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Find the six hidden words that make up the Properties of the Operations on
Integers.
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Properties of the Operations on Integers
Closure
Commutative
Associative
Distributive
Identity
Inverse
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14 + 30 = 44
14 + (-5) = 9
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Closure Property
If a and b are two integers: (a + b), (a - b), and (a x b) is also an integer.
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Commutative Property
This property states that changing the order of the addends does not affect
the sum.
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6 + 4 = 4 + 6
(-6) + 4 = 4 + (-6)
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________ + ________ = ________ + ________ a b b a
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Associative Property
This property states that changing the grouping of numbers being added does
not change its value.
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(6 + 2) + 1 = 6 + (2 + 1)
[6 + (-2)] + 3 = 6 + [(-2) + 3]
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( _____ + _____ ) + _____ = _____ + ( _____ + _____ ) a b c a b c
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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.
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-2 (4 + 3) = (-2 x 4) + (-2 x 3)
2 (4 - 3) = (2)(4) - (2)(3)
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_____ ( _____ + _____ ) = ( _____ x _____ ) + ( _____ x _____ ) a b c a b a c
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Identity Property for Addition
Identity Property for Addition states that the sum of any number and zero is
the number itself.
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5 + 0 = 5
0 + (-4) = -4
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________ + ________ = ________ a 0 a
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Identity Property for Multiplication
Identity Property for Multiplication states that the product of any number
and one is the number itself.
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8 x 1 = 8
1 x (-9) = -9
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14
-14
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Inverse Property for Addition
Inverse Property for Addition states that the sum of any number and its
additive inverse is zero.
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10 + (-10) = 0
-6 + 6 = 0
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Inverse Property for Multiplication
Inverse Property for Multiplication states that the product of any number
and its multiplicative inverse or reciprocal is 1.
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4 x 1/4 = 1
-8 x (-1/8) = 1
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GROUPACTIVITY
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THINK OF
THIS!