Even plus even stays even
Pairs put together are still pairs.
Adding even numbers
Even numbers can be arranged in pairs with nothing left over. Think of adding 4 + 6 + 8 + 2 (all even).
What kind of number will the total be?
What this lesson covers
The idea
Adding any number of even numbers gives an even number, since the sum can still be arranged in pairs without any leftovers.
Adding even numbers
Even numbers can be arranged in pairs with nothing left over. Think of adding 4 + 6 + 8 + 2 (all even).
What kind of number will the total be?
- Always even
- Always odd
- Sometimes even, sometimes odd
Try many sums
Each even number is a row of pairs. Tap numbers to add them. Look at the total: does a leftover dot ever appear? Save sums with 2, 3, 4 and 5 numbers.
Pairs plus pairs are pairs
Every number we add is already in pairs. Putting rows of pairs together gives more pairs, and no dot is ever left over. It does not matter how many numbers are added.
Adding any number of even numbers gives an even number, since the sum can still be arranged in pairs without any leftovers.
- Even numbers added | Total
- 4 + 6 | 10 = 5 pairs
- 2 + 8 + 6 | 16 = 8 pairs
- 12 + 10 + 4 + 2 | 28 = 14 pairs
- 2 + 4 + 6 + 8 + 10 | 30 = 15 pairs
Notes
Adding any number of even numbers gives an even number, since the sum can still be arranged in pairs without any leftovers.
Check yourself
Reena adds forty even numbers together. What can we say about her total?
Some even numbers add up to 72. The total is arranged in pairs. How many pairs are there?
Answer: 36
72 dots in pairs: 72 ÷ 2 = 36 pairs, with nothing left over.
Four even numbers are added. Which total is impossible?
Five even numbers add up to 60. Four of them are 10, 12, 14 and 16. What is the fifth number?
Answer: 8
10 + 12 + 14 + 16 = 52. The fifth number is 60 − 52 = 8, and it is even, as it must be.
- It could be odd, because forty is a lot of numbers. The count of numbers does not matter for even numbers: pairs plus pairs are always pairs.
- It is even, however many numbers she adds — correct. Yes! Every number is in pairs, so the total is in pairs, however many numbers there are.
- It is even only if the number of numbers added is even. That idea belongs to odd numbers. Even numbers never leave a single dot, so the count does not matter.
- 30. It is possible: 10 + 8 + 6 + 6 = 30.
- 41 — correct. Yes! 41 is odd: it always has one dot left over, but a sum of even numbers has none.
- 64. It is possible: 20 + 20 + 14 + 10 = 64.
- 100. It is possible: 50 + 30 + 10 + 10 = 100.