How do i use distributive property and mental math to find 5×198

So what you can do is just simplify your problem down to something much more complex. For example you can put 5x190---> 5x (190+8) and you would simplify 5 into 190 and 8 and then you can get 950 from multiplying 5 and 190 and then by multiplying 5 and 8 you get 40 so you add your answer from 190x5 to 40. So it would look something like this...
5x(190+8)
5x190=950
5x8=40
950+40=990
To check your answer
198x5=990

Is this the whole problem? I have only seen it used with parentheses. 
Example 4(8+3)

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