Question

Why is the sum of two odd numbers even?

a. Think of the problem 11 + 15. Draw dots to represent each number.
b. Circle pairs of dots to determine if any of the dots are left over.
c. Is this true every time two odd numbers are added together? Why or why not?

Answer 1

a) and b) in photo.

there is no point left outside the circles, then 11+15 is even.

c) yes it is, because if both numbers are odd, they will have one point outside the circles each, and those two points will form an other pair.

odd number: 2n+1

even number: 2m

(m and n represent any natural number)

2n+1 + 2k+1= the sum of two odd numbers

=2(n+k) +2

=2(n+k) +2 =2(n+k+1)

the sum of 3 natural numbers will be a natural number too. let be m=n+k+1 with m n and k natural numbers.

=2m even number