Elementary arithmetic, with brief notices of its history... by Robert Potts.

13

VIL
Find the respective quotients arising from the following dividends
and divisors:1. 2 by A. 2. 8 by 2-. 3. 3~ by 4n. 4. 21 by I of 63. 5. 1 of
by 5 of 31. 6. I-of by of 17o. 7. -of I of - by -of 1 of 1.
8. 2 of 21 by 3 of 15. 9. o o f byof o f 41. 10. - of -
S 5 Y 1 1 of of
by of -. 11. 12157by 512. 12. -of '- of 10000 by -l0 of
317.
VIII.
1. How may the relative magnitudes of two or more fractions be
compared? Express by the least integers the relative magnitudes of
the fractions 11 1 - and 2 -2. Express 11, 13, 17, as fractions, each with the same denomlinator, 23.
3. What part of 15 is -- of 4-?
4. Arrange the fractions -,, S - 29 in order of magnitude.
5. Change the fraction - |- into one whose numerator is 209; and
25 into one whose denominator shall be 729, so that the values of
27
the two fractions may retain the same value.
6. Which is the greater of the two of the following sets of
fractions- - or; 4 of 8 or i of -; } of 11 or - of 11, and 2 of -
or -- of -2?
7. Find the alteration produced in the value of a proper fraction
-7-, first by adding, next by subtracting, the same number 3 from the
numerator and denominator.
8. If the number 5 be added to the numerator and denominator
of any im6proper fraction -r-, or taken from it, when is the value
of the fraction increased or diminished?
9. Show that the fraction 2~+3 lies between 2 and 3.
10. Show that the fractions 4- + 7 and 42-, are equal to each ot
the fractions 7 or 4, and explain the reason.
11. The fraction 2+4 6 lies between the greatest and least of
the fractions -, -,.
12. If any number of fractions be equal, then any one of them is
equal to the fraction whose numerator is equal to the sum of all the
numerators, and whose denominator is equal to the sum of all the
denominators. Exemplify this in the case of six equal fractions.
IX.
1. Show that the sum of - of 3-, and 2 of 1 — is equal to 1.
2. To 479 add 104- and repeat the addition six times.
3. Add together the greatest and least of the fractions 4-, 8, -, 2,
and subtract this sum from the sum of the other two fractions.
4. Change the fractions 8, A4, and } 4, into fractions having a