### Adding Numbers

When adding numbers you must write down your sum with one number on top of the other with the digits lined up in the correct columns.

It doesn’t matter whether you put the bigger number or smaller number on top when you are adding.

BUT it is very important that each digit is **in the correct column**. The units from one number need to be above the units from the other, the tens above the tens, the hundreds above the hundreds and the thousands above the thousands…

Example

What is 1241 + 592?

1) First I will write my sum with one number above the other and the digits in the correct columns, you can see I have labelled the columns for Units, Tens, Hundreds and Thousands.

2) Now I can begin adding **starting at the Units column**. We always start adding at the column the furthest on the right. The sum for this column is 1 + 2 = 3. So I can fill in 3 in to the answer box below that column:

3) Next I will add the Tens column. It is 4 + 9 which adds up to 13. When the number is 10 or greater we put the unit in to the answer box and carry over the ten to the next column. So in this case, 3 goes in the answer box and 1 gets carried over:

4) Now we can add the Hundreds column which is 2 + 5. But **remember** we also need to add on the 1 that was carried over from the previous column, so the sum is 2 + 5 + 1 = 8:

5) Finally we can add up the Thousands column which is dead easy in this question as there is a 1 on the top row but there are no digits on the bottom row, so the 1 is simply placed in to the answer box:

### Subtracting Numbers

If you are asked to **find the difference** between two numbers you are being asked to **subtract** the smaller one from the bigger one.

Subtracting one number from another means taking it away. This is the opposite of adding.

Look:

10 + 14 = 14

14 – 4 = 10

A good way to check your answer is to do the reverse operation and see if you get back to the number in the question.

When doing a subtraction, just like with addition, it is important to line up your numbers on top of each other with the digits in the correct columns. We usually put the largest number on the top row.

Example

Find the difference between 132 and 419.

1) Lay out the sum in columns:

2) Starting at the right most column, take away the bottom number from the top one. With this sum it is 9 – 2 = 7, so we can fill that in to the answer box:

3) Now we move on to the next column to the left, the hundreds column. In this column the top digit is smaller tyhan the bottom one, look it is 1 – 3. When this is the case we need to **borrow**.

Borrowing is when we take a 1 from the column to the left and give it to our smaller number.

In our example we are taking a 1 from the left and the generous number 4 who is sat there becomes a 3. Then we give this borrowed 1 to the 1 sat in the Tens column and it becomes 11. Why 11 and not 2? Well think about it, we borrowed a 1 from a column that is 10x bigger than the digit we are giving it to, so even though we take 1 off the left column, the right column increases by 10. Look:

4) Finally we can subtract the digits in the Hundreds column, 3 – 1 = 2. The 3 is our old number 4 who was kind enough to let us borrow a 1:

Now we have an answer:

287

### Missing Digits

You may be asked to fill in the **missing digits** in a sum like this:

We can fill in the **missing digits** by using our **knowledge of addition sums**.

Let’s start with the **first column** on the **right**. It shows us that **4 plus something equals 6**. What must we add to 4 to get 6? Easy, **2**, so we can fill that in. You could work backwards and say 6 – 4 = 2.

Next we can look at the **middle column** and say **4 plus what equals 3?** Well, that isn’t so simple, because **4 is bigger than 3**, but we know that in addition sums digits can be **carried over**. So we need to think **what can we add to 4 to get 13** as this will give us the **3** we need.

4 + 9 = 13

So the **missing digit** in the middle column must be **9**.

Finally we look at the **last column**, it is a simple addition:

3 + 2 = 5

**BUT** we need to remember our 1 carried over, so the answer is:

5 + 1 = **6**.

If you can understand this example then you have understood addition really well. If not then do go back and read about the section about addition and carrying over again.

### Some Tricks

Example 1

97 + 98 = **?**

If you think about it we can take 97 and add 3 to it to get 100.

And we can also take 98 and add 2 to it to get 100.

Knowing this, we can add 100 + 100 = 200.

Now we can take away the 3 and the 2 that we added earlier:

100 – 3 – 2 = **95**

Example 2

48 + 632 = **?**

In this example I am going to break the calculation down in to two parts.

Lets add the 8 from 48 first to 632:

8 + 632 – 640

Now lets add the 40 from 48 to 640:

640 + 40 = **680**

Do you see what we did? We split the 48 in to 40 and 8 and added these separately.

Example 3

123 – 39

When you are asked to do a calculation involving a number that ends in 9 you might be able to make things easier for yourself. I am going to take the 39 in this sum and add 1 to it so that it equals 40. Now I have an easier sum:

123 – 40 = 83

Finally we just need to remember that we subtracted 1 more than we should of (because we added 1 to 39 to turn it in to 40) so we just need to add 1 on to the answer:

83 + 1 = **84**