Properties
Identify the property shown below:
(x + 2) + 5 = (2 + x) + 5
commutative: order doesn't matter
5(6 - 2) + 32
29
2x + 3y when x = 4 and y = -2
2
Is the set of fractions closed under multiplication? If not, provide a counterexample.
No, because (2/3)(3/2) = 1 which is not a fraction.
7
R, Q, Z, W, N
Identify the property shown below:
3(1/3) = 1
Inverse of multiplication: using the opposite to cancel
2[3(4 + 2) - 5]
26
(x - y)2 + z when z = 3, y = 7, z = -5
11
Is the set of rational numbers closed under division? If not, provide a counterexample.
Yes
-1.5555555555...
R, Q
Identify the property shown below:
If a=b, and b=c, then a=c
Transitive
|5 - 12| + 24
23
2(|x - y| + z2) when x = -3, y = 5, z = -2
24
Is the set of natural numbers closed under multiplication? If not, provide a counterexample.
Yes
sqrt 10
R, I
Identify the property shown below:
2=x, x=2
symmetric
3{23 + [4(6 - 9) + 52]}
63
[(x - y)2 / z] + |y| when x = 8, y = -6, z = 2
104
Is the set of perfect squares closed under subtraction? If not, provide a counterexample.
No, because 16 - 9 = 8 which is not a perfect square.
sqrt 15 - sqrt 15
R, Q, Z, W
Provide a numerical example of the transitive property.
If 3-4 = -1, and (-1)3 = -1, then 3-4 = (-1)3
2{[32 - (8 - 12)] + |-4|}
34
9
Is the set of irrational numbers closed under multiplication? If not, provide a counterexample.
No, because (sqrt 2)(sqrt 2) = 2 which is not irrational.
-14/2
R, Q, Z