Operation. 8z=:4X2; 10 = 5X2. Dividing the

8 4 X j2 4 numerator an^ denominator each by strik*

U) ^^ fc V rf J' ^S out the common factor 2, the value of

the fraction will pot be altered (Art. 119,
Prop. IV.), and will be expressed in its lowest terms. Hence the

Rule. To reduce a fraction to its lowest terms : Remove
from the numerator and denominator all their cominon factors,

1S3» Examples.
Reduce to their lowest terms,
1. |-f. Ans. f.
' 2. f J. Ans. f.
3. t|. Ans, I.
13. Reduce ^f

r • Note I. — 1, being a factor of all numbers, will remain when all other
factors are struck oiit, as in the numerator of example 18.
Note n, — In case the factors of the numerator and denominator can-
not readily be ascertained, find the G, C. D. of the two t^rms, and divide
each of ther^ by it.
Reduce to their lowest terms, ^



4. 11^. Ans.^.
7. m-


10. m


5. iVf-


8. T^a^.
11. m-


6. if.
9- m-


12. m-


its lowest terms.
Ans, 4*



14.
15.
16.
17.
342

•rrns'



For Dictation Exercises, see Key.
18.
19.
20.
21.
68' COMMON FRACTIONS.
Cancellation.
133. Cancellation consists in rejecting equal factors from
dividend and divisor.
124:* All arithmetical operations in division may be ex-
pressed in the form of a fraction, the dividend being the numer-
ator, and the divisor the denominator ; since dividing both terms
of a fraction by the same number does not alter its value, it fol-
lows, that we may strike out, or cancel, any factors common to the
dividend and divisor without changing their relative value.
