Hi Liz and Samantha,
If I have a bag of lollipops and I want to divide them all between the two of you than I can organize the lollipops in two rows, one for Liz and the other for Samantha. If I can do it so that you each gets the same number of lollipops then the number I had in the bag must have been even. If I can't organize them into a 2-row array with the same number in each row then the number of lollipops must have been odd.
Liz and Samantha wrote back.
I am in 5th grade & was not sure about this...
If you call the numbers that cannot be arranged into 2-row arrays, Odd Numbers, would you call the numbers that can be arranged into 2-row
arrays, Even Numbers?
Would I have been wrong if I called them "Products"?
This was the third question in our homework. The one before it was a group of numbers, we had to take out the ones that could be put into 2-row arrays.
The question before that was multiplication questions that you had to put the answers into the 2-row arrays They were all the even numbers...
Therefore, Samantha said that they were "Products", when the teacher may not have been connecting all of the questions & just was looking for "Even Numbers"...
What do you think...
Thanks so much.
Liz & Samantha
You are correct when you say "the numbers that can be arranged into 2-row
arrays are even numbers". To call them products however is erroneous. the number 15 is a product, 15 = 3 5 but 15 is odd not even. In fact
- the product of two even number is even
- the product of an even number and an odd number is even
- the product of an odd number and an even number is even, but
- the product of two odd numbers is odd.
What you can say is that a number is even if it can be written of the product of two numbers, one of which is 2. Thus, for example
- 6 is even since 6 = 2 3
- 4 is even since 4 = 2 2
- 2 is even since 2 = 2 1
but 9 is not even since you can't write 9 as 2 times another integer.