Positive & Negative Integers

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Transcript of Positive & Negative Integers
Course 1
111 Integers in RealWorld SituationsPositive & Negative Integers
Course 1
Warm UpWarm Up
Cornell Notes on 111 & 112Cornell Notes on 111 & 112
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111 Integers in RealWorld Situations
Warm UpCompare. Write <, >, or =.
1. 8,426 8,246
2. 9,625 6,852
3. 2,071 2,171
4. 2,250 2,250
>
>
<
=
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111 Integers in RealWorld Situations
Learn to identify and graph integers, and find opposites.
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111 Integers in RealWorld Situations
Vocabulary
positive numbernegative numberoppositesinteger
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111 Integers in RealWorld Situations
Where do we see examples of negative numbers?
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111 Integers in RealWorld Situations
Positive numbers
Negative numbers
Numbers that are greater than 0. They may be written with a positive sign (+), but they are usually written without it.
Numbers that are are less than 0. They are always written with a negative sign (–).
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111 Integers in RealWorld Situations
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
B. taking $15 out of the bank
Positive numbers can represent climbing or rising.
+20,000
Negative numbers can represent taking out or withdrawing.
–15
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111 Integers in RealWorld Situations
Additional Example 1: Identifying Positive and Negative Numbers in the Real World
Name a positive or negative number to represent each situation.
C. 7 degrees below zero
Negative numbers can represent values below or less than a certain value.
–7
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111 Integers in RealWorld Situations
Define opposites
Define integers
On a number line, opposites are the same distance from 0 but on different sides of 0.
the set of all whole numbers and their opposites.
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111 Integers in RealWorld Situations
You can graph positive and negative numbers on a number line.
–5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5
Opposites
Positive IntegersNegative Integers
0 is neither negative nor positive.
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111 Integers in RealWorld Situations
Additional Example 2: Graphing Integers
Graph each integer and its opposite on a number line.
A. +2
–5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5
B. –5
–2 is the same distance from 0 as +2.
–5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5
+5 is the same distance from 0 as –5.
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111 Integers in RealWorld Situations
• We read 3 as “the absolute value of 3.”
• We read 3 as “the absolute value of negative 3.”
Define absolute value The distance of a number from zero on a number line. The symbol for absolute value is  .
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111 Integers in RealWorld Situations
Example 3
Use a number line to find the absolute value of each integer
A. 2
–5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5
2 is 2 units from 0, so 2 is 2
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111 Integers in RealWorld Situations
Additional Example 3: Writing Integer Expressions to Represent Situations
Mark enters his office building on the ground floor. Using the elevator, he goes up 6 floors to place a call, then down 4 floors for lunch, and then up 8 floors for a meeting. Write an expression to represent this situation.
Mark starts on the ground floor, 0.0
Mark goes up 6 floors.6
Mark goes down 4 floors.4
Mark goes up 8 floors. 8
You can use a number line to model Mark’s movements on the elevator.
+8
0
2
4
6
8
10
+6
4
+ 6 – 4 + 8
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111 Integers in RealWorld Situations
Additional Example 1: Comparing Integers Use the number line to compare each pair of integers. Write < or >.
A. –2 2
B. 3 –5
C. –1 –4
–5 –4 –3 –2 –1 0 1 2 3 4 5
–2 is to the left of 2 on the number line.–2 < 2
3 > –5 3 is to the right of –5 on the number line.
–1 is to the right of –4 on the number line.–1 > –4
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111 Integers in RealWorld Situations
Additional Example 2: Ordering Integers
Order the integers in each set from least to greatest.
A. –2, 3, –1
B. 4, –3, –5, 2
–3 –2 –1 0 1 2 3
Graph the integers on the same number line.
Then read the numbers from left to right: –2, –1, 3.
–6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6
Graph the integers on the same number line.
Then read the numbers from left to right: –5, –3, 2, 4.
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111 Integers in RealWorld SituationsLesson Quiz
Name a positive or negative number to represent each situation.
1. saving $15
2. 12 feet below sea level
3. What is the opposite of –6?
4. 4
5. When the Swanton Bulldogs football team
passed the football, they gained 25 yards.
Write an integer to represent this situation.
–12
+15
6
+25