Algebra

3. positive integers greater than 1 that have more than two factors
6. fundamental rules that govern operations, including the commutative, associative, and distributive laws for arithmetic, and various exponent laws for powers
9. states that when adding or multiplying three or more numbers, the grouping (using parentheses) does not change the result
12. referring to fundamental principles where an element or proposition remains unchanged when combined with a specific identity element
13. the set of non-negative integers (0, 1, 2, 3, ...) that do not include any fractional, decimal, or negative components
14. the actual value a digit represents based on its position within a number, often calculated as the face value multiplied by its place value
15. breaks down a number to show the place value of each digit, expressed as a sum
18. mathematical symbols or words (e.g., 1, 7, 100, one, seven) used for counting, measuring, labeling, and ordering quantities
22. stating that multiplying a sum by a number is the same as multiplying each addend individually and then adding the products.
23. a whole number that does not have a fractional or decimal component
24. Counting numbers, also known as natural numbers or positive integers, are the set of numbers \(\{1, 2, 3, 4, 5, \dots\}\) used for counting items

1. a structure, shape, or document with spaces for collecting information, often used for surveys, quizzes, and registration
2. a mathematical rule stating that the order of numbers in addition or multiplication does not change the result
4. the numerical value a digit holds based on its position within a number
5. positive and negative numbers, including zero, that represent both magnitude and direction, often used for temperature, bank balances, or movement
7. the actual value of a digit in a number, regardless of its position
8. a method of breaking down a number into a sum of each digit multiplied by its corresponding place value
10. the oldest and most elementary branch of mathematics, focusing on the study of numbers and the properties of traditional operations like addition, subtraction, multiplication, and division
11. The value refers to the worth of each digit depending on where it lies in the number.
16. integers divisible by 2 with no remainder
17. the act of replacing one person, object, or variable with another
19. This is the study of numbers, structure, space, and change,
20. integers not divisible by two, leaving a remainder of 1 when divided
21. whole numbers greater than 1 that have exactly two factors: 1 and themselves