Order of Operations with Rational Numbers

 $-7+8\cdot-3$  
Be sure that you followed order of operations and did the multiplication first.
Was your product negative, since negative times positive is negative?
Finally, when you added, was your sum negative, since negative plus negative is more negative?

 $-8.2+4.5\cdot-1.4$  
Be sure that you followed order of operations and did the multiplication first.
Was your product negative, since negative times positive is negative?
Finally, when you added, was your sum negative, since negative plus negative is more negative?

 $-2\frac{2}{3}+3\frac{5}{6}+-1\frac{1}{4}$  

This problem is far simpler if you take advantage of the commutative property, so rearrange it to add the two negative numbers first.
Remember that a negative plus a negative is a bigger negative.
Then when you add the positive number, remember that when you combine a negative and a positive, the mental math or scratch paper math is really SUBTRACTION, and the sign of the answer depends on the number with the greatest magnitude.

 $-4\frac{1}{2}+1\frac{3}{8}-1\frac{1}{4}$  
Start left to right.
Be sure your first sum is negative, and that the mental math or scratch math is subtraction.
Next, complete the final operation of subtraction. 
Subtracting from a negative often trips us up, so it's valuable to change the problem to adding the opposite number instead.

 $-\frac{3}{2}\div\frac{5}{6}\times\frac{2}{3}$  
Be careful--the order operations does NOT say multiply before you divide!!
Go left to right when multiplying and dividing.
Don't forget to turn division into multiplying by the reciprocal.
Multiply all numerators, then all denominators.

 $2\frac{4}{5}+3\frac{3}{4}\div-2\frac{1}{2}$  
Start with division. Change it to multiplying by the reciprocal.
Multiply numerators and denominators. Be careful to make the product negative, because negative times positive is negative.
Combine the $2\ \frac{4}{5}$  and your product. Be caureful that the mental math or scratch math is subtraction, and that the sign of the suum is the sign of the number with the highest magnittude.