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And bd - 60dddbbb add,
"main tdtb the new Denominator,
+b bd - 666
0 0 Let both be multiplied with b, and then you will have dth the Numerator,
of the Fraction required. dd +60 +66 the Denominator, S
But if after all Means used (as above) there cannot be found one common Measure to both the Numerator and Denominator ; then is that Fraction in it's least Terms already. · Note, These Operations will be understood by a Learner after he hath passed thro' Multiplication, and Division of. Fractions.
Sect. 5. addition and Subtraction of Fractional
Duantities. THE given Fractions being of one Denomination, or if they.. are not, make them so, per Sect. 4. Then,
RUL E. Add or subtraft their Numerators, as Occasion requires, and to their Sum or Difference, subscribe the common Denominator s as ir Vulgar Fractions.
Examples in addition.
la to 12a-6 12-bte id 1 dti
dta | 2 ate 2b-a lat b-d dtol
|dta fa a 13a +b+cathy
• 2 a Id toch
d ta Examples
Sect. 6. gultiplication of Fractional Quantities. FIRST prepare mixed Quantities (if there be any) by making I them improper Fractions, and whole Quantities by subscribing an Unit under them; as per Sect. 3. Then,
6 2 dto
Suppose it were required to multiply 20+.25 with 36 + 46. These prepared for the Work (per Sect. 3.) will itand
CL:12 actob-- 250 Thus31
13b + 40
N. B. Any Fraction is multiplied with it's Denominator by calling off, or taking the Denominator away. Thus xa gives 4. For == &c.
Sect. 7. Division of Frational Quantities. THE Fractional Quantities being prepared, as directed in the last Section. Then,
RUL E. Multiply the Numerator of the Dividend, into the Denominator of the Divifor, for a new Numerator ; and multiply the other two together for a new Denominator ; as in Vulgar Fractions.
EX A M P L E S. Let abd be divided by the Work may fand thus; abd abdc d of labcf- f
labdl att laaabbb Or thus i
d. I atb cb laaab t66
per Sect. 4.
Suppose it were required to divide
by a tbi The Work will fand thus, atb, ana+4 a ab + 3 abbinaat-4 a ab+306 B.
Il a + 4b laat 5ba +40b a aa + 4 a ab+3abb aet36,
† (per Sect. 4.) aatsbat 406 at 46 When Fractions are of one Denomination, cast off the Deno. minators, and divide the Numerators. Thus, if ac were to be divided by bb it will be b) a 63 (ab the Quotient required.
: Sect. 8. Jnvolution of Fractional Quantities. TNvolve the Number into itself for a new Numerator, and the I Denominator into itself for a new Denominator ; cach as often as the Power requires.
Sect. 9. Evolution of Fractional Quantities. IF the Numerator and Denominator of the Fraction have each
of them such a Root as is required (which very rarely happens) then evolve them; and their respective Roots will be the Numerator and Denominator of the new Fraction required. Thus 19a abbja a to 2ab +68
1 40 d laa - 2ab +66
3 ab la tb I ov 1 21 ano
27 a a abbbla a ato 3e ab + 3abb +-bbb
Sometimes it fo falls out, that the Numerator may have such a Rgot as is required, when the Denominator bach not; or the Deno
But when neither the Numerator, nor the Denominator have juft such a Root as is required, prefix the radical Sign of the Root to the Fraction; and then it becomes a Surd ; as in the last Sep, which brings me to the Business of managing Surds.
Se&. 1. Addition and Subtraction of Surd Quantities. Cafe 1. W HEN the Surd Quantities are Homogeneal, (viz are alike) add, or subtract the racional Pari, if they