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Rational Numbers Worksheet

1. Which of the following are true?

(a) The rational numbers are commutative under addition.
(b) The rational numbers are commutative under subtraction.
(c) The rational numbers are commutative under multiplication.
(d) The rational numbers are commutative under division.
(e) The rational numbers are associative under addition.
(f) The rational numbers are associative under subtraction.
(g) The rational numbers are associative under multiplication.
(h) The rational numbers are associative under division.
(i) The rational numbers are closed under addition.
(j) The rational numbers are closed under subtraction.
(k) The rational numbers are closed under multiplication.
(l) The rational numbers are closed under division.
(m) Every rational number has an additive inverse.
(n) Every rational number has an multiplicative inverse.
(o) Every rational number has a unique additive inverse.
(p) Every nonzero rational number has a unique multiplicative inverse.
(q) One is the multiplicative identity for the set of rational numbers.
(r) Zero is the additive identity for the set of rational numbers.
(s) If are distinct rational numbers with , then there is a rational number such that a
(t) (problem 21 from section 6.1) There are infinitely many rational numbers between 0 and 1.
(u) (problem 21 from section 6.1) There are infinitely many ways to replace two fractions
with two equivalent fractions that have a common denominator.
(v) (problem 21 from section 6.1) There is a unique least common denominator for a given
pair of fractions.
(w) (problem 21 from section 6.1) There is a least common fraction.