Application.

Let it be required to bring of a shilling to the fraction of a pound. From what hath been remarked it will be very easy to conceive that of a shilling is of of a 7. which being reduced to a simple fraction becomes 3 3 of a l. equal is.

Examples.

73. What part of a l. is ¡d. ?

Answ..

74. What part of a Hb. Avoirdupois is of an ounce ?

I

76. What part of a yard is of a nail?

Problem X.

To reduce a fraction of a higher denomination to the fraction of a lower.

Rule.

Multiply the numerator of the given fraction, by that number which 1 of the higher contains of the lower, for a new numerator to the denominator of the given fraction.

Application.

Let it be required to bring of a . to the fraction of a shilling; multiply 7 by 20, I find the product 140, viz. 140 of a shilling, (in its least terms 35s.') equal to 71.

8

Rule.

Make the lesser the numerator, and the greater the denominator of a fraction, and reduce the said fraction to its lowest terms.

So if it were required to know what part 15 is of 20, I say 15, or its lowest terms 3.

QUESTIONS relating to Reduction.

Quest. How must I reduce a fraction to its least terms? Answ. By the measure, the greatest of the numerator, Which likewise will measure the denominator;

Divide both the terms of the fraction; 'twill find
The terms of a fraction the least in their kind.
But rather than thus it may probably please
The least numbers to approximate by degrees:
If the numbers be even still 2 will divide,

But an odd number always in odd must be try'd;
If cyphers end,-both of like cyphers deprive;
5, or 5 and a cypher?-divide them by 5.

2. How shall I bring a fraction to another, which shall have a given denominator?

A. Make the denominator of the given fraction the first, the numerator the second, and the given denominator the third number, of a stating in the Rule of Three, and find a fourth proportional; which will be the numerator to the given denominator.

2. How must I reduce fractions of different denominators to others having one common denominator?

A. Find the least number which all the denominators of the given numbers will measure, for a common denominator, and reduce each fraction to another whose de nominator shall be the said common denominator.

2. How must I reduce an improper fraction to a whole or mixt number?

A. Divide the numerator by the denominator.

2 How must I make a whole number an improper fraction

A. By

A. By subscribing 1 under it for a denominator.
2. But if the denominator be given?

1

A. Multiply the whole number thereby for a nume

Fator.

2. How must I reduce a mixt number to an improper fraction?

A. Multiply the whole number by the denominator of the annexed fraction, and add the numerator to the product for the numerator, and the denominator of the frac tional part is the denominator.

2. How must I bring a compound fraction to a simple

one?

A. Multiply all the numerators together for a numerator, and the denominators for a denominator.

2. How must I bring numbers of lesser denominations to the fraction of a greater?

A. Reduce the given denominations to the least mentioned for a numerator, and 1 of the greater to the same for a denominator.

2. How must I find the value of a fraction, which is a part of a unit of coin, weight and measure, &c.?

A. If of coin, weight or measure the fraction is assign'd, In the tables the fit multipliers we find,

So multiply by 20 the given numerator,
The product divide by the denominator,

The shillings contain'd in the quotient are found;
If the fraction propos'd be the parts of a pound;
Multiply next by 12 the remainder from thence,
The product divide as before for the pence;
Repeat the like process again and again,
Till the lowest name's got, or till nothing remain.

IF

CHAP. III.

ADDITION OF FRACTIONS.

Rule I.

the fractions have a common denominator, add the numerators together, and under their sum place the common denominator; if the sum be an improper fraction it may be reduced to a mixt number, if not to the least

terms.

Examples.

If the fraction have different denominators reduce them to equivalent fractions which shall have one common denominator, and add the said equivalent fractions, (last Rule.)

Add the fractions as before, and if the sum of the fractions found be an improper fraction, reduce it to a mixt number, and add the integral part with the whole numbers of the given mixt numbers.

Application.

1

Application.

So 5, 7 the sum of and to be which is found equal to 1 I put down 3 for the fractional part of the sum and carry 1, the integral part to the units of the given whole numbers, and adding them the sum is found 283

and 15 being given to be added: I first find

Examples.

5/

7 7 15

28 3

: 4 (8

7

11

8)11

1 3

1. A merchant buys 5 pieces of sloth, the first was 40 yards; the second 27 yards; the third 347 yards; the fourth 43, and the fifth 39 yards: I desire to know how many yards were in the 5 pieces?

Answ. 185 yards.

2. Bought 4 bales of spice. No. 1, weight 150 b.; No. 2, weight 1393 b.; No. 3, weight 162fb.; No. 4, weight 170: How many b. weighed they together? Answ. 623 lb.

I

24

3. A grocer sold the following parcels of sugar, viz. 161b.; 19b; 133b.; 204b; 25b.: 30.; and 1. I demandhow many pounds he sold in all ?

:

Answ. 136271b.

CHAP.