About Sum of Even Numbers
What is an Even Number?
Any number ending with 0, 2, 4, 6 or 8 is an even number. As even numbers are divisible by 2, they can always be grouped into pairs. For instance, say you have 6 bottles of water, how many pairs will you have?
You can make a total of three pairs. Items in even numbers always form pairs.
Any number not ending in 0, 2, 4, 6 or 8 are termed as odd numbers. When odd numbers are divided by 2, we get a remainder of 1. But when even numbers are divided by 2 we get the remainder as 0. Hence, to check if a number is even or odd, simply divide the number by 2 and check the remainder. If the remainder is 1 the number is odd, if the remainder is 0 the number is even.
Sum of two Even Numbers
When two even numbers are added, the sum is always an even number.
Even + Even = Even
For example, 6 + 8 = 14
Example: There are two baskets and each has an even number of apples. Is the total number of apples even or odd?
Solution:
We know that the sum of two even numbers is always an even number.
Even + Even = Even
Since both buckets have an even number of apples, the total number of apples will also be even.
Solved Examples
Example 1: You have 6 glow sticks and you bought 4 new ones like them. How many glow sticks do you have ?
Solution:
6 + 4 = 10
Hence in total there are 10 glow sticks.
Example 2: A box has 12 pieces of chalk and you added 8 pieces to them. How many pieces are there inside it now?
Solution:
12 + 8 = 20
Hence, in total there are 20 pieces of chalk.
Example 3: Tia has 45 beads. She needs at least 50 beads to make a chain she has in mind. Her father tells her that he could give her some, only if she can tell him the smallest even number of beads she may need such that she gets in total more than 50 beads. Can you help Tia, so she can make her chain?
Solution:
Tia needs more than 50 beads, she has 45 now. We need to find the smallest even number to be added to 45, such that we get the sum greater than 50.
Even numbers: 0, 2, 4, 6, 8 …
45 + 0 = 45
45 + 2 = 47
45 + 4 = 49
45 + 6 = 51
Hence the smallest even number that needs to be added to 45 is 6.
Yes, the sum of two odd numbers is always even.
odd + odd = even
Example:
7 + 5 = 12 ,
17 + 3 = 20,
11 + 19 = 30
No, odd numbers cannot be multiples of two. In other words, odd numbers can not be divided into two equal parts.
But,
6 \( \div \) 2 = 3 or 2 \( \times \) 3=6
It is clear that 6 is divisible by 2 and also 6 is a multiple of 2. So, 6 is not an odd number.
No, the product of an odd number and an even number is not an odd number. That is because even numbers are multiples of 2 and this means that the product of even and odd numbers are also multiples of 2.
For example
1. 5 \( \times \) 4 = 20
(5 \( \times \) 2) \( \times \) 2 = 20
10 \( \times \) 2 = 20
2. 7 \( \times \) 8 = 56
(7 \( \times \) 4) \( \times \) 2 = 56
28 \( \times \) 2 = 56
No, Because:
- 12 has 2 as the ones digit
- 12 \( \div \) 2 = 6R0, 12 is completely divisible by 2 leaving zero as remainder.