1.1.5 Even/Odd Numbers
Even and Odd Numbers
Even (E): Any integer which is divisible by 2. The list of even integers is: {…-8, -6, -4, -2, 2, 4, 6, 8, …}.
Odd (O): All the other integers that are not divisible by 2. The list of odd integers is: {..-7, -5, -3, -1, 1, 3, 5, 7, …}.
Properties of Even and Odd Numbers
① E + E = E (f.e. : 2 + 2 = 4)
② O + O = E (f.e. : 1 + 1 = 2)
③ E + O = O + E = O (f.e. : 2 + 1 = 1 + 2 = 3)
④ O x O = O (f.e. : 3 x 3 = 9)
⑤ E x E = E (f.e. : 2 x 2 = 4)
⑥ E x O = O x E = E (f.e. : 2 x 3 = 3 x 2 = 6)
Don't memorize, generalize!
If you need to find out the result of an operation between generic even and odd numbers, you don’t need to memorize these properties.
Instead, simply take two random numbers that represent your even and odd integers (like 1 and 2) and perform the operations on them.
For example: Deducing property 3 (the sum of an even and odd number is odd). Using 2 (even) and 1 (odd) you can quickly see that: 1+2 = 3 (odd). Generalize from here!
Instead, simply take two random numbers that represent your even and odd integers (like 1 and 2) and perform the operations on them.
For example: Deducing property 3 (the sum of an even and odd number is odd). Using 2 (even) and 1 (odd) you can quickly see that: 1+2 = 3 (odd). Generalize from here!
Exercises: Even/Odd Numbers
1) What type of integer do you have when you add an odd integer to the multiplication of two even numbers?
Pick numbers that will serve as your even and odd integers, for example, odd = 1, even = 2.
First, we multiply the even numbers together: 2 x 2 = 4 (even).
Second, we add the even number: 4 + 1 = 5 (odd).
We obtain an odd integer and we can generalize this result.