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Denominate Numbers — Weight, 350. Troy weight is used in weighing gold, silver, and jewels.

TROY WEIGHT.
24 grains (gr.) = 1 pennyweight (pwt.).
20 pennyweights = 1 ounce (oz.).
12 ounces

= 1 pound (lb.).

351. Apothecaries' weight is used in mixing medicines and in selling them at retail.

APOTHECARIES' WEIGHT.

20 grains (gr.)= 1 scruple (O).
3 scruples = 1 dram (3).
8 drams = 1 ounce (3).
12 ounces = 1 pound (lb).

NOTE 1. - The pound Troy and the pound Apothecary are equal, each weighing 5760 grains. The pound Avoirdupois weighs 7000 Troy or Apothecary grains.

NOTE 2. — The ounce Troy and the ounce Apothecary are each 486 grains; the ounce Avoirdupois is 4371 grains.

QUERY. — Which is heavier, a pound of feathers or a pound of gold? An ounce of feathers or an ounce of gold ?

PROBLEMS.

1. Change 5 lb. Avoirdupois weight to pounds, ounces, etc., Apothecaries' weight. 2. How many

5 gr. powders can be made from one Avoirdupois ounce of quinine?

3. One Avoirdupois ton of gold is how many Troy pounds?

4. Twenty-four Troy pounds equal how many Avoirdupois pounds ?

(P. 379.)

352. MISCELLANEOUS TABLES.

12 units
12 dozen

1 dozen. 20 units = 1 score.

24 sheets (paper)= 1 quire. 1 great gross. 20 quires = l ream.

1 gross.

12 gross

353. APOTHECARIES' FLUID MEASURE.

60 minims (m) = 1 fuid dram (f 3).

8 fluid drams = 1 fluid ounce (f 3).
16 fluid ounces = 1 pint (O).
8 pints

1 gallon (Cong.).
One minim of water is about 1 drop.

=

354. ANGULAR MEASURE.
60 seconds ("') = 1 minute (1).
60 minutes = 1 degree ().
360 degrees = 1 circumference.

355. MEASURE OF TIME.

60 seconds (sec.)= 1 minute (min.).
60 minutes 1 hour (hr.).
24 hours

= 1 day (da.).
7 days

1 week (wk.). 365 days

=1 common year. 52 wk. 1 da. = 1 common year. 366 days

= 1 leap year. 52 wk. 2 da.

: 1 leap year.

=

(P. 379.)

So tcach us to number our days that we may apply our hearts unto wisdom."

וי

SHORT METHODS

IN

MULTIPLICATION AND DIVISION.

Art. 1. To multiply a number by 50: Multiply 1 of the number by 100. Why?

46 x 50 1 of 46 x 100 = 2300
47 x 50 of 47 x 100 = 2350

Multiply:
44 by 50 32 by 50 35 by 50
36 by 50 38 by 50 27 by 50
64 by 50 42 by 50 55 by 50

82 by 50 76 by 50 43 by 50
(a) Find the sum of the twelve products.

Art. 2. To multiply a number by 51: Take 50 times the number, to which add the number itself. Why?

48 x 51 50 times 48 = 2400 2400 + 48 = 2418
37 x 51 50 times 37 = 1850 1850 + 37 = 1887

Multiply:
26 by 51 34 by 51 35 by 51
46 by 51 32 by 51 29 by 51
24 by 51 42 by 51 43 by 51

66 by 51 84 by 51 33 by 51
(b) Find the sum of the twelve products.

= 2250

Art. 3. To multiply a number by 52: Take 50 times th. number, to which add twice the number. Why?

34 x 52 50 times 34 = 1700 1700 + 68=1768
45 x 52 50 times 45

2250 + 90 = 2340
Multiply:
26 by 52 38 by 52 27 by 52
18 by 52 14 by 52 17 by 52
24 by 52 32 by 52 35 by 52

36 by 52 44 by 52 23 by 52

(c) Find the sum of the twelve products. Art. 4. To multiply a number by 49: Take 50 times the number, from which subtract the number itself. Why?

24 x 49 50 times 24=1200 1200 - 24 = 1176
33 x 49 50 times 33 = 1650 1650 - 33=1617

Multiply:
18 by 49 22 by 49 27 by 49
28 by 49 34 by 49 35 by 49
16 by 49 46 by 49 43 by 49

26 by 49 38 by 49 31 by 49

(d) Find the sum of the twelve products. Art. 5. To multiply a number by 331: Multiply of the number by 100. Why? 36 x 33}

of 36 x 100 = 1200 37 x 331

Žof 37 x 100 = 1233}

Multiply:
24 by 33} 27 by 33}

28 by 333
18 by 33 21 by 33} 22 by 33
30 by 33} 33 by 33} 35 by 33}
15 by 33}
39 by 33}

41 by 333
(e) Find the sum of the twelve products.

Art. 6. To multiply a number by 343: Take 333 times the number, to which add the number itself. Why? 24 x 343

33] times 24 = 800 800 + 24 = 824 25 x 343 333 times 25 = 833} 833} + 25 = 8583

Multiply: 18 by 343 27 by 343

24 by 343
21 by 34

33 by 313 39 by 34}
30 by 343
36 by 34}

15 by 343
12 by 343 16 by 34} 17 by 343

'f) Find the sum of the twelve products. Art. 7. To multiply a number by 353: Take 33} times the number, to which add twice the number. Why? 24 x 35}

33} times 24 = 800 800 +48= 848 25 x 353 33] times 25 = 833} 833} + 50 = 8831

Multiply:
21 by 35} 30 by 351 27 by 35}
18 by 353

66 by 35} 36 by 35}
33 by 35} 39 by 353 31 by 35}
15 by 35}
20 by 35}

42 by 35} (g) Find the sum of the twelve products. Art. 8. To multiply a number by 321: Take 333 times the number, from which subtract the number itself. Why? 21 x 321

331 times 21 = 700 700 21= 679 22 x 32}

33} times 22= 733} 733– 22 = 7111

Multiply :
15 by 32
21 by 32

18 by 321
24 by 32
30 by 32}

27 by 32}
33 by 32 39 by 32

36 by 321
66 by 32

19 by 32 20 by 321
(h) Find the sum of the twelve products.

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