Final answer:
The arithmetic statements demonstrate properties like the Reflective Property of Multiplication, Distribution Property of Multiplication over Subtraction, Commutative Property of Addition, and associative property.
Step-by-step explanation:
Properties of Arithmetic Operations
Through those arithmetic statements, various mathematical properties are expressed:
- Reflective Property of Multiplication: This property states that a number multiplied by itself remains unchanged. For example, 75 x 69 x 85 = 75 x 69 x 85 illustrates that the multiplication of these numbers in a particular order gives the same product when the order is not changed.
- Distribution Property of Multiplication over Subtraction: This states that the product of a number and the difference of two other numbers is the same as the difference of the product of that number and each of the two numbers. For instance, 45 x 35 - 45 x 5 follows this property, which can be written as 45 x (35 - 5).
- Commutative Property of Addition: It indicates that the order in which numbers are added does not affect the sum. The equation 56 + 34 = 34 + 56 shows this property.
- Lastly, 123 + 235 + 340 = 123 + 235 + 340 is an example of the associative property, which states that the grouping of addends does not change the sum.
When dealing with integer powers and scientific notation, remember that raising a number to a power is a shorthand for repeated multiplication, like 4³, which stands for 4 x 4 x 4. It saves a lot of space, especially in expressions such as 4²³. When multiplying numbers with powers, we add the exponents, as in xP x xQ = x(P+Q). The rule follows the same pattern when dealing with numbers in scientific notation.