Download 1-4 Properties of Real Numbers

1-5 Adding and Subtracting
Real Numbers
TODAY YOU NEED – PENCIL, NOTEBOOK
CALCULATORS NOT ALLOWED TODAY
(YOU ALL ARE HIGHLY CAPABLE!)
We’re preparing for R.N.3 –
Understanding the Real Number
System!
Student Objective
• I can find sums and differences of real numbers.
• This needs to be done with precision even when
faced with a situation where you have no
calculators.
Thought Provoking Beginnings
What are two methods for finding the sums and
differences of real numbers?
What are two methods for finding the sums and
differences of real numbers?
Vocabulary
• The absolute value of a number is its distance
•
•
•
from 0 on a number line.
Two numbers that are the same distance from 0
on a number line but lie in opposite directions
are opposites.
A number and its opposite are called additive
inverses.
To find the sum of a number and its opposite,
you can use the inverse Property of
Addition.
Problem 1 – Using Number Line
Models
This strategy is beneficial if you don’t have a calculator and are struggling with
making a calculation.
• What is each sum? Use a number line.
a. 3 + 5
b. 2 + (-4)
c. -1 + 2
d. -2 + (-4)
Adding Real Numbers
• Adding Numbers With the Same Sign
– To add two numbers with the same sign, add their
absolute values.
– The sum has the same sign as the addends.
– Ex. 3 + 4 =7
-3 + -4 = -7
• Adding Numbers With Different Signs
– To add two numbers with different signs, subtract
their absolute values.
– The sum has the same sign as the addend with the
greater absolute value.
– Ex. -3 + 4 = 1
3 + (-4) = -1
Inverse Property of Addition
• For every real number a, there is an
additive inverse –a such that a + (-a) = -a
+ a = 0.
– Ex: 14 + (-14) = 0
– -14 + 14 = 0
Subtracting Real Numbers
• To subtract a real number, add its
opposite: a – b = a + (-b).
– Ex. 3 – 5 = 3 + (-5) = -2
– 3 – (-5) = 3 + 5 = 8
LET’S SEE WHERE WE’RE AT!
• Find each sum or difference.
1. -5 + 2
2. -2 + (-1)
3. -12 + 9
4. -4 + (-3)
5. -3 – (-5)
6. 1.5 – 8.5
ANSWERS [You’ve Got This!]
•
1.
2.
3.
4.
5.
6.
Find each
-5 + 2
-2 + (-1)
-12 + 9
-4 + (-3)
-3 – (-5)
1.5 – 8.5
sum or difference.
=
-3
=
-3
=
-3
=
-7
=
2
=
0
Wrap Up
• What are two methods for finding sums
and differences of real numbers?
• Answer: You can use a number line, or
you can use rules involving absolute value.
Exit Ticket
1. What is the sum of a number and its
opposite?
1. -5 – (-5)