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An odd number is defined as a number that leaves a remainder of 1 when divided by 2.
So, if a is an odd number then there exists an integer x such that a = 2x+1 where x belongs to N, the set of integers.
Also, an even number is defined as a number that leaves a remainder of 0 when divided by 2.
So, if b is an even number then there exists an integer y such that b = 2y where y is in N.
Then an odd number + an even number = a + b = 2x+1+2y
=2x+2y+1 (by commutativity)
=2(x+y)+1 (by distributivity, in reverse)
Now x is in N and y is in N means that x+y is in N, say z (closure of N under addition)
Thus a+b = 2z+1 which, by the definition of odd numbers, is odd.
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All multiples of odd natural number can be written as the sum of consecutive natural numbers?
No. Odd numbers can be written as the sum of consecutive integers, but some multiples of odd numbers are even.
There are nine pong balls numbered 1-9 in a bag If three balls are randomly selected without replacement what is the probability expressed as a common fraction that the sum of the number be odd?
10/21 First, observe that for the sum of the three balls to be odd, either one is odd and two are even, or all three are odd. Since the sum of two odd numbers is even, the sum of two even number is even, and the sum of an even number and an odd number is odd. P(exactly one is odd)=(5/9)*(4/8)*(3/7)*3=180/504=5/14 P(all three are odd)=(5/9)*(4/8)*(3/7)=60/504=5/42 P(sum is odd)=5/14+5/42=15/42+5/42=20/42=10/21, which is approximately .48
What 4 numbers are multiples of 5 all numbers are odd their sum is 80 what are the numbers?
Oh, what a lovely puzzle to solve! Let's paint a happy little picture here. If we have four odd numbers that are multiples of 5 and their sum is 80, we can see that the numbers are 5, 15, 25, and 35. Each number is odd, a multiple of 5, and when you add them together, you get a beautiful total of 80. Happy painting!
Sum of two consecutive odd numbers divisible by 4?
Yes, that is true.
What is the sum of even factors of a number?
2, 4, 6, 10, 12, 20, 30, 60 add up to 144.
What five odd numbers add up to 100?
No 5 odd numbers add up to 100. The sum of any two odd numbers is even. The sum of any two even numbers is even. So the sum of any 4 odd numbers must be even. Take that and add an odd number and the sum must be odd. Therefore, the sum of any 5 odd numbers must be odd. 100 is even. In conclusion: The sum of any odd number of odd numbers is odd.
If you add two odd numbers will the sum be odd or even?
even
Can 5 odd numbers that if you add them make 32?
37
Can you add an even and an odd number where the sum of the numbers will be even?
No. No matter what you use, the sum of an odd number and an even number will always be odd.
What happens when you add two odd numbers?
The sum turns out even.
What happens when you add an odd number and an odd number?
Two odd numbers always sum to an even number. Always. Two even numbers always sum to an even number, and an odd number and an even number always sum to an odd number.
When you add 4 even numbers will the sum be even or odd and why?
The answer will be even because if the numbers are even, the answer will be even.
When you add an odd number and odd number what kind of number is sum?
The sum of two odd numbers is an even number.
What 5 odd numbers add up to 30?
35
Is sum of odd numbers always even?
The sum of two odd numbers is always even; the sum of three odd numbers is always odd; the sum of four odd numbers is always even; the sum of five odd numbers is always odd; etc
Is the sum of two odd numbers is always odd?
The sum of two odd numbers is always even.
Can the sum of an even and odd number be even?
no, it can't be. that's because only an even and even numbers or odd and odd numbers add up to be even. so no it cannot be even.
