Final answer:
The concept of single-ruled and double underlined lines denoting addition, subtraction, and final totals is not a standard mathematical convention. The rules for addition and subtraction with significant figures and the commutative property (A+B=B+A) are fundamental concepts in mathematics.
Step-by-step explanation:
The statement that a single-ruled line denotes addition and subtraction and double underlines indicate the final totals is not universally true or recognized as standard notation in mathematics. Different educators, textbooks, and exams may follow their specific marking strategies. However, the focus of the question seems to be on the rules of performing addition and subtraction and understanding the proper application of significant figures in mathematical operations.
When performing addition or subtraction, a key point to remember is that one should limit the reported answer to the rightmost column where all the numbers involved have significant figures in common. This ensures precision in the result that reflects the least precise measurement. Additionally, understanding the rules for the sign of the result in calculations is fundamental. When two positive numbers are added, the sign of the sum is positive. Conversely, adding two negative numbers results in a negative sum. If two numbers with opposite signs are added, they effectively subtract, and the result’s sign is that of the larger magnitude number.
An important and universally valid principle in mathematics is the commutative property of addition, which states A+B=B+A. This means that the order in which two numbers are added does not affect their sum. Likewise, subtraction can be viewed as adding a number with an opposite sign. For instance, subtracting 3 from 5 is the same as adding -3 to 5, which provides an answer following the rules of addition. These fundamental principles are true irrespective of the time or place, highlighting the universality of mathematical rules.