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Grade 6 - Mathematics
2.19 Properties of Addition in Integers

Property I: For any two integers a and b, their sum a+b is also an integer.
Examples:
1. 3 + (-4) = -1
2. (-4) + (-5) = -9

Property II: For any two integers a and b, a+b = b+a.
Examples:
1. 2+(-6) = (-6) + 2 = -4
2. (-3) + (-4) = (-4) + (-3) = -7

Property III: For any three integers a, b, and c; a+(b+c) = (a+b)+c.
Example:
1. (-2)+[4+(-5)] = [(-2)+4]+(-5) = -3

Property IV: For any integer a; a+0 = 0+a = a.
Here, zero is called the identity element under addition of integers.
Examples:
1. 0+(-4) = -4
2. 5+0 = 5

Property V: For any integer a; a+(-a) = (-a)+a = 0.
Here, -a is called the additive inverse of the integer a.
Examples:
1. 1+(-1) = 0
2. (-4)+4 = 0


Directions: Answer the following questions. Also write at least five examples for each property of your own.
Q 1: 18+(-20) = ?
Answer:

Q 2: (-2)+[5+(-6)] =?
Answer:

Q 3: 8+(-8) = 0; in this statement -8 is called _____?
additive inverse
identity element
identity reverse
additive double

Q 4: 8+(-8) = ?
Answer:

Q 5: 8+(-2) = (-2)+8
Answer:

Q 6: (-6)+(-6) = ?
Answer:

Q 7: 2+(-8) = (-8)+2 = ?
Answer:

Q 8: 6+[(-2)+3] = ?
Answer:

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Question 10: This question is available to subscribers only!


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