Final answer:
When using algebra tiles for adding and subtracting integers, it's important to follow the basic principles of arithmetic, like combining like terms and changing the sign for subtraction. Intuition can aid in addition and subtraction of fractions by allowing visual estimation or constructing rules. Always simplify algebra and check for reasonable answers.
Step-by-step explanation:
When comparing and using algebra tiles for the purpose of adding and subtracting integers, a student should be aware of several key points. First, it is important to observe the basic principle of addition and subtraction, which is to combine like terms in the case of addition and change the sign of the number to be subtracted before combining in the case of subtraction. Second, when working specifically with whole numbers, you should pay attention to the signs of the numbers to determine the final sign of the answer.
Our intuition can guide us in the process of adding and subtracting fractions by allowing us to visually estimate the answer or by using our understanding of whole number operations to experiment and construct the rules for fractions. For example, we know that to add fractions, we need a common denominator, and our intuition can help ensure that the process feels reasonable and aligns with our natural understanding of quantities.
It is essential to eliminate terms whenever possible to simplify the algebra and always to check the answer for reasonableness. These steps are part of the universal validity of mathematical rules, which are consistent regardless of time or place.
Remember that when two positive numbers add, the result is positive; when two negative numbers add, the result is also negative. When numbers with opposite signs add, subtract the smaller number from the larger and assign the sign of the larger number. For subtraction, simply change the sign of the number being subtracted and follow the addition rules.