Download presentation

Presentation is loading. Please wait.

Published byRafe Gilmore Modified over 8 years ago

1
1)12 (–28) 2) –23 + (–15) 3) 28 ÷ ( –12) 4) 0.314, 0.0978, 0.309, 0.3131 1.1 Warm-Up Simplify. Order the numbers from least to greatest. -336-38 7 3 0.0978,0.309,0.3131,0.314

2
Alg2 Lesson 1-1 Properties of Real Numbers Objectives: 1.Identify the subsets of real numbers. 2.Identify the properties of real numbers. 3.Find the opposite and reciprocal of a number. 4.Order real numbers and graph on a number line.

3
SUBSETS OF THE REAL NUMBERS WHOLE NUMBERS: 0, 1, 2, 3, ……………. INTEGERS: ……., -3, -2, -1, 0, 1, 2, 3, …………. RATIONAL NUMBERS: A ratio of two integers (3/4, 1/3, -4/1, ….) when written as decimals, rational numbers terminate or repeat. (3/4 = 0.75, or 1/3 = 0.3333….) IRRATIONAL NUMBERS: They neither terminate or repeat. (л, 2, etc.) NATURAL NUMBERS: 1, 2, 3, …………….

5
Example 1 Graph the real numbers, 3, and – 1.8 5 2 –5–4–3–2–112543 0 Where is the origin? –5–4 –3–2–112543 0

6
Properties of Real Numbers Opposite or Additive Inverse of any number a is –a –The sum of any two opposites is 0 The Reciprocal or Multiplicative Inverse of any nonzero number a is 1/a –The product of reciprocals is 1

7
Example 4 Find the opposite and the reciprocal of each number a) -3b) Opposite: Reciprocal:

8
PROPERTIES OF ADDITION AND MULT. ASSOCIATIVE: (a + b) + c = a + (b + c) & (ab)c = a(bc) COMMUTATIVE: a + b = b + a & ab = ba DISTRIBUTIVE: a(b + c) = ab + ac IDENTITY: a + 0 = a & a 1 = a INVERSE: a + (-a) = 0 & a = 1 1 a CLOSURE: a + b is a real number & ab is a real number

9
Example 2 Identify the property shown. a. 14 + 7 = 7 + 14b. 5 = 1 Commutative property of addition Inverse Property of multiplication 1 5

10
Operations with Real Numbers. Example 3 a.The difference of -3 and -15 is: b.The Quotient of -18 and 1/6 is: Sum + Difference – Product x ÷ Quotient -3 – -15 18 -3 + 15 = 12 1 6 6 1 6 1 -18 6 =-108

11
The Absolute Value of a real number is its distance from zero on the number line Example 5 Find the absolute value of: a)|-4| b)|0| c)|-1 (-2)| 4 0 2

12
HOMEWORK Due Wednesday: Pg. 8 – 9 12 – 24, 34 – 36, 42 – 62 even

Similar presentations

© 2024 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google