Download Day 142 Activity - High School Math Teachers

Day 142 Activity
Name ___________________________
A set of numbers is said to be closed under an operation if any two numbers from the original
set are than combined under the operation and the solution is always in the same set as the
original numbers.
For example, the sum of any two even numbers always results in an even number. So,
the set of even numbers is closed under addition.
56
4
24
8
36
88
106
-18
The Set of All
EVEN NUMBERS
56
4
UNDER
ADDITION
24
8
36
88
106
-18
The Set of All
EVEN NUMBERS
For example, the sum of any two odd numbers always results in an eve number. So, the
set of even numbers is NOT closed under addition.
37
23
7
97
51
67
-17
The Set of All
ODD NUMBERS
Algebra1Teachers @ 2015
56
4
UNDER
ADDITION
24
8
36
88
106
-18
The Set of All
EVEN NUMBERS
Page 1
Day 142 Activity
Name ___________________________
1. Is the set of Integers closed under addition?
Example:
yes
no
2. Is the set of Integers closed under subtraction?
Example:
yes
no
3. Is the set of Integers closed under multiplication?
Example:
yes
no
4. Is the set of Integers closed under division?
Example:
yes
no
5. Is the set of Rational Numbers closed under
addition?
Example:
yes
no
6. Is the set of Irrational Numbers closed under
addition?
Example:
yes
no
7. Is the set of Rational Numbers closed under
multiplication?
Example:
yes
no
8. Is the set of Irrational Numbers closed under
multiplication?
Example:
yes
no
9. Is the set of Even Numbers closed under division?
Example:
yes
no
10. Is the set of Odd Numbers closed under
multiplication?
Algebra1Teachers @ 2015
Example:
yes
no
Page 2
Day 142 Activity
Name ___________________________
Answer Key
1. YES: −3 + 12 = 9
2. YES: 16 − 4 = 12
3. YES: 3 ∗ 2 = 6
4. NO: 5 ÷ 2 = 2.5
1
3
8
2
5. YES: ÷ = 3
6. NO: (√2) + (3 − √2) = 3
3 1
3
1
2 3
6
2
7. YES: ∙ = =
8. NO: √2 − √2 = 2
9. NO: 10 ÷ 2 = 5
10.YES: 5 ∙ 3 = 15
Algebra1Teachers @ 2015
Page 3