Addition and Subtraction of Whole Numbers - Vocabulary Flashcards

Vocabulary flashcards covering key terms from the lecture on adding and subtracting whole numbers, including properties, methods for large-number calculations, and order of operations.

Commutative Property of Addition

Swapping the order of addends does not change the sum: a + b = b + a.

Associative Property of Addition

Grouping of addends does not change the sum: (a + b) + c = a + (b + c).

Additive Identity

Adding zero to any number leaves it unchanged: a + 0 = a.

Number Line Modeling (Addition)

A visual method where you move along a number line to represent adding numbers (start at a, move right by b).

Expanded Notation

Representing numbers by their place values (e.g., 213 = 200 + 10 + 3) to facilitate addition/subtraction.

Traditional Algorithm (Addition)

Column-based method for adding numbers; aligns digits by place value and may involve carrying.

Borrowing (Regrouping) in Subtraction

When a minuend digit is smaller than the subtrahend digit, borrow 1 from the next left place (add 10 to the current place).

Subtraction is Not Commutative

Order matters; a - b ≠ b - a; results can differ and can be negative depending on order.

Subtraction is Not Associative

Grouping of multiple subtractions affects the result; (a - b) - c ≠ a - (b - c).

Adding Up Method (Subtraction Alternative)

Start with the smaller number and successively add increments to reach the larger number; the difference is what was added.

Lattice Method (Addition)

A grid-based, place-value method for addition that can reduce the need for regrouping.

Order of Operations

Rules for evaluating expressions with multiple operations; equal-precedence operations (like + and -) are handled left to right; PEMDAS is a common mnemonic but additions/subtractions are tied.

PEMDAS

Mnemonic for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction; note that + and − have the same precedence and are evaluated left to right.

Left-to-Right Rule for Add/Sub

When only addition and subtraction are present, compute from left to right to ensure consistent results.