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EXAMPLES.

1. Reduce of a penny to the fraction of a pound

of is of 17 = the answet.

And 75g of of S=d. the proof. 2. Reduce of a farthing to the fraction of a pound.

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Ans. Ito

Ans. 40

3. Reduce £. to the fraction of a penny. 4. Reduce of a dwt. to the fraction of a pound Troy.

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Ans. is

5. Reduce of a pound avoirdupois to the fraction of a cwt.

Ans.

784 6. Reduce 757 of a hhd. of wine to the fraction of a pint. 7. Reduce 1 of a month to the fraction of a day.

, 8. *Reduce 78. 3d. to the fraction of a. pound. Ans. 9. Express 6fur. 16pls. in the fraction of a mile. Ans.

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AODITION of Vulgar FRACTIONS.

RULE. Reduce compound fractions to single ones ; mixed numbers to improper fractions ; fractions of different inte

gers

The rule might have been distributed into tivo or three different cases, but the directions bere given may very easily be applied to any question, that can be proposed in those cases, and will be more easily understood by an example or two, than by a multiplicity of words.

* Thus 7. 3d. =87d. and il. = 2400... =* the answer

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+ Fractions, before they are reduced to a common denominator, are entirely dissimilar, and therefore cannot be incorporated with one another ; but when they are reduced to a common denominator, and made parts of the same thing, their sum or differ

ence,

1

gers to those of the same ; and all of them to a common denominator ; then the sum of the numerators, written over the common denominator, will be the sum of the fractions required.

EXAMPLES

1. Add 3$, ž, of į and 7, together.

First 3f=of = 7=.
Then the fractions are in s 1. and ; ..
29 X 8 X10 X 1=2320
7X8X1OX I= 560
7X8 X 8 X 1= 448
7 X 8 X 8 X10=4480

Ans. 81

1

OO

7808

=12548=12the answer. 8X8X10X 1640. 2. Add f, 71 and į of į together. 3. What is the sum of j of and 916 ? Ans. 10 4. What is the sum of 4 of 6, of and 7 ?

Ans.-13102 5. Add 1. s. and of a penny together.

Ans. 36?s, or 3s. Id. 1-19. 6. What is the sum of of 151. 31. Ź of of of a pound and į of of a shilling ?

Ans. 71. 175. 5.d. 7. Add í of a yard, of 'a foot and į of a mile together.

Ans. 66oyds. 2ft. gin. 8. Add ; of a week, $ of a day and of an hour together.

Ans. 2d. 14 h.
SUBTRACTION

ence, may then be as properly expressed, by the sum or difference of the numerators, as the sum or difference of any two quantities whatever, by the sum or difference of their individuals ; whence the reason of the rules, both for addition, and sabtraction, is manifest

K

SUBTRACTION of VULGAR FRACTIONS,

RULE.

Prepare the fractions as in addition, and the difference of the numerators, written above the common denominator, will give the difference of the fractions required.

EXAMPLES,

3
• 14.

21

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Ans. 378

700

1. From į take of Ž.
Ź of , and į=;

=*=, the anwser required. 2. From 9 take

Ans. 8111 3. From 961 take 14. 4. From 14 take of 19.

Ans. 17 5. From 1. take s.

Ans. 95. 3d.

Ans. Iidwt. 3gr. 6. From oz. take ždwt. 7. From 7 weeks take 976 days. Ans. 5W. 4d. 7h. 12.

MULTIPLICATION of VULGAR FRACTIONS.

"RULE.*

Reduce compound fractions to single ones, and mixed numbers to improper fractions ; then the product of the numerators is the numerator ; and the product of the denominators, the denominator of the product required.

EXAMPLES

* Multiplication by a fraction implies the taking some part or parts of the multiplicand, and, therefore, may be truly expressed by a compound fraction. Thus multiplied by is the same as of ; and as the directions of the rule agree with the method already given to reduce these fractions to single ones, it is shewn to be right.

EXAMPLES.

Required the continued product of 2 of and 2.

IX5
2 = , of = y, and 2= }}

3х6
Then {X}x75x}=5 X 1 X 5x2

1 the answer.

X X 8 X 18 XI 2. Multiply by 4 3. Multiply 47 by :

Ans. 16 4. Multiply of 7 by.

Ans. I 5. Multiply of } by sof 37. 6. Multiply 4, of and 185, continually together.

Ans. is

Ans. *

Ans. 9140

Division of VULGAR FRACTIONS.

RULE.*

Prepare the fractions as in multiplication ; then invert the divisor, and proceed exactly as in multiplication.

EXAMPLES.

1. Divide of 19 by j of $

2x3 of 195 58 1=, and ŷ of t=%24

IX19

::**=i=*=7} the quotient required.

2. Divide

* The reason of the rule may be shewn thus : Suppose it were required to divide by . Now $-2 is manifestly of }, or 3

; but }=of 2,.. of 2, or ; must be contained 5 times 4X2 as often in as 2 is

that is

3X5

= the answer ; which is according to the rule ; and will be so in all cases.

Note.--A fraction is multiplied by an integer, by dividing the denominator by it, or multiplying the numerator.

And divided by an integer, by dividing the numerator, or multiplying the de Dominator.

4 X 2

2. Divide by ý
3. Divide om by of 7.
4. Divide 3ž by oz.
5. Divide [ by 4.
6. Divide of j by jof

Ans. Ans. 221 Ans.

.

32 Ans.

Ans. ?

DECIMAL FRACTIONS,

75

or T60

2415

02

Tão or

A DECIMAL is a fraction, whose denominator is an unit, or 1, with as many cyphers annexed as the numerator has places ; and is commonly expressed by writing the numerator only, with a point before it called the separatrix. Thus, 05 is equal to or . 0:25

20 or 0975

* 1'3

H or it's 24:6

. *0015 Tohto or do ਨੂੰ A finite decimal is that, which ends at a certain number of places. But an infinite decimal is that, which is understood to be indefinitely continued.

A repeating decimal has one figure, or several figures, continually repeated, as far as it is found. As -33, &c. which is a single repetend. And 20*2424, &c. or 20*246246, &c. which are compound repétends. Repeating decimals are also called circulates, or circulating decimals. A point is set over

a single

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