By keeping track of your units, tens, hundreds, or other place values with many digits, you can add numbers using mental maths.

Adding a small number

Adding is just counting up. So $4+2$ is just counting up two from four. If you know how to count, you know how to add.

Example 1

Calculate

$10+8$

You can do this by starting at ten and counting up eight places:

So,

$10+8=\underline{18}$

Adding a bigger number

For bigger numbers however, it is harder to simply count in steps of one and would take too long. Instead, a number should be broken down into its units, tens, hundreds etc, and counted up.

Example 2

Calculate

$43+25$

Start by counting up the units, then move on to the tens. So initially you can add the five units and then you add the two tens.

So,

$43+25=\underline{68}$

Changing tens and hundreds

When using this method to add mentally there will be times when by adding units, you will end up changing the tens. Similarly, when adding tens you sometimes have to change the hundreds. As you add bigger and bigger numbers, the same thing will happen with thousands, tens of thousands, and so on.

Example 3

Calculate

$89+43$

Start with the units. Notice that though you are adding units, the tens value has also changed. This is because units value has exceeded ten. Next add the tens to what you have so far.

This means that:

$89+43=\underline{132}$

Notice that here you were adding tens but the hundreds value also changed from zero to one. This is because the tens value exceeded one hundred.

A number can be broken down into its units, tens, hundreds, etc, and each can be counted up correspondingly. For example, to add 638, you can count up 8 units, then 3 tens, then 6 hundreds.

How can you add mentally?

Adding is just counting up. If you know how to count, you know how to add. To add 2 is the same as counting up by 2.

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