Transcript Columbus State Community College

Columbus State Community College
Chapter 1 Section 2
Introduction to Signed Numbers
Ch 1 Sec 2: Slide #1
Introduction to Signed Numbers
1.
2.
3.
4.
Write positive and negative numbers used in everyday situations.
Graph signed numbers on a number line.
Use the < and > symbols to compare integers.
Find the absolute value of integers.
Ch 1 Sec 2: Slide #2
Negative Signs and Subtraction Signs
NOTE
To write a negative number, put a negative sign (a dash) in front of it:
–12. Notice that the negative sign looks exactly like the subtraction
sign, as in 7 – 2 = 5. The negative sign and subtraction sign do not
mean the same thing (more on that in the next section). To avoid
confusion for now, we will write negative signs in red and put them
up higher than subtraction signs.
–12
means negative 12
15 – 6 means 15 minus 6
Raised dash
Ch 1 Sec 2: Slide #3
Writing Positive and Negative Numbers
EXAMPLE 1
Writing Positive and Negative Numbers
Write each negative number with a raised negative sign. Write
each positive number in two ways.
(a)
Andy improved his test score by 10 points.
+10
points
or
Raised positive sign
(b)
10 points
No sign
Lauren lost $20.
–$20
Raised negative sign
Ch 1 Sec 2: Slide #4
The Number Line
-5
-4
-3
-2
-1
Negative numbers
0
1
2
3
4
5
Positive numbers
Zero is neither
positive nor negative
Ch 1 Sec 2: Slide #5
Graphing Numbers on a Number Line
EXAMPLE 2
Graphing Numbers on a Number Line
Graph each number on the number line.
(a)
–3
(c) 2 1
2
(b) 4
(d)
-5
-4
(a)
-3
(d)
(c)
-2
-1
0
1
2
–
4 1
2
(b)
3
4
5
Ch 1 Sec 2: Slide #6
Integers
NOTE
A list of integers can be written like this:
…, –3, –2, –1, 0, 1, 2, 3, …
The dots show that the list goes on forever in both directions.
Ch 1 Sec 2: Slide #7
Relational (or Comparison) Operators
NOTE
Relational (or comparison) operators can be used to compare numbers.
The < symbol is called the “less than” symbol, and
the > symbol is called the “greater than” symbol.
Ch 1 Sec 2: Slide #8
Comparing Two Integers Using a Number Line
Using the < and > symbols, we can compare two integers.
-5
-4
-3
-2
-1
0
1
2
3
4
5
–1
is to the left of 4.
4 is to the right of –1.
–1
is less than 4.
4 is greater than –1.
Use < to mean “is less than.”
Use > to mean “is greater than.”
–1
4
–1
<
4
is less than 4
>
–1
4 is greater than –1
Ch 1 Sec 2: Slide #9
The “Less Than” and “Greater Than” Symbols
NOTE
One way to remember which symbol to use is that the “smaller end of
the symbol” points to the “smaller number” (the number that is less).
0 > –2
3 < 8
Smaller
number
Smaller end
of symbol
Smaller end
of symbol
Smaller
number
Ch 1 Sec 2: Slide #10
Comparing Integers, Using the < and > Symbols
EXAMPLE 3
Comparing Integers, Using the < and > Symbols
Write < or > between each pair of numbers to make a true statement.
(a)
> 0
4 _____
(b)
–5
<
_____
12
–5
(c)
–7
< –2
_____
–7
4 is to the right of 0 on the number line, so 4 is
greater than 0.
is to the left of 12 on the number line, so –5
is less than 12.
is to the left of –2 on the number line, so –7
is less than –2.
Ch 1 Sec 2: Slide #11
Absolute Value
Absolute Value
The absolute value of a number is its distance from 0 on the number
line. Absolute value is indicated by two vertical bars. For example,
|3|
is read
“the absolute value of 3.”
Two vertical bars
Ch 1 Sec 2: Slide #12
Finding Absolute Values
EXAMPLE 4
Finding Absolute Values
Find each absolute value.
(a)
|5|
The distance from 0 to 5 on the number line is 5
spaces. So, | 5 | = 5.
5 spaces
-5
-4
-3
-2
-1
0
1
2
3
4
5
Ch 1 Sec 2: Slide #13
Finding Absolute Values
EXAMPLE 4
Finding Absolute Values
Find each absolute value.
(b)
| –2 |
The distance from 0 to –2 on the number line is 2
spaces. So, | –2 | = 2.
2 spaces
-5
-4
-3
-2
-1
0
1
2
3
4
5
Ch 1 Sec 2: Slide #14
Introduction to Signed Numbers
Chapter 1 Section 2 – Completed
Written by John T. Wallace
Ch 1 Sec 2: Slide #15