put. 21 gr. how many grains 2 Ans. 92589. 23. How many inches long must a rope be to reach across a yard which is 8 rods across 2

Ans. 1584. 24. 6 shillings equal 1 dollar, how many peace in 1000 dollars 2 Ans. 72000.

25. How many seconds has that person lived whose age is 27 Y. 2 w. 3 d. 25 m. ” Ans. 850'609°500. 26. If 1 square rod of land produce 1 p.k. of corn, how many pecks will 5 A. 3 R. produce 2

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28. How many seconds in 15° 2 Ans. 54'000. 29. How many pints in one hogshead 2 Ans. 504. 30. How many pints in a hbd. of beer 2 Ans. 432. 31. 28 shillings equal one guinea, how many shillings in 18 guineas' Ans. 504. 32. A gentleman wishes to draw off 5 hlid. of wine into bottles of 1 pt. each; how many bottles will be required ? Ans. 2520. 33. A farmer gives his sheep one bushel and one peck of corn a day, giving to each sheep half a pint ; how many sheep has he ” Ans. 160. 34. How many cubick blocks, each containing one solid inch, can be made from a stick of timber containing 39 solid ft. 500 in., allowing 230 solid in. for waste 7 Ans. 67662.

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