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Addition and Subtraction of Fractions. XVIII. Add together and and
This addition may be expressed by writing the fractions one after the other with the sign of addition between them; thus 6 + g +
N. B. When fractions are connected by the signs + and - the sign should stand directly in a line with the line of the fraction.
It is frequently necessary to add the numerators together, in which case, the fractions, if they are not of the same denomination, must first be reduced to a common denominator, as in Arithmetic, Art. XIX.
1. Add together and
Ans. 372. =
3. Add together in anderen
Ans. 34.720 = 6
3 cd. 5. Add together and 4.
These must be reduced to a common denominator. It has been shown above that if both numerator and denominator be multiplied by the same number, the value of the fraction will not be altered. If both the numerator and denominator of the first fraction be multiplied by 7, and those of the second by 5, the fractions become and you. They are now both of the same denomination, and their numerators may be added, The answer is ; }
6. Add together and Multiply both terms of the first by d, and of the second by
ami adondb c b, they become
The denominators are now alike
dan 6 and the numerators may be added. The answer is a d + b c
bd 7. Add together to g o, and
In all cases the denominators will be alike if both terms of each fraction be multiplied by the denominators of all the others. For then they will all consist of the same factors.
Applying this rule to the above example, the fractions become a
ad fh bcfh bdeh and bdfg. come ha fh 6dfh bdfh and bath
The answer is a dfh+bcfh+bdeh thdfg
8. Add together 3.4 and 24 Ans. 15ad + 4bc.
It was shown in Arithmetic, Art. XXII, that a common donominator may frequently be found much smaller than that produced by the above rule. This is much more easily done in algebra than in arithmetic.
9. Add together as , and L.
Here the denominators will be alike, if each be multiplied by all the factors in the others not common to itself. If the first be multiplied by e g, the second by cg, and the third by bce, each becomes b c eg. Then each numerator must be multiplied by the same quantity by which its denominator was multiplied, that the value of the fractions may not be altered.
aeg c d gondeb cf The fractions then become
b c eg beeg
6c eg The answer is aeg tcdg + bcef :
it at eg
11. Add together samt en anden sista on? 12. Add together 2mm and 3 mo žining. isés
ar 2. 13. Add together 5 6 ma 57
2 mon h 3 m’s - 2ar
14. Add together , and 3 mnogi
15. Add together 19 e 2 mr and
18. Add together
13 ani -40 and 11 ac-5n.
2 an 19. Add together
15 amc2 ab
7 amb 36m 20. Add together
ther 13 a' b - 2c à 7 ab + 8C
4abu 26 + 16 ab
21. Subtraction from
This subtraction may be expressed thus,
But if they are reduced to a common denominator, the numerators may be subtracted.
XIX. Division of whole numbers by Fractions, and Fractions by
is contained i 'as
How many times is contained in 7 ? Ans. Į is contained in 7, 35 times, and many times; that is, or 11f times.
2. How many times is contained in a ?
Ans. šis contained in a, 8 a times, and many times; that is, *.