Three Properties of Addition: 1.Commutative Property of Addition 2.Associative Property of Addition 3.Identity Property of Addition
Commutative Property of Addition… The word commutative comes from the verb “to commute.” Commuting means changing, replacing, or exchanging People who travel back and forth to work are called commuters
Commutative Property of Addition… Every day you ride your bike to school. The distance from home to school is 2 miles. The distance from school to home is 2 miles. How do we know this??
Commutative Property of Addition… The distance from Home to School is the same as the distance from school to home. Home + School = School + Home H + S = S + H A + B = B + A
Commutative Property of Multiplication A * B = B * A 3 * 5 = 5 * 3 3 * 5 = _______ 5 * 3 = _______
Associative Properties of Addition… The word associative comes from the verb “to associate.” Associate means connected, joined, or related People who work together are called associated.
Associative Properties of Addition… Three people work together. Associate B needs to call Associates A and C to share some news. Does it matter who B calls first???
Associative Properties of Addition… A CB B calls A first He calls C last NO!NO!
Associative Properties of Addition… The role of Parentheses - In math, we use parentheses to show groups - In the order of operations, the numbers and operations in parentheses, are done first (PEMDAS)
Associative Properties of Addition… (A + B) + C = A + (B + C) A C B A C B THEN
Associative Properties of Multiplication… A * ( B * C ) = ( A * B ) * C 2 * ( 3 * 4 ) = ( 2 * 3 ) * 4 _______ = _______
Identity Property of Addition… Your identity is who you are. Changing your clothes or getting a new haircut does not change your identity. Your identity remains the same.
Identity Property of Addition… A number also has an identity. The identity of a number is the value of the number. The additive identity is the number that when added to another number does not change the identity of the original number. 3 + ___ = 3
Identity Property of Addition… The additive identity is zero. We can add zero to any number and the answer is the original number
Identity Property of Multiplication… 3 * ___ = 3 We can multiply any number by one and the answer will be the original number
Identity Properties… Identity Property of Addition Identity Property of Multiplication A + 0 = A A * 1 = A
Distributive Property… Distribute means to deliver or pass out If we distribute food to three boxes, we put food in each of the three boxes. If the teacher ask you to distribute the papers to the students, then you will give each student a paper.
Distributive Property… A ( B + C ) = A * B + A * C The A is the food and the boxes are B and C. We pas out A to each of B and C. In this case that means that we multiply A by both B and C separately and then add the resulting products.
Summary… Property NameRule Commutative Property of AdditionA + B = B + A Commutative Property of Multiplication A * B = B * A Associative Property of AdditionA + (B + C) = (A + B) + C Associative Property of Multiplication A * (B * C) = (A * B) * C Identity Property of AdditionA + 0 = A Identity Property of MultiplicationA * 1 = A Zero PropertyA * 0 = 0 Distributive PropertyA(B + C) = A*B + A*C