Mental Math: Adding Numbers Near Multiples of 10

People who are very good at mental math calculations are not all gifted. Some of them just know simple strategies in order to calculate numbers easily and fast.

In this post, I am going to teach you a math trick on adding numbers that will simplify and speed up calculations. With enough practice, you can even use this strategy to perform mental calculations.

This strategy uses numbers that are near multiples of tens, hundreds, thousands, and so on. We can add a certain number to one addend and subtract that number to another addend in order to make one of the addends a multiple of 10. Sounds complicated? Not really.

Example 1:  49 + 36

This looks really hard to calculate mentally, but it’s easier than you think. First, we see that 49 is nearly 50. So, we can add 1 to 49.

This becomes 50 + ? Well, we add 1 to 49, so we have to subtract 1 from 36. So, 36 becomes 35. Therefore, the addition 

49 + 36 became 50 + 35 which is very easy to add mentally.

That is

(49 + 1) + (36 – 1)= 50 + 35

= 85.

Example 2: 82 + 55

In this example, 82 is nearer a multiple of 10. So, we can remove 2 from 82, then add it to 55. That is

(82 – 2) + (55 + 2)

= 80 + 57 = 137

Notice that it is also possible to remove 5 from 55 and add it to 82 even though 82 is nearer to a multiple of 10. That is,

(82 + 5) + (55 – 5)

= 87 + 50 = 137

If the calculation will not produce a carry over, then, you can add/subtract from any of the addends.

Example 3: 198 + 120

In this example, it is easier if 198 becomes 200 since it is easer to add. So, we add 2 to 198 so that it becomes 200 and then subtract 2 from 120.  That is,

(198 + 2) + (120 – 2) = 200 + 118

= 318

As you can see, it is a lot easier than to calculate mentally after adding/subtracting 2 from the addends.

Why the Method Works

If you add a number and then subtract the same number, then you are not actually changing anything. For example, if I have 300 and then I added 30 but subtracting 30, then it is like adding 0. In the examples above, you are just manipulating the calculations but not changing the values. In general, if you have numbers m and n, adding them will result to

m + n.

If we add a to m and then subtract a to n, then it is also m + n. That is

(m + a) + (n a) = m + n + (a a)

= m + n + 0

= m + n

That is the reason why the method works.

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