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Math Word Problems - GED, PSAT, SAT, ACT, GRE Preparation
4.17 Integers

{......-3,-2,-1,0,1,2,3,......} is called the set of Integers and is denoted by 'Z'.

Properties of Integers in Addition

Closure : For any two integers a, b their sum a+b is also an integer.

Commutative : For any two integers a, b; a+b = b+a.

Associative : For any three integers a, b, c; a+(b+c) = (a+b)+c.

Identity : For any integer a; a+0 = 0+a = a.
Here, zero is called the identity element under addition integers.

Inverse : For any integer a; a+(-a) = (-a)+a = 0.
Here, -a is called the additive inverse of the integer a.

Properties of Integers in Multiplication

Closure: For any two integers a, b their product a*b is also a integer.

Commutative: For any two integers a, b; a*b = b*a.

Associative: For any three integers a, b, c; a*(b*c) = (a*b)*c.

Identity: For any integer a; a*1 = 1*a = a.


Directions: Answer the following questions.
With examples, show why the properties doesn't' work for subtraction and division.
Also, write five examples of your own for each property of integers.

Q 1: For any three integers a, b and c, a*(b*c) = (a*b)*c.
False
True

Q 2: {......-3,-2,-1,0,1,2,3,.........} is called the set of ______.
Integers
Natural Numbers
Rational Numbers
Whole Numbers

Q 3: What is the multiplicative identity in integers.
-1
None of these
0
1

Q 4: For any integer a, what is the additive inverse____.
1
-a
a
0

Q 5: For any three integers a, b and c, (a+b)+c = a+(b+c).
False
True

Q 6: Set of integers are denoted by ______.
N
Z
I
W

Question 7: This question is available to subscribers only!

Question 8: This question is available to subscribers only!


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