How do you evaluate #(-9)+14#?

Question

Nova Allen · Accepted Answer

There are various way of approaching this. I am going to show you one you may not have seen before. #color(brown)("Explained in detail. With practice you will do a lot")##color(brown)("of this in your head and be much more efficient.")# Split the 14 into #9+5#. This is called partitioning. There is no sign to the left of the brackets so it is automatically: #+(-9)# Think of this as #+1(-9)" which is the same as "(+1)xx(-9)# In multiply, if the signs are different then the answer is negative #(-9)"   "="   "(+1)xx(-9)"   " ="  " -9#
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#color(blue)("Having dealt with the above we now answer the question")# Write: #color(green)((-9))color(red)(+14)"  as  "color(green)(-9color(red)(+9+5)# But #-9+9" " ->" "+9-9=0# giving #0+5# so #(-9)+14=+5# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~ More efficient approach ~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #(-9)+14 = 14-9 = 5#