Understanding Closure Under Addition

What does the closure property for addition of whole numbers state?

• The sum of two whole numbers is always a whole number.

• The sum of two whole numbers is always an integer.

• The sum of two whole numbers is always a fraction.

• The sum of two whole numbers is always a decimal.

Is the set containing only the number zero closed under addition?

• No, because zero added to any number is zero.

• Yes, because zero added to any number is not zero.

• No, because zero added to zero is not zero.

• Yes, because zero added to zero is zero.

What happens when you add two even whole numbers?

• The result is always a fraction.

• The result is always zero.

• The result is always even.

• The result is always odd.

What is the result of adding two odd whole numbers?

• The result is always even.

• The result is always a fraction.

• The result is always odd.

• The result is always zero.

Is the set {1, 2, 3} closed under addition?

• No, because the set contains only even numbers.

• Yes, because the set contains all whole numbers.

• No, because some sums are not within the set.

• Yes, because all sums are within the set.

What is the result of adding 5 with itself in the set of whole numbers less than 6?

• The result is 6, which is not in the set.

• The result is 0, which is in the set.

• The result is 10, which is not in the set.

• The result is 5, which is in the set.

Is the set of whole numbers greater than 6 closed under addition?

• No, because the set contains only odd numbers.

• Yes, because the set contains all even numbers.

• No, because some sums are not within the set.

• Yes, because all sums are within the set.

What is the smallest sum you can get by adding two numbers from the set of whole numbers greater than 6?

• The smallest sum is 6.

• The smallest sum is 7.

• The smallest sum is 13.

• The smallest sum is 14.

What is the result of adding 7 and 8 in the set of whole numbers greater than 6?

• The result is 15, which is in the set.

• The result is 14, which is in the set.

• The result is 16, which is not in the set.

• The result is 13, which is not in the set.

Why is the set of whole numbers greater than 6 closed under addition?

• Because the smallest sum is less than 6.

• Because every sum is greater than 6.

• Because the set contains only odd numbers.

• Because the set contains only even numbers.