Addition:

Addition is a mathematical process, where by adding two or more numbers together, we calculate their total. What does this mean, why do we need to know and how do we calculate the total?

Well, before the addition takes place, there are two, separate, individual numbers, which represent something. As an example, we can point to Jennifer, who has two dolls and her sister Jessie, who has three dolls. They decide that for Halloween, they will dress up their dolls in scary witch costumes and they will ask their Mom to sew these with time to spare. How many costumers should they ask their Mom for?

Their Mom will have to sew five costumes, so that all the dolls can get dressed for Halloween. That is the meaning of a total and now we can see that there is a good reason to know what the total may be.

To give you another example, which may seem even more relevant. You have a bank account, where you save money that is left over from your allowance, that you receive as gifts from your grandparents and that you get for getting a good mark. In September, you have managed to make two deposits of $5.00 during the second week and $5.00 again during the last week of September. Would you not be interested in how much money you have in your bank account at the end of the month?

And your two deposits total $10.00.

Why? How can we explain why 2 + 3 = 5 and why 5 + 5 = 10?

One way of showing you is to have you take a bunch of marbles. Count off two marbles and put them aside. Then count off three marbles and place them together with the two you have already put aside. Now count this small pile of marbles: you will count to 5. This will prove to you that 2 + 3 = 5

Similarly, if you count 5 marbles and put them aside and then count another 5 marbles and place them together with the first five and then count the whole small pile, you will count to 10, proving that

A better way is to look at a graph. On the horizontal axis, which is marked 0, 1, 2 and so on to 12, you will see the value of 2 marked in red.

On the graph below, you will see the value of 3 marked in blue.

The total of 2 + 3 is shown on graph below, where we have started with the first graph, with the value of 2 marked in red, then taken the value of 3 in blue from our second graph and placed it next to the value of 2. You will see that the combined value of the two numbers, the red and blue segments together end at 5 and that is our total

Now repeat the same exercise, by preparing a graph showing the addition of 5 + 5.

While addition is usually expressed as:

When we do the calculation, we write it down as:

We will se the reason for this in the next section, when we discuss addition of numbers that have two or more digits. Let us briefly outline the procedure for adding of two numbers and how we use carryovers:

We always start with the bottom number, with the singles digit. In the following example that is 2. We will add the number in the singles digit of the number above and that is 9. Since 2 + 9 equals 11, we will write down:

only the singles digit of our answer and we have to remember our carryover of 1. This carryover of 1 must be added to the tens digit, which is also 1, so that 1 + 1 = 2 and our answer will be:

Addition of double digit numbers:

Once you understand the use of the carryover, it makes no difference whether you are adding a single and a double digit number or whether you are adding two (or more) three or even four digit numbers, as the procedure and mechanism is identical.

Le us take a look at the following example:

We start with the singles digits and add 6 + 5 to get 11. We will write 1 under our 6 and remember the carryover of 1:

Now, we will add the tens digit and we must remember to add the carryover of 1: 6 + 7 = 13 + carryover of 1 = 14. We will write down 4 in the tens digit and again, we have a carryover of 1:

Now we will add the hundreds digits and remember to add the carryover of 1: 8 + 3 = 11 plus the carryover of 1 = 12. We will write down 2 and remember the carryover of 1:

Now we add the thousands digits with our carryover: 0 + 1 = 1 plus the carryover of 1 = 2:

No matter how many digit numbers you are adding and how many there may be, the procedure will always be identical. Now try the following examples:

Examples:

Answers: