Lesson 1

Whole Number Addition

Here you'll learn how to add whole numbers.

Vocabulary

Here are the vocabulary words found in this Concept.

Addend The numbers being added

Sum The answer to an addition problem

Place value Writing each number in order according to the decimal place value it has.

Carry digit A value carried from one column to another to maintain place values

Horizontally Across or left to right

Vertically Up and down

INFORMATION

A general concept overvew statement or word problem exercise can be placed in the concept introduction section.

Depending on the monitor size and orientation this page should be adjusted for optimal reading using Alt-U to select columns or scrolling and to adjust the text size.

Guidance

You are already used to adding whole numbers and have been using addition for some time. We are now going to move your addition skills further forward with this learning module on long-addition.

We are assuming you are comfortable with a familiar problem like this:

In this problem, we are adding four and five. There are four whole things plus five whole things and this gives an answer of nine things.

The numbers that we are adding together are called addends. The answer to an addition problem is the sum.

This first problem was written horizontally or left to right across the page.

In this lesson you will be learning how to write your problems vertically on your own.

How do we do this?

We can add whole numbers by writing them vertically according to place value.

Place value is when you write the numbers in order according to the decimal value that it has. These can be Units, Tens, Hundreds, Thousands and more.

This place value table shows the abbreviations we use in this lesson. Note that "Units" is also called "Ones" in some countries.

Ten Thousands	Thousands	Hundreds	Tens	Units
TTh	Th	H	T	U
5	4	3	2	1

This number is 54,321. In words this is said, fifty-four thousand, three hundred and twenty-one.

It can also be shown as an arithmetic sum which highlights how the place values work together.

50,000

4,000

300

Adding whole numbers

When you add whole numbers, it is easier to understand the problem and solve it by writing them vertically according to place value. We started with this very simple example.

To write this vertically it is important to line up the digits vertically. Because they are both in the units place value they are placed directly in-line vertically.

	U
	4
+	5
	9

Guided Tutorial 1

Now that was too simple. Just mental arithmetic. But what happens when there are more digits in an addition problem?

When we have more digits we line up the place values vertically. Here we have 456 which is 4 Hundreds, 5 tens and 6 units being added to 27 which is 2 tens and 7 units.

Remember we have to vertically align all place values. So here they are:

	H	T	U
	4	5	6
+		2	7

Remember H is Hundreds, T is Tens and U is Units place values.

Now use this Guided Tutorial to see how to line up the place values, and how keeping the place values lined up makes long-addition easy. Don't just look at the tutorial. Practice writing your own sums on paper.

Step 1. Place values aligned

	H	T	U
	4	5	6
+		2	7

We are going to add 456 and 27.

The biggest place value in 456 is 4. That is a Hundreds place value.

The biggest place value in 27 is 2. A Tens place-holder.

It is best to put the biggest number at the top. Then it is easy to line the shorter numbers under that.

See how the Units (U), Tens (T) and Hundreds (H) are all each lined up vertically in their correct column.

Step 2. Ready to Start


	4	5	6
+		2	7

We are going to add 456 and 27 together.

Remember our vocabulary terms. The big number 456 is an addend and the smaller number 27 is also an addend.

When we have added them together the result is the sum.

Notice we have a carry-forward area at the top of the vertical problem. We will be learning how to use this.

Step 3. Add the Units

		1
	4	5	6
+		2	7
			3

First we add the Units column. That is:

6 + 7 = 13

The number 13 has 1 Tens and 3 Units.

The unit value 3 is placed in the Units answer line and the 1 is carried forward to the tens column.

That means you write the carry-forward value above the Tens column as shown here.

Step 4. Add the Tens

		1
	4	5	6
+		2	7
		8	3

Now we add the Tens column.

The 1 that was carried forward in the Tens column must also be added into the total. So the Tens sum is:

1 + 5 + 2 = 8

There is only the single digit so it is written into the Tens place value in the answer row.

There is no carry forward value.

Step 5. Add the Hundreds

		1
	4	5	6
+		2	7
	4	8	3

The last step is to add the Hundreds place value column.

There is only one value 4 in this column.

The 4 can be put directly into the answer line in the Hundreds place value position.

Step 6. Finished

		1
	4	5	6
+		2	7
	4	8	3

Here is our final answer.

The sum of 27 added to 456 is 483

As you get better at long-addition, try keeping the carry forward value for each column in your memory rather than writing it down.

◄ Slide for more ►

EXERCISE: TRY IT YOURSELF

Exercise 1-1. Simple Long-Addition ►

Download the Exercise as a printable PDF ►

Guided Tutorial 2

So far in this lesson we have learnt how to add numbers with up to three digits. We can add numbers having five digits or more the same way. So let's see what happens when we add this huge looking sum:

It may look hard, but once you get the place values aligned and work steadily through the problem it is easy to learn and do.

Step 1. Arrange Place Values

HTh	TTh	Th	H	T	U
8	8	9	4	5	6
+	7	5	9	2	7

We are going to add 889,456 and 75,927 together.

First set the sum up vertically being careful to line up the place values.

This time we have Hundred-Thousands (HTh), Ten-Thousands (TTh), Thousands (T), Hundreds (H), Tens (T) and Units (U) place values.

All numbers are carefully placed into their correct place value column.

Step 2. Add the Units

				1
8	8	9	4	5	6
+	7	5	9	2	7
					3

First we add the Units column. 7 is added to 6.

7 + 6 = 13

The number 13 has 1 Tens and 3 Units.

The Units value 3 is placed in the answer line in the Units column.

The 1 is carried forward to the Tens column.

When doing this by writing make sure you keep the place values lined-up.

Step 3. Add the Tens

				1
8	8	9	4	5	6
+	7	5	9	2	7
				8	3

Now we add the Tens column. That is:

1 + 5 + 2 = 8

The total for the Tens column is 8. We put it in the answer line.

This time there is no carry forward number.

Step 4. Add the Hundreds

		1		1
8	8	9	4	5	6
+	7	5	9	2	7
			3	8	3

We now move across to add the Hundreds column. Here the sum is:

4 + 9 = 13

The total is 13.

This is the total for the Hundreds column so we put 3 into the answer line.

The 1 is carried forward to the Thousands column

Step 5. Add the Thousands

	1	1		1
8	8	9	4	5	6
+	7	5	9	2	7
		5	3	8	3

We are now up to adding the Thousands column. The sum is:

1 + 9 + 5 = 15

Remember to include the carry forward number from the Hundreds column.

We place the five into the answer line.

The 1 is carried forward into the Ten-thousands column.

Step 6. Add the Ten-thousands

1	1	1		1
8	8	9	4	5	6
+	7	5	9	2	7
	6	5	3	8	3

We are now adding the Ten-thousands column. The sum is:

1 + 8 + 7 =16

We repeat the steps as before. The six is placed in the answer-line in the Ten-thousands column.

The 1 is carried-forward to the Hundred-thousands column.

Step 7. Add the Hundred-thousands

1	1	1		1
8	8	9	4	5	6
+	7	5	9	2	7
9	6	5	3	8	3

We are now up to the last column, the Hundred-thousands. Here the sum is easy:

1 + 8 = 9

We put the 9 in the answer-line in the Hundred-thousands column.

There is nothing to carry forward so the problem is finished.

Step 8. The Answer

1	1	1		1
8	8	9	4	5	6
+	7	5	9	2	7
9	6	5	3	8	3

The final answer is:

889,456 + 75,927 = 965,383.

In words that is Nine-hundred and sixty-five thousand, three-hundred and eighty-three.

You can see adding big numbers is the same as smaller numbers and you just move carefully across the place value columns.

◄ Slide for more ►

EXERCISE: TRY IT YOURSELF

Exercise 1-2. Very Long-Addition ►

Download the Exercise as a printable PDF ►

Guided Tutorial 3

An addition problem can have more than two addends. We just have to take more care as we arrange the digits into vertical columns. So we are going to take this very large looking problem and arrange it into vertical columns.

The horizontal problem becomes this vertical layout. It looks more organized already.

	Th	H	T	U
	8	7	6	8
	3	2	4	3
		4	7	9
+	6	6	1	5

Now go though the guided practice to see how this is added together:

Step 1. Place values

TTh	Th	H	T	U
	8	7	6	8
	3	2	4	3
		4	7	9
+	6	6	1	5
1	9	1	0	5

The first step is to arrange the numbers vertically with the place value columns correctly aligned.

In this sum we have Thousands (Th), Hundreds (H), Tens (T), and Units (U) place value columns.

The vertical alignment is very important when your sum has multiple addends.

Step 2. Add the Units Column

			2
	8	7	6	8
	3	2	4	3
		4	7	9
+	6	6	1	5
				5

First we add the Units column.

That is 8+3+9+5 = 25

25 = 20 + 5

The 5 is placed in the Units column and the 2 (representing 20) is carried forward into the Tens column.

Step 3. Add the Tens Column

		2	2
	8	7	6	8
	3	2	4	3
		4	7	9
+	6	6	1	5
			0	5

Next we add the Tens column. We have to remember to include the 2 that was carried forward.

2 + 6 + 4 +7 + 1 = 20

The 0 is placed into the answer-line in the Tens position and the 2 is carried forward into the Hundreds column.

[ Remember we are actually adding Tens shortened for convenience. We actually added:

20 + 60 + 70 + 10 = 200 ]

Step 4. Add the Hundreds Column

	2	2	2
	8	7	6	8
	3	2	4	3
		4	7	9
+	6	6	1	5
		1	0	5

Now it is time to add the Hundreds column. The sum is:

2 + 7 + 2 + 4 + 6 = 21

The one is placed in the answer line in the Hundreds position and the 2 is carried forward to the Thousands Column.

[ Remember we are actually adding 100s shortened for convenience. We actually added:

200 + 700 + 200 + 400 + 600 = 2100 ]

Step 5. Add the Thousands Column

1	2	2	2
	8	7	6	8
	3	2	4	3
		4	7	9
+	6	6	1	5
1	9	1	0	5

The last step is to add the digits in the Thousands column. The sum is:

2 + 8 + 3+ 6 = 19

Put the 9 in the answer line Thousands column.

The 1 is carried forward to the Ten-thousands column.

Because there is no other numbers in the Ten-thousands column you can just write the 1 into the answer-line.

Step 6. The Answer

1	2	2	2
	8	7	6	8
	3	2	4	3
		4	7	9
+	6	6	1	5
1	9	1	0	5

Here is the final answer. 19,105.

In words that is Nineteen Thousand, One Hundred and Five.

◄ Slide for more ►

EXERCISE: TRY IT YOURSELF

Exercise 1-3.Vertical Long-Addition

Download the Exercise as a printable PDF ►

Video Review

These videos may help you with learning how to add whole numbers.

WATCH THE VIDEO

Adding Whole Numbers. (1:13min).

Interactive Practice and Test

Interactive Practice

Practice your addition here.

Interactive Practice will keep on generating long-addition problems for you to solve for as long as you want to keep on practicing.

Interactive Test

Test your addition here.

You will be presented with 10 sums. Solve each one as fast as you can.

Your final score will be saved.

Take the time to complete all the Exercises and use the Practice and Test Interactive tools to make sure addition becomes your friend. Learn to enjoy the numbers. They are fun and these exercises let you do it all at your own speed anytime you want.