The reason of division will best appear by an example as

From this example it appears, that the greatest number of hundreds that 36 can be contained in 16324, is 4, and the remainder is 1924; and the greatest number of tens that 36 can be contained in 1924, is 5, or 50, and the remainder is 124; and lastly, the greatest number of units that 36 can be contained in this last remainder, viz. 124, is 3, and the remainder 16, therefore the whole number of times that 36 can be contained in 16324, is 400+50+3=453 times; and by observing this work, it will be found to be the same as the general rule explains.

Division may be quickly proved by throwing out the 9's, as in multiplication; but as this method is not so certain a proof, it may be very easy proved by addition only, by adding the remainder to all the products of the divisor by the quotient figures, and if this sum is equal to the dividend, then the work is right.

Thus in the above example, begin at the right hand of the remainder, and say, 6+8=14, set down 4 and carry 1; and say, 1 carried and 1 is 2, set down 2; and say, 1+8+4 =13, set down 3 and carry 1; and again say, 1 carried and 1+4=6, set down 6; lastly, set down 1, and the whole is 16324, which agrees with the dividend.

Tables

A farthing is always marked thus, ; a halfpenny, or two farthings, thus, ; and three farthings, thus, ..

TROY WEIGHT.

By this weight are weighed gold, silver, amber, &c.

AVOIRDUPOISE WEIGHT.

By this weight are weighed, butter, cheese, flesh, grocery wares, and all goods that have waste.

Note, that 14 ounces 11 penny weights, and 15 and a half grains troy, are equal to one pound Avoirdupoise.

A Table of Feet, Inches, &c.

By this table, artificers in the building branch measure their work; but this sort of measure extends to length only.

By this measure is measured all things that have length and breadth, such as carpenter's work, joiner's work, bricklayer's work, plasterer's work, &c.

144 inches make 1 foot.

9 feet make 1 yard.

100 feet make 1 square flooring.

COM

I. Place the numbers of the same denomination under each other, and draw a line under them.

II. Begin at the lowest denomination, and add up the figures in that place: find how many units of the next denomination is contained in that sum, by dividing it by so many as will make one of the next denomination.

III. Write the remainder or overplus underneath: add the quotient to the next place, and proceed through each column, as in the first place, writing the several remainders under their respective columns, till you get to the last place, which sum must be set down in full: by this means you will have the total sum of the whole.

I. In example I. by adding up the farthings, you will find that their sum is 6, and because that four farthings is equal to one penny, therefore the 4's out of 6, is once and 2 over; set down 2, and carry 1 to the place of pence.

II. Add up all the pence together, as in simple addition, and their sum will be 30, and because that 12 pence is equal to 1 shilling, therefore divide 30 by 12, then the quotient is 2, and the remainder 6; set down 6, and carry 2, or two shillings, to the next place.

III. Proceed in the same manner with the shillings, and divide their sum by 20, because 20 shillings make one pound, then there is four 20's and 7 over, or 4 pounds 7 shillings, set down 7 and carry 4 to the place of pounds.

IV. Then add the pounds together, and set their sum under, then the whole sum will be 1273 pounds 7 shillings and 6 pence halfpenny.

In the same manner may any other kind of denominations be added together, by observing how many of any denomination make one of the next.

VOL. I.

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