The secret to being able to add two digit numbers in your head is to simply the problem.
For example, conside the problem of adding two two-digit numbers 83 and 25.
We can simplify the problem mentally by splitting the problem into two simpler sums, like this:
Which essentially breaks the problem into two smaller additions:
And then to the next (simpler) step:
Note that there is no magic here. We are simply adding the tens digits together and the units digits together. The above works if there is no carry involved from adding the the tens digit.
If there is a carry from the lower digits, then we can round up the second number to the next multiple of 10 and add in two steps. For example, consider the following problem:
Adding 8 to 4 involves a carry and it is cumbersome to remember the carry. Instead, we can simplify the addition as:
And calculate like this:
Once again, note that there is no magic here. We are simply pre-adding the carry to the ten's digit by rounding it up to the next multiple of 10.
Also, by rounding the number to the next multiple of 10, the units addition in the first step is trivial.
We could round up either the first number or the second number. In the above examples, we always rounded the second number simply because it is easier to grasp the concept. However, you could round either of the numbers. In general, round the number which is closer to the next multiple of 10.
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