Final answer:
In summary, using intuition in addition and subtraction of fractions involves understanding the need for a common denominator, estimating using familiar fraction values, and knowing shortcuts like common reciprocals. These strategies can lead to quicker mental calculations.
Step-by-step explanation:
Our intuition can be quite helpful when it comes to addition and subtraction of fractions. The key principle to keep in mind while working with fractions is that you must have a common denominator before you can add or subtract the numerators. This fundamental principle is similar to paying attention to base values when working with whole numbers — a necessary step to ensure accuracy.
Sometimes, we apply the distributive property in mathematics to simplify expressions and solve equations. For fractions, while this property doesn’t apply directly for addition or subtraction, being familiar with it can help us understand similar concepts like combining like terms (which is more akin to what happens with fractions' numerators once they have the same denominator).
By practicing approximation and mental math, we can enhance our numerical intuition. For instance, understanding that 1/2 is close to 0.5 can help us quickly estimate the results of adding or subtracting fractions without calculating the exact answer. Knowing shortcuts, like common reciprocals that multiply to 10, can also speed up mental calculations. A table of these reciprocals, as suggested, could be an excellent reference tool.