Exam. 1. The Numerator 6 being multiplied by 20, and the Product divided by the Denominator 10, the Quotient is 12 Shillings, the exact Value of of a Pound, as nothing remains. And this appears to be true; for the one Tenth of a Pound is 2 Shillings, and, confequently, fix Tenths must be 12 Shillings.

The fame of the other two Examples.

Exam. 1. The Numerator 15 being multiplied by 20, and the Product divided by the Denominator 40, we have 7 Shilfings in the Quotient, and a Remainder of 20; which being multiplied by 12, the Product is 240, and, this being ftill divided by the Denominator 40, the Quotient is 6 Pence, and nothing remains: Whence the exact Value of of a Pound Sterling is 7 s. 6d. And this is true; for the one Fortieth of a Pound is 6 Pence, and, confequently, fifteen Fortieths muft be 7s. 6d.

The fame of the other two Examples.

40

Exam. 7.

1

Exam. 7. The Numerator 457 being multiplied by 20, and the Product 9140 divided by the Denominator 960, the Quotient is 9 Shillings; and there remains 50, which being multiplied by 12, and the Product 600 divided by 96, (the Cypher of the Divifor being cut off at the laft Operation) the Quotient is 6 Pence; and there remains 24, which being multiplied by 4, and the Product 96 divided by 96, the Quotient is 1 Farthing, and nothing remains: Whence the exact Value of of a Pound is 9s. 6d. 4. Which is true; for the ninehundred-and-fixtieth Part of a Pound is I Farthing, and, confequently, four hundred and fifty-feven fuch Parts are fo many Farthings, or 9s. 6d. 1.

The fame of the eighth and ninth Examples.

Exam. 10.

Exam. 10. The Numerator 5 being multiplied by 20, and the Product 100 divided by the Denominator 7, the Quotient is 14 Shillings; and there remains 2, which being multiplied by 12, and the Product 24 divided by 7, the Quotient is 3 Pence; and there remains 3, which being multiplied by 4, and the Product 12 divided by 7, the Quotient is 1 Farthing; and 5 remains; but, there being in English Money nothing less than Farthings, the Remainder is neglected: Hence we call the Value of of a Pound, 14 s. 3d., tho' it is strictly, or five Sevenths, of a Farthing more; that is, the Remainder is made a Numerator and the Divifor a Denominator of a Fraction, which is a Part of the Integer laft found. Thus, at Example 11, the true Answer is 8s. 2 d. 3 和 and of a Farthing; and, at Example 12, the true Anfwer is 125. 4d., and of a Farthing; but the Fractions of the lowest Denomination are generally neglected in Practice.

And, if it was required to find the Value of a Vulgar Fraction of a Yard, multiply the Numerator by 3, the Feet

in Yard, then divide the Product by the Denominator, and the Quotient is Feet, and is the true Value of the Fraction, if there is no Remainder: But, if there is a Remainder, multiply it by 12, the Inches in 1 Foot, then divide the Product by the Denominator, and the Quotient is Inches, and, if there is no Remainder, the Feet and Inches thus found is the true Value fought: But, if there is ftill a Remainder, multiply it by 4, the Quarters in 1 Inch, then divide the Product by the Denominator, and the Quotient is Quarters of an Inch, which, being added to the Feet and Inches before found, will be the Value of the Fraction in Feet, Inches, and Quarters of an Inch: After which, the Remainder may be neglected, unless greater Exactness is required.

I

To find the Value of the following Fractions of one Yard. Exam. 1. Of.

8

Exam. 2. Of

5

Exam. 3. Of

16

The Operation in thefe Examples will appear very easy by

the Directions.

Exam. 4. The Numerator 18 being multiplied by 3, and the Product 54 divided by 36, gives 1 Foot; and 18 remains, which being multiplied by 12, and the Product 216 divided by

G

36, gives

36, gives 6 Inches, and nothing remains: So is 1 F. 6 Inch. the exact Value of of a Yard.

The fame of the fifth and fixth Examples.

FFF

18

9) 36 (4 Inches.

36

36

36

36

Anf. 10 Inches.

Anf. 4 Inches.

Anf. 11 Inches.

Exam. 7. The Numerator 5 being multipied by 3, and the Product 15 divided by the Denominator 18, it gives o Feet in the Quotient; then multiply the 15, which is now the Remainder, by 12, and it makes 180, which being divided by 18 gives 10 Inches, the exact Value of of a Yard. And fo of the eighth and ninth Examples.