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

EXERCISES.
ABSTRACT FRACTIONS.
I.
1. Define a fraction, and explain the notation of fractions.
2. What is meant by an improper fraction and a mixed number?
How are improper fractions converted into mixed numbers, and
conversely?
3. Convert the improper fractions -,, 1 6, -— 1, -'32323- to
mixed numbers: and conversely; reduce the mixed numbers, 4-, 53,
75 142Y7 and 57841- to improper fractions.
4. Simplify 12~9+G and 12xsx5, and find what part the former
3 3
is of the latter.
5. What are the advantages in arithmetical operations of employing
fractions expressed by the smallest numbers possible? State how
fractions expressed by large numbers may be reduced to equivalent
fractions expressed by smaller numbers. Is this always possible?
6. State the rules for changing any given fractions to others of equal
value, but having the least common denominator.
7. Explain why fractions having different denominators must be
altered in form before their sum or difference can be expressed by one
fraction.
8. Define the multiplication of two integers and the multiplication
of two fractions, and show how the multiplication of two fractions is
not inconsistent with the multiplication of two integers.
9. How is it shown that the product of any two fractions as 3 and
-7 is equivalent to either of the compound fractions 3 of - or - of 3a?
10. Explain how it is that the product of two proper fractions gives
a fraction less than either of them: and the quotient, a fraction greater
than either of them.
11. Show how the rule for the division of one fraction by another
may be deduced from the method of the multiplication of one fraction
into another.
12. Of the eleven numbers less than 12, which are aliquot parts of
12? Show how those numbers which are not aliquot parts of 12,
may be expressed as the sum of two or more aliquot parts.
II.
Reduce the following fractions to equivalent fractions, each having
the least possible numerator and denominator:909 825 216 1155 7854 3300 2993 11385 42237 1 03
T~R',R1lo' RTRR T-6'- 20's 4235' TWY T0635-Z- 715582 242579
14628 217800 243936 135135 140971 87968 294025
1 ---1'') -245'-4 g-i13532,' T145530 48-7-212 2 772 88-, 59675'