Final answer:
Mathematical operations like addition, subtraction, multiplication, and division are performed on different types of numbers such as whole numbers, fractions, decimals, and negatives. These operations follow specific rules, for example, finding a common denominator for fractions. Scientific notation is used for very large or small numbers.
Step-by-step explanation:
There are various types of numbers, including whole numbers (like 1, 2, and 3), fractions (like 1/2 and 3/4), decimals (like 0.5 and 2.75), and negative numbers (like -1, -2, -3). Operations such as addition, subtraction, multiplication, and division can be performed with these numbers. When working with addition and subtraction, the basic principle is to combine like terms and pay attention to the signs of the numbers involved.
Whole numbers follow straightforward rules for these operations, but with fractions, you need to find a common denominator before you can add or subtract them. Multiplication and division have their own set of rules, notably that the product of two positive or two negative numbers is positive, whereas the product of numbers with opposite signs is negative. The same sign rules apply for division.
To work with very large or very small numbers, you should be comfortable with scientific notation, which simplifies these numbers into a product of a number and a power of ten. This is also useful for carrying out arithmetic operations with such numbers and keeping the answer in scientific notation.