Question

50 POINTS!! Use these four expressions to make a hypothesis about the closure property of integers under each operation. Select yes or no for each operation.

Answer 1

1. Yes

2. Yes

3. Yes

4. No

Explanation:

The expression -8 + 5 shows the sum of two integers. This expression has a value of -3. Because -3 is also an integer, the set of integers appears to be closed under addition.

The expression 9 − (-11) shows the difference of two integers. This expression has a value of 20. Because 20 is also an integer, the set of integers appears to be closed under subtraction.

The expression 3 · (-4) shows the product of two integers. This expression has a value of -12. Because -12 is an integer, the set of integers appears to be closed under multiplication.

The expression, -1 ÷ 6, shows the quotient of two integers. This expression has a value -1/6, Because -1/6 is not an integer, the set of integers is not closed under division.

Answer 2

+ closed

- closed

* closed

÷ not closed

Explanation:

When you add integers, you will always get an integer so it is closed under addition

When you subtract integers, you will always get an integer so it is closed under subtraction

When you multiply integers, you will always get an integer so it is closed under multiplication

When you divide integers, you will not always get an integer so it is not closed under division

1/5 = .2 which is not an integer