6th Grade Math Textbook, Fundamentals

Practice & Activities

Lesson 1-8 for exercise sets. Chapter 1 17

True or false? Give examples to justify your answer.

1.The set of numbers 1, 0, and 1 is closed under multiplication.

2.The set of the multiples of 10 is closed under division.

3.Discuss and Write If 7  2 5 and 13  11 2, are all the sums of

two prime numbers between 0 and 25 prime?

(Hint:A prime number is a whole number greater than 1 having

exactly two factors, itself and 1.)

Explore the set of integers for closure under addition, subtraction,

multiplication, and division.

Is the set of integers closed

under addition?

Set:integers

Operation:addition

Check: 15  15  0

0 is an integer.

Result:The set of integers could beclosed

under addition.

(^1) Is the set of integers closed under
subtraction?
Set:integers
Operation:subtraction
Check: 13 (4)  9
9 is an integer.
Result:The set of integers could beclosed
under subtraction.
2
Is the set of integers closed under division?
Set:integers
Operation:division
Check: 0.5
0.5 is not an integer.
Result:The set of integers is notclosed
under division.
 1
2
 2
4
3 Is the set of integers closed under
multiplication?
Set:integers
Operation:multiplication
Check:5 • 10  50
50 is an integer.
Result:The set of integers could beclosed
under multiplication.
4
Mathematicians agree that the set of integers is closed under addition,
subtraction, and multiplication, but the set of integers is not closed under division.