Google Classroom
GeoGebraGeoGebra Classroom

Mixing Things Together

How do you mix things together?

How do you mix things together?

OBJECTIVE: To learn about the axioms of addition

In a previous lesson, you learned about the AXIOMS OF EQUALITY. Keeping Your Balance: https://www.geogebra.org/m/v5jyuhxm In this lesson, you're going to learn about the AXIOMS OF ADDITION. The following axioms define the rules for adding real numbers. 1. CLOSURE AXIOM FOR ADDITION — If a and b are real numbers, then a + b is equal to a unique real number, i.e., if two real numbers are added together, the sum is a real number. 2. IDENTITY AXIOM FOR ADDITION — For any real number a, a + 0 = a or 0 + a = a. Zero ( 0 ) is the identity element for addition. 3. ADDITIVE INVERSE FOR ADDITION — Every real number a has an additive inverse -a such that a + (-a) = 0 or (-a) + a = 0. 4. COMMUTATIVE AXIOM FOR ADDITION — If a and b are real numbers, then a + b = b + a, i.e., the order in which two or more numbers are added together does not affect the sum. 5. ASSOCIATIVE AXIOM FOR ADDITION — If a, b, and c are real numbers, then (a + b) + c = a + (b + c); i.e., the grouping of three or more numbers for addition does not affect the sum. Algebraic Examples: 1. CLOSURE AXIOM FOR ADDITION — 5 + 7 = 12 Since 5 and 7 are real numbers, 12 is also a real number. 2. IDENTITY AXIOM FOR ADDITION — 10 + 0 = 10 & 0 + (-12) = -12 3. ADDITIVE INVERSE FOR ADDITION — 5 + (-5) = 0 & (-7) + 7 = 0 4. COMMUTATIVE AXIOM FOR ADDITION — 2 + 3 = 5 3 + 2 = 5 5. ASSOCIATIVE AXIOM FOR ADDITION — (6 + 7) + 13 = 13 + 13 = 26 6 + (7 + 13) = 6 + 20 = 26
Below is a set of problems involving axioms of addition.

Axioms of Addition

ANSWER BOX:

Check your answers below.

In this lesson, you learned about the axioms of addition.

In the next lesson, you'll learn about the axioms of multiplication. Did you ENJOY today's lesson?