1-3 Properties of Numbers Goals: Recognize the properties of equality and identity. Recognize the Commutative and Associative Properties.

Vocabulary Reflexive Property of Equality – any real number is equal to itself. Symmetric Property of Equality – if a = b, then b = a Transitive Property – if a = b and b = c, then a = c

Vocabulary Additive Identity Property – the sum of a number and 0 is always the number. Additive Inverse Property – the sum of a number and its opposite is always 0.

Vocabulary Multiplicative Identity – multiplying by 1 does not change a number Property of Zero – anything multiplied by 0 is 0 Multiplicative Inverse Property – any number times its reciprocal is 1 Property of Opposites – anything multiplied by -1 is the opposite.

Vocabulary Commutative Property – the order that you add or multiply numbers does not change the answer. Associative Property – the way you group three numbers when adding or multiplying does not change the answer.

Name the property used in each step. Evaluate Using Properties Name the property used in each step. Substitution: 12 – 8 = 4 Substitution: 15 ÷ 5 = 3 Substitution: 3 – 2 = 1

Multiplicative Identity: 3(1) = 3 Evaluate Using Properties Multiplicative Identity: 3(1) = 3 Multiplicative Inverse: (4) = 1 = 4 Substitution: 1 + 3 = 4 Answer: 4

Examples 7(4 – 3) – 1 + 5 ∙ 1 5 2 · 3 + (4 · 2 – 8) 1 4 12−8 +3 15÷5−2 6 1 4 12−8 +3 15÷5−2 4

A. 4 B. 5 C. 1 D. 0

Word Problem # 1 HORSEBACK RIDING Myra made a list of trail lengths to find the total miles she rode. Find the total miles Myraa rode her horse. Bent Tree Knob Hill Meadowrun Pinehurst 4.25 + 6.50 + 9.00 + 7.75 Answer: Myra rode 27.5 miles on the trails.

Word Problem #2 TRANSPORTATION Darlene rode the city train from the Winchester Street Station to the airport. How far did she travel on the train?

Practice Page 19 #1-8 You do not have to write property names!!

Homework Pages 19-20 #10-36 even You do not have to write property names!!