Closure Property
According to the closure property of addition, for all real numbers a and b:
a + b is a _______
real number
According to the Commutative property of multiplication:
a x b = b x _____
a
According to the associative property of multiplication:
(a + b) + c = a + ______
be specific - name all the parts
(b + c)
Name the multiplicative identity number
1
According to the Inverse Property, two real numbers are called additive inverses if their sum is equal to ________
The additive identity, 0
The fact that multiplying any two real numbers will always produce another real number is an example of this property.
The closure property of multiplication
This property explains why 7+3=3+7
The commutative property of addition
100(50) = 50(____)
100
Name the additive identity number
0
According to the Inverse Property, two real numbers are called multiplicative inverses if their product is equal to _________
The set of positive real numbers is not closed under this operation, since 5−8=−3
subtraction
This operation is not commutative because 8−5 ≠ 5−8
subtraction
The fact that 3×(2×5)=(2×5)×3 is not the commutative property—it’s this property instead.
The associative property
____ + 0 = 27
27
5 x _____ = 1
1/5
The closure property fails here: dividing 5 by 2 does not give an integer, showing integers are not closed under this operation.
division
This operation is not commutative because 23 does not equal 32.
exponents or exponentiation
This operation is not associative because (8−5)−2 ≠ 8−(5−2)
subtraction
(-1/4) x 1 =
-1/4
5/7 + ______ = 0
-5/7
Because the square root of −1 is not a real number, the set of real numbers is not closed under this operation.
square roots
Maria has 5 boxes with 8 pencils each. Jamal has 8 boxes with 5 pencils each. They still have the same total pencils because of this property.
The commutative property of multiplication
This property allows us to regroup numbers when adding without changing the result.
associative property of addition
A store sells pencils in packs of 12. Buying 1 pack gives exactly _____ pencils.
12
Every number has an additive inverse, but this number has no multiplicative inverse.
0