Adding Two-Digit Numbers
Adding double-digit numbers is just like adding single-digit values, you just go through the process of addition more than once. When you add two-digit numbers you add the columns together, not the entire numbers. For example, you wouldn't want to try and add 78 and 57 as complete numbers in your head. It's easier to break those numbers down into bite-sized pieces. You would start by adding the numbers in the ones column and then move to add the numbers in the tens column. That example was a little tough because it includes some carrying. Let's look at some simple examples...24 + 45 = 69
37 + 11 = 48
82 + 6 = 88
Here's another way to see the problem. It will be easier for you to solve these in a vertical (up and down) format when you start out with addition. It's much easier to see the way the numbers line up in the columns. In this example, the ones column adds up to nine (9) and the tens column adds up to six (6).
24 + 45 69 |
Remember to always work to the left. You will write down your addends with the ones columns lined up and then start adding. If you wind up with one column that doesn't have a value for the tens, that's okay. Just think of it as a zero. Any number added to zero is itself.
82 + 6 88 |
To Carry or Not to Carry
The next challenge in adding two-digit numbers will have you adding numbers that involve carrying or regrouping. We already spoke a bit about carrying in an earlier tutorial. If the sum from ones column is greater than nine (9), you carry the "1" to the next column on the left.What if you have the problem 78 + 57? You would start with the ones column (8 + 7 = 15). Write down the "5" in your answer and move the "1" to the tens column. Your next step is to add all of the values from the tens column (1 + 7 + 5). That sum is "13", which you would write down in your answer. Your final sum would be "135."
Example:
78 + 57 ? 1 78 + 57 5 78 + 57 135 |
More examples:
48 + 32 = 80
(8+2=10, write the 0 and carry the 1, 1+4+3=8)
29 + 29 = 58
(9+9=18, write the 8 and carry the 1, 1+2+2=5)
95 + 16 = 111
(5+6=11, write the 1 and carry the 1, 1+9+1=11)
75 + 87 = 162
(5+7=12, write the 2 and carry the 1, 1+7+8=16)
Useful Reference Materials
Wikipedia:https://en.wikipedia.org/wiki/Arithmetic
Encyclopædia Britannica:
http://www.britannica.com/topic/arithmetic
Encyclopedia.com:
http://www.encyclopedia.com/topic/arithmetic.aspx