Final answer:
The rules of integers do apply to negative and positive fractions, as the basic principles for operations such as addition, subtraction, multiplication, and division are consistent between integers and fractions. Multiplication sign rules and the requirement of a common denominator for addition and subtraction extend to fractions as well.
Step-by-step explanation:
The rules of integers can indeed be applied when dealing with negative and positive fractions. When adding, subtracting, multiplying, and dividing fractions, whether they are positive or negative, the same basic principles apply as with integers. For example, the rule stating that multiplying two negative numbers results in a positive product holds true for fractions as well: multiplying -1/2 by -3/4 gives 3/8, a positive fraction.
Moreover, when dealing with addition and subtraction of fractions, a common denominator is required to combine the terms, regardless of whether the fractions are positive or negative. Just like with integers, a positive fraction multiplied by a negative fraction results in a negative fraction, following the multiplication rule that a positive number times a negative number gives a negative product. This demonstrates that our intuition about the sign rules for multiplication and division transfers to fractions as well.
These consistent patterns allow us to formulate rules for fraction operations based on the established integer operations. This is why students can apply their foundational knowledge of positive and negative integers when they begin working with fractions.