Lesson 3.3.1 R&P 3-81 to 3-86

3-82) a. Is the set of even numbers closed under addition? That is, if you add two even numbers, do you always get an even number? Explain your answers.

• No if you add two even numbers, you will get 0.

• No, if you add two even numbers, you get an odd number.

• Even numbers are closed under addition. If you add even numbers like 2 and 4, you will always get an even number because both numbers are divisible by 2, they will always be even.

• Even numbers are closed under addition because I can add an even number by 0 and it still is an even number.

3-82) b. Is the set of odd numbers closed under addition? Explain your answers.

• No if you add two odd numbers, you won't always get an odd number. For instance, 7+1=8, which isn't odd.

• No, if you add two odd numbers, you get an odd number.

• Odd numbers are closed by addition. When you add any two odd numbers, it will always be an odd number.

• Odd numbers are closed under addition because I can add an odd number by 0 and it still is an odd number.

3-83) Find the dimensions of the generic rectangle at right. Then write an equivalency statement (length⋅width=area) of the area as a product and as a sum.