This video demonstrates the way that we use Base 10 to add two 2-digit numbers together. The first method doesn't require regrouping which has been referred to as the simple version. The second method uses regrouping and explains the language that is used when we talk about this in the classroom.
This video demonstrates the method that we use in school to subtract a 2-digit number from a larger 2-digit number. The video shows an example where no regrouping is needed and another example where regrouping is required.