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2. In 6.86 143, how many pence?

20

1734 the shillings in £.86 14.

12

Answer, 20811 the pence in £.86 14 3.

In this example, in multiplying by 20, I added in the 14 shillings, and by 12, the 3 pence.

The method of proof is, by dividing the last product by the last multiplier ; and so on to the first The first question is proved thus :

4)174720 farthings.

12 43680 pencer
20)3640 shillings.

£.182 equal to the first sum.
3. In £.876 14 8 how many farthings?

Answer, 841665. 4. In 85 guineas how many pence ?

Answer, 28560. 5. In 21/b. 3pwt. 18gr. troy, how many grains ?

16. 02. pwt. 87 21

3 18 12

252 the ounces in 211b.
20

5043 the pennyweights in 21lb. 3pwt,

24

20180 10087

Auswer, 121050 the grains in 2113. 3pwt. 18gr.

6. In 81Cwt. 3qr. 18/b. how many pounds ?

Answer, 9174. 7. In 67. 2Cwt. how many drams?

Answer, 3497984. 8. In 141b. 2oz. 17gr. Apothecaries' weight, how many grains ?

Answer, 81617. 9. In 76yds. 2gr. how many nails ?

Answer, 1224. 10. In 149 English Ells, how many nails?

Answer, 2980. 11. How many barley-corns will reach from Boston to Haverhill, it being 33 miles ?

Answer, 6272640. 12. In 2 miles 1 fur. 18 rods, how many feet?

Answer, 11517. • 13. Reduce 143 acres, to rods.

Answer, 22880. 14. In 36yds. 3ft. square measure, how many inches?

Answer, 47088. 15. In 132 cubic yards, how many inches ?

Answer, 6168592. 16. In 14 cords of wood, how many inches?

Answer, 3096576. 17. In 84 gallons, how many gills?

Answer, 2688. 18. In 35 gallons, 2 qts. how many pints ?

Answer, 284. 19. In 17 hhd. 14 gal. of wine, how many quarts?

Answer, 4340. 20. In 148 barrels of beer, how many pints ?

Answer, 42624. 21. In 846 bushels, how many quarts ?

Answer, 27072. 22. In 347 days, how many minutes ?

Answer, 409680

23. In 72 Julian years, 10 days, 18 h. 12 m. how many seconds?

Answer, 2273076720.

In the last example, I brought the years into days, by multiplying them by 365, and adding one fourth of the number of years to the product, for the 6 hours: in the Julian year.

Reduction Ascending.

RULE. Divide the lowest denomination given, by so many of that denomination as make one of the next greater ; so continue, till you have brought it to the denomination required. The proof of this rule is by Reduction Descendinga

EXAMPLES. 1. In 174720 farthings, how many pounds?

Farthings. Farthings in a penny 4) 174720

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Shillings in a pound 20) 3640

Answer, 4.182
2. In 547329 pence, how many pounds!

d.
12) 547329

20) 45610 9

Answer, £.2280 10 9

3. In 121050 grains, how many pounds troy?

20 12 lb. oz. pwt. gr. 24)121050(5043(2526-21 o* 3

0 3 18 Answer. 120 40

[blocks in formation]

:90 43 0 Note--. The first and third 72 40 of these questions,are proofs

of the first and fifth in re18 gr. 3 prut. duction descending.

In 430728 grains, apothecaries' weight, how many pounds?

Answer, 741b. 10oz. 4dr. 2sc. 8gr . In 851200 ounces, avoirdupois, how many hundred weight?

Answer, 475Cwt. 6. In 1143210 drams, how many pounds ?

Answer, 44651b. 1002. 10dr. 7. In 46732 nails, how many yards ?

Answer, 2920yds. 3gr. 8. In 3205 quarters, how many English Ells?

Answer, 641. 9. In 12345 barley-corns, "how many rods?

Answer, 20r. 12ft. 11in. 10. In 35721805 inches, how many miles ?

Answer, 563m. 6. 13rod. 2ft. Tin. 11. In 39042 rods, how many acres ?

Answer, 244 A. 2rods. 12. In 5673578 square inches, how many square rods?

Answer, 144rods, 21yd. 6ft. 122in. 13. In 7032864 cubic inches, how many cubic yds.?

Arswet, 150yds. 19ft, 1632 in.

14. In 4567890 gills, how many hogsheads of wine?

Answer, 2265hhd. 51gal. 2qr. 2gil. 15. In 9987 pints, how many gallons ?

Answer, 1248gal. 19t. 1 pt. 16. In 80535 quarts,how many hogsheads of beer?

Answer, 372hhd. 45gal. 3qr. 17. In 45030 pints, how many bushels ?

Answer, 703bu. 2pk. 398. 18. In 5791356 seconds, how many days?

Answer, 67da. 42m. 368. 19. In 8321700 minutes, how many years?

Answer, 15%. 300da. 5h.

COMPOUND MULTIPLICATION.

Compound Multiplication is when the multiplicand consists of several denominations.

CASE 1. When the multiplier does not exceed 12, set it under the lowest denomination of the multiplicand; then multiply each denomination by the multiplier, observing to carry as in compound addition.

EXAMPLES. 1. What will 3 tons of hay come to at £.3 y 5 per ton ?

1.

d.
7 *5 priće' of 1 ton.

3

2

Answer, 6.10

3 price of 3 tons. In this example, I say, 3 times 5 åre 15 pence,equal 1 Surg and 3 pance; I set down 3, and proceeding

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