Final answer:
Intuitively, we can estimate sums and differences of fractions and use strategies like finding a common denominator to add or subtract them properly. Multiplication of fractions involves a clear process of multiplying numerators and denominators. Simplification and checking answers ensure our solutions are reasonable.
Step-by-step explanation:
Our intuition can be a useful tool when working with fractions, particularly in identifying strategies for addition and subtraction of fractions. Intuition helps us estimate and assess the reasonableness of our answers. For instance, when adding ½ and ⅓, we naturally sense that the sum will be more than ¾ but less than 1. Graphical representations show how overlays of these fractions reveal a common gap, which is filled by finding a common denominator. The least common multiple of the denominators 2 and 3 is 6, allowing us to convert ½ into ⅓ and ⅓ into ⅖, making the addition straightforward as we now have like denominators.
Prior to cross multiplying, we simplify fractions whenever possible. After finding the sum or difference, we should always check our results to confirm they make sense. For multiplication, we multiply the numerators and divide by the denominators, simplifying before and after as necessary to ensure our units are consistent and our math is clean.
In sum, natural intuition, along with a systematic approach to finding common denominators, simplification, and consistent checking of our answers, allows us to verify the correctness of our operations with fractions.