7. About Integers
Integers consist of natural
numbers (positive integers),
their negatives, and zero.
Integers do not contain
fractions, decimals, and roots.
8. Integers can be represented
using a number line.
A number line is composed of three
basic parts. In the middle, we the
origin usually plotted with zero. You
can remember the origin is zero by
applying this mnemonic: “The origin
of most things is nothing.”
9. Integers are of two types: positive and negative. On a number line or
coordinate graph, positive integers are to the right of or above the zero point
and negative integers are to the left or below.
Positive numbers are plotted to the right of the origin while negative numbers
are plotted to the left of the origin. Arrows are put on the ends of the
horizontal line to show that the line continues to infinity.
10. To plot integers on the number line, we first locate an arbitrary point to
represent zero (0).
Zero is neutral; that is, it is neither positive nor negative.
11. Next, from 0 going to the right, plot the positive numbers starting from 1 with equal
spaces.
Positive integers are natural numbers or whole numbers greater than 0.
These are located to the right of 0 on the number line.
12. Finally, plot the negative numbers starting from 1 going to the left.
These are less than indicated with a negative sign.
Negative integers are the opposites of positive integers on the number line.
These are less than 0 indicated with a negative sign.
Now, we have an example of integers on the number line. To extend the line,
just continue the numbers on both sides of the line.
14. represent integers on the number line
Example 1: Locate 4 and -2 on the
number line.
Thus, -2 is 2 units to the left of 0, and 4 is 4 units to the right of 0 .
SOLUTION: Draw a number
line that includes 4 and -2.
15. Example 2: How far is -3 from 4 ?
Solution: Draw a number line that includes -3 and 4.
From -3, count the number of units until you reach 4:
Therefore, -3 is 7 units away from 4 .
16. Example 3: List the five integers immediately to the right of -3.
Solution:
Step 1: Draw a number line that includes -3.
Step 2: From -3 , jump five units to the right.
Thus, the five integers immediately to the right of -3 are -2,-1,0,1 and 2.
17. solve routine and nonroutine problems involving basic operations of
integers using appropriate strategies and tools.
Real-World Problems
Example 4: A mountain is 15 000 ft
above sea level. Below the mountain is
a valley which is 300 ft below sea level.
What is the distance from the top of the
mountain to the bottom of the
valley?
18. Solution:
Step 1: Identify what is asked.
The distance from the top of the mountain to the bottom of the valley
Step 2: List what are given.
The top of the mountain is 15 000 ft above sea level.
The bottom of the valley is 300 ft below sea level.
Step 3: Represent the elevation as integers.
Step 4: Solve the problem.
The distance from the top of the mountain to the bottom of the valley
may be represented as the distance from 15, 000 to -300 on the
number line.
We add the distance from 15 000 to 0, which is 15 000, and the distance
from 0 to-300, which is 300. The sum of 15 000 and 300 is 15 300
Thus, the distance from the top of the mountain to the bottom of the
valley is 15 300 ft.
19. In a singing competition, positive points are
given for correct singing and negative
points are given for incorrect singing. If
Sophia got points in five rounds were 50, –
15, – 10, 75 and 40, what were her total
points in all five rounds?
LET’S TRY!
20. 1. Write an integer to describe each situation.
Deposited 2, 000 pesos Example: - 2, 000
10 meters below sea level
Gained 3 kilos
3 kilometers north
5 steps forward
Spending 75 pesos
9 steps backward
13 years from now
A loss of 100 pesos
Gain od 165 pesos
21. 2. Plot the following integers on a number line.
A. 3
B. -5
C. 1
D. 0
E. 2
F. -4
3. On the number line what is units to the right of 3?
4. Analyze and solve the following problem carefully:
Jennifer moves for picnic from school which is far away from the school 55km north.
Her house is at distance of 25km south along the same road from picnic place. If she
she returns back to the house after a picnic directly, how will you represent the
distance that she has to travel everyday to reach to the school towards south?
