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Blast into Math! ets of nummers: mathematical plaagrounds
and so 1 is the “p ” in the theorem, and n is the “q ” in the theorem. If a rational number is the product
of an integer p and the multiplicative inverse of a natural number n , then it is
p
,
n
and so p is again the “p ” in the theorem, and n is the “q ” in the theorem.
We also need rules for playing games in the playground of rational numbers.
1. Let x and y be rational numbers, and a and c be elements of Z , and b and d elements
of N such that
a c
x = , y = .
b d
Then
ac
xy = .
bd
If b = d , then
a + c
x + y = ,
b
and
a − c
x − y = .
b
2. The multiplicative inverse of an integer z ∈ Z with z< 0 is
−1
,
−z
and
a −a
x = = .
b −b
3. If x =0 and a> 0, then the multiplicative inverse of x is
b
.
a
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