61. If a number be divided by any number, and the quotient be multiplied by the divisor, the product will be the dividend; thus,

15 ÷ 3 =

COROLLARY.

5, and 5 × 3 = 15, the dividend.

Since dividing the dividend divides the quotient (59, b), and dividing the divisor multiplies the quotient (59, d), .. dividing both dividend and divisor by the same number does not affect the quotient; thus,

62. NUMBERS are either Simple or Compound.

63. A Simple Number consists of but one kind or denomination; thus, 3, 15, 8 books, 4 men, 7 apples, etc. are simple

numbers.

NOTE. - All operations in the preceding pages are upon simple numbers.

64. A Compound Number is composed of two or more denominations; thus, 4 days and 7 hours; 3 bushels, 2 pecks and 5 quarts; etc., are compound numbers.

NOTE.- The several parts of a compound number, though of different denominations, are yet of the same general nature; thus, 2 weeks, 3 days and 6 hours are SIMILAR quantities and constitute a compound number; but 2 weeks, 3 miles and 6 quarts are UNLIKE IN THEIR NATURE and do NOT constitute a compound number.

65. The first division of each of the following tables should now be THOROUGHLY committed to memory.

NOTE 1.- Federal Money is the National Currency of the United States. NOTE 2. - The terms, eagle and dime, are seldom used in computation; eagles and dollars being read collectively and called dollars, and dimes and cents being called cents; thus, 3 eagles and 5 dollars are called $35, and 4 dimes and 3 cents are called 43 cents.

NOTE. - English Money is the National Currency of Great Britain.

NOTE. Troy weight is used in weighing gold, silver and precious

stones.

NOTE 1.

- Medicines are mixed or compounded by this weight, but are

usually bought and sold by Avoirdupois weight.

NOTE 2.- - The pound, ounce and grain in Apothecaries' and Troy weight are equal, but the ounce is differently subdivided.

NOTE 1.

The coarser articles of merchandise, such as hay, cotton, tea,

sugar, copper, iron, etc., are weighed by Avoirdupois weight.

NOTE 2. It was the custom, formerly, to consider 28 lbs. a quarter, 112 lbs. a cwt., and 2240 lbs. a ton; but now the usual practice is in accordance with the table.

These different tons are distinguished as the long or gross ton = 2240 lbs., and the short or net ton = 2000 lbs.

NOTE 3. -A pound in Avoirdupois weight is equal to 7000 grains in Apothecaries' or Troy weight.

NOTE. - Cloths of every description, ribbons, braids, etc. are measured

by this measure.

72. LONG MEASURE.

3 Barleycorns (b. c.) make 1 Inch,

1 Foot,

in.

ft.

yd.

rd. fur.

m.

1.

NOTE.

- This measure is used in measuring distances, i. e. where length

is required without regard to breadth or thickness.

* Expressions like,, etc. are called fractions. = one fourth; } = two thirds; 24 = two and one-fourth. The principles of fractions will be discussed in §§ 10 and 11.

NOTE. This measure is used by engineers in measuring roads, canals, etc.; also by surveyors in measuring the boundaries of fields.

sq.m.

1 640

NOTE 1.

a.

1=

1=

40=

1210=

10890- 1568160

NOTE 2. 100 links.

4= 160- 4840

2560-102400-3097600-27878400-4014489600

This measure is used in measuring surfaces.

In measuring land, surveyors use a 4-rod chain composed of Sometimes the half-chain of 50 links is used.

43560- 6272640