Transcript Representing Integers

Integers 11-1
I can identify positive and negative
integers
SPI 6.2.8
Positive numbers are greater than
0. They may be written with a
positive sign (+), but they are
usually written without it.
Negative numbers are less than 0.
They are always written with a
negative sign (–).
Additional Example 1: Identifying Positive and
Negative Numbers in the Real World
Name a positive or negative number to represent
each situation.
A. a jet climbing to an altitude of 20,000 feet
Positive numbers can represent climbing or rising.
+20,000
B. taking $15 out of the bank
Negative numbers can represent taking out or
withdrawing.
–15
Check It Out: Example 1
Name a positive or negative number to
represent each situation.
A. 300 feet below sea level
Negative numbers can represent values below or
less than a certain value.
–300
B. a hiker hiking to an altitude of 4,000 feet
Positive numbers can represent climbing or rising.
+4,000
Representing Integers
11-2
SPI 6.1.3
I CAN use pictorial, concrete, and
symbolic representation for integers.
You can graph positive and negative numbers on a
number line.
On a number line, opposites are the same
distance from 0 but on different sides of 0.
Integers are the set of all whole numbers and
their opposites.
Opposites
–5
–4 –3 –2
–1
Negative Integers
0 +1 +2 +3 +4 +5
Positive Integers
0 is neither negative nor positive.
The absolute value of an integer is its distance
from 0 on a number line. The symbol for absolute
value is ||.
|–3| = 3
|3| = 3
|<--3 units--> |
–5
–4
–3 –2
–1
0
<--3 units-->|
+1 +2
+3 +4
+5
• Absolute values are never negative.
• Opposite integers have the same absolute value.
• |0| = 0
Additional Example 3A: Finding Absolute Value
Use a number line to find the absolute value of
each integer.
A. |–2|
–5
–4
–3 –2
–1
0
+1 +2
+3 +4
–2 is 2 units from 0, so |–2| = 2
2
+5
Additional Example 3B: Finding Absolute Value
Use a number line to find the absolute value of
each integer.
B. |8|
–1
0
1
2
3
4
5
6
7
8 is 8 units from 0, so |8| = 8
8
8
9
Mt. McKinley
The total distance is 20,602 feet.
Additional Example 1: Comparing Integers
Use the number line to compare each pair of
integers. Write < or >.
–5 –4 –3 –2 –1
A. –2
0
1
2
3
4
5
2
–2 < 2
–2 is to the left of 2 on the number line.
B. 3
–5
3 > –5 3 is to the right of –5 on the number line.
C. –1
–4
–1 > –4 –1 is to the right of –4 on the number line.
Additional Example 2: Ordering Integers
Order the integers in each set from least to
greatest.
A. –2, 3, –1
Graph the integers on the same number line.
–3 –2 –1
0
1
2
3
Then read the numbers from left to right: –2, –1, 3.
B. 4, –3, –5, 2
Graph the integers on the same number line.
–6 –5 –4 –3 –2 –1
0
1
2
3
4
5
6
Then read the numbers from left to right: –5, –3, 2, 4.
Additional Example 3: Problem Solving Application
In a golf match, Craig scored +2,
Cameron scored +3, and Rob scored –1.
Who won the golf match?
1
Understand the Problem
The answer will be the player with the lowest
score. List the important information:
• Craig scored +2.
• Cameron scored +3.
• Rob scored –1.
Check It Out: Example 3 Continued
2
Make a Plan
You can draw a diagram to order the scores from
least to greatest.
3
Solve
Draw a number line and graph each player’s score
on it.
•
•
•
–6 –5 –4 –3 –2 –1
0
1
2
3
4
5
6
Trista’s score, –3, is farthest to the left, so it is
the lowest score. Trista won the golf match.
Check It Out: Example 3 Continued
4
Look Back
Negative integers are always less than positive
integers, so Melissa cannot be the winner.
Since Trista’s score of –3 is less than Alyssa’s
score of –1, Trista won.
Name 4 real life situations in
which integers can be used.
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Spending and earning money.
Rising and falling temperatures.
Stock market gains and losses.
Gaining and losing yards in a football game.