Denominate Numbers - Weight,

350. Troy weight is used in weighing gold, silver, and

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

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 437 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.)

"So teach us to number our days that we may apply our hearts unto

wisdom."

SHORT METHODS

IN

MULTIPLICATION AND DIVISION.

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

(a) Find the sum of the twelve products.

Art. 2. To multiply a number by 51: number, to which add the number itself.

=

48 × 51 50 times 48
37 x 51 50 times 37 = 1850

1850 + 37 = 1887

2400

Take 50 times the Why? 2400+48

2448

(b) Find the sum of the twelve products.

Art. 3. To multiply a number by 52: number, to which add twice the number.

50 times 34 = 1700

Take 50 times th.
Why?

1700 +681768
2250+90=2340

34 × 52

45 x 52

50 times 45 = 2250

Multiply:

(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?

(d) Find the sum of the twelve products.

Art. 5. To multiply a number by 331: Multiply of the number by 100. Why?

36 × 331

of 36 x 100 = 1200

(e) Find the sum of the twelve products.

Art. 6. To multiply a number by 341: the number, to which add the number itself.

Take 331 times

Why? +24= 824 8331+25=8581

(f) Find the sum of the twelve products.

Art. 7. To multiply a number by 351:

the number, to which add twice the number.

331 times 24 = 800

Take 33 times
Why?

800 +48 848

=

8331+50= 883

24 × 351

25 × 351

33 times 258331

Multiply:

(g) Find the sum of the twelve products.

Art. 8. To multiply a number by 321: Take 33 times the number, from which subtract the number itself. Why?

(h) Find the sum of the twelve products.