Download Lesson 1.3 – Operations on real numbers

Lesson 1.3 –
Operations on real
numbers
Honors 1 Algebra
Warm – Up
 Add



A. -3 + (-11)
C. -10 + 15
E. 2 3

3

B. 3 + (-7)
D. -8.3 + (-1.9)
7
 Subtract



F. 2 – 8
H. 1 – 0.06
E. 2  1
3
2
G. -11 – 5
I. Subtract 7 from 4
Simplify the following
expressions
 11 + 2 – 7
 -5 – 4 + 2
Multiplying two real numbers
 The product of two numbers with the
same sign is positive
 The product of two numbers with
different signs is negative.
 Examples:



(-8)(-1) =
3(-3) =
(7)(1)(-2)(-3) =
Dividing two real numbers
 The quotient of two numbers with the
same sign is positive.
 The quotient of two numbers with
different signs is negative.
 Examples:

A. 20
B. - 9 ÷ - 3
4

C.
1
2
 
10
5
D. - 40 ÷ 10
Exponents
exponent
43 = 4 x 4 x 4 = 64
4 is a factor 3 times
base
Examples:
A. 32
B.
1
 
2
4
 1  1  1  1 
    
 2  2  2  2 
1
 
 16 
Exponents
 Warning: Be very careful when
simplifying expressions such as -52 and
(-5)2
-52 = - (5 x 5) = - 25 and
(-5)2 = (-5)(-5) = 25
Square Roots
 The opposite of squaring a number is
taking the square root of a number.
 The negative square root of 16 is written
 16
 The square root of a negative number,
such as 16 is not a real number.
There is no real number, that when
squared gives a negative number.
Examples
9
1
4
 36
36
Find the roots
3
27
5
1
4
16
Order of Operations
 1. Raise to powers or take roots in order
from left to right.
 2. Multiply or divide in order from left to
right.
 3. Add or subtract in order from left to
right.
 Do example 9 C on page 24