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This Maths article explains both the mental method and written method for multiplying a 2-digit number by a 1-digit number.
There are different ways to approach a 2-digit by a 1-digit multiplication problem. Look at this multiplication problem. 16 × 4 = ? Here are some different ways you might solve it.
To help you understand the algorithm, the video shows a simple two-digit by two-digit multiplication. You can see that the first and last digits are essentially the result of one multiplication.