The document discusses the six properties of operations on integers: closure, commutative, associative, distributive, identity, and inverse. It provides examples for each property. The closure property states that operations on integers result in an integer. The commutative property states that changing the order of operands does not change the result. The associative property states that grouping does not affect the result of operations.

3. Find the six hidden words that make up
the Properties of the Operations on
Integers.

5. Properties of the
Operations on Integers
Closure
Commutative
Associative
Distributive
Identity
Inverse

7. 14 + 30 = 44
14 + (-5) = 9

8. Closure Property
If a and b are two integers: (a + b), (a -
b), and (a x b) is also an integer.

10. Commutative Property
This property states that changing the
order of the addends does not affect
the sum.

11. 6 + 4 = 4 + 6
(-6) + 4 = 4 + (-6)

12. ________ + ________ = ________ + ________
a b b a

14. Associative Property
This property states that changing the
grouping of numbers being added does
not change its value.

15. (6 + 2) + 1 = 6 + (2 + 1)
[6 + (-2)] + 3 = 6 + [(-2) + 3]

16. ( _____ + _____ ) + _____ = _____ + ( _____ + _____ )a b c a b c

18. Distributive Property
This property states that when two
numbers have been added/subtracted
and then multiplied by a factor, the
result will be the same when each
number is multiplied by the factor and
the products are then
added/subtracted.

19. -2 (4 + 3) = (-2 x 4) + (-2 x 3)
2 (4 - 3) = (2)(4) - (2)(3)

20. _____ ( _____ + _____ ) = ( _____ x _____ ) + ( _____ x _____ )a b c a b a c

22. Identity Property for Addition
Identity Property for Addition states
that the sum of any number and zero is
the number itself.

23. 5 + 0 = 5
0 + (-4) = -4

24. ________ + ________ = ________
a 0 a

25. Identity Property for Multiplication
Identity Property for Multiplication
states that the product of any number
and one is the number itself.

26. 8 x 1 = 8
1 x (-9) = -9

27. 14
-14

28. Inverse Property for Addition
Inverse Property for Addition states
that the sum of any number and its
additive inverse is zero.

29. 10 + (-10) = 0
-6 + 6 = 0

30. Inverse Property for Multiplication
Inverse Property for Multiplication
states that the product of any number
and its multiplicative inverse or
reciprocal is 1.

31. 4 x 1/4 = 1
-8 x (-1/8) = 1

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44. THINK
OF
THIS!