Final answer:
Our intuition can guide us in adding and subtracting fractions by using our understanding of common denominators and aligning like terms, similar to how we handle whole numbers. Calculators perform tasks exactly as input, necessitating our oversight for rounding and significant figures, especially when dealing with money.
Step-by-step explanation:
Our intuition can assist us in figuring out the addition and subtraction of fractions or mixed numbers by building on natural problem-solving skills. For example, when we see fractions with the same denominator, we understand we can simply add or subtract the numerators. However, when working with fractions that have different denominators, we know we need to find a common denominator before performing the operation. This is much like the way we pay attention to place values when working with whole numbers — aligning ones with ones, tens with tens, and so forth.
When using a calculator, we must remember that calculators perform calculations exactly as input without considering significant figures or context. It's up to us to round appropriately, especially after intermediary steps. Similarly, when adding or subtracting money, we must ensure to keep track of decimals representing cents accurately.
Ultimately, understanding the basic principle that like terms (or units) can be combined directly and unlike terms (or units) require some form of conversion or commonality is key to successfully adding and subtracting fractions, mixed numbers, or any other quantities.