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Integers – An Introduction

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What are integers?


Integers are a set of numbers that include all the natural numbers (0, 1, 2, 3, 4, and so on) and their negatives.

integers_intro



The sign of an integer is either positive (+) or negative (-), except zero, which has no sign.




Positive Integers

Positive integers are all the whole numbers greater than zero: 1, 2, 3, 4, 5 ...These numbers are to the right of zero on the number line.


Negative integers

Negative integers are all the whole numbers less than zero: -1, -2, -3, -4, -5 ...These numbers are to the left of zero on the number line.


Zero

The integer zero is neutral. It is neither positive nor negative.


Example: Write the opposite of each integer given below :

integers2


Example: Write the number that best represents each statement.

a) It is 6 degrees warmer than yesterday.
+6
b) I lost $2:00 through a hole in my pocket.
 -2
c) What is the absolute value of the number | -915 |?
915
d) What is the absolute value of the number | 712 |?
712


Try this now:


Write the number that best represents each statement
i) The price was reduced by $12.

ii) I improved my mark by 16.

iii) The building is 312 meters tall.

iv) My sister is 3 years younger than me.

v) We cut 9 inches off the timber plank.

vi) I have 2 arms.

vii) An elevator went down 10 floors. What integer describes the trip the elevator made?

viiii) 10 degrees above zero

ix) A loss of 16 dollars

x) A gain of 5 points

(Answers: 1. i) -12 (ii) 16 (iii) 312 (iv) -3 (v) -9 (vi) 2 (vii) -10) (viii) +10 (ix) -16 (x) +5)


Absolute Value

The absolute value of an integer is the numerical value without regard to whether the sign is negative or positive. On a number line it is the distance between the number and zero.
The absolute value of -15 is 15. The absolute value of +15 is 15.
The symbol for absolute value is to enclose the number between vertical bars such as |-20| = 20 and read "The absolute value of -20 equals 20".


Example: Evaluate if a = 4, b = 3 and c = -2.

 |c| + b
= |-2| + 3
= 2 + 3 = 5


Try this now:


Evaluate if a = 4, b = 3 and c = -2.

|a| + |b| - 3
(Answer: 4)


                                      
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