3.4 Rational numbers
The rational numbers, denoted Q, take care of the problem of the integers not being closed under division by non-zero values.
3.4.1 Fractions
Let’s start by talking about fractions, also known as the rational numbers, the way you may have been first introduced to them. This is elementary but useful to review to relate to what we have in the big picture with Q.
Given a loaf of bread, if we cut it right down the middle, we say we have divided it into halves. Fraction-wise, one-half = 1/2. The two halves equal one whole loaf, so 1/2 + 1/2 = 2 × 1/2 = 1. Two halves is 2/2, which is 1. Four halves would make two loaves: 4/2 = 2.
Considering whole loaves, 1/1 is one loaf, 2/1 is two loaves, and 147/1 is one hundred and forty-seven loaves. We can represent any integer n as a fraction 
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To multiply fractions, we multiply the tops (numerators) together and put those over the product (the result of multiplication) of the bottoms (denominators...
