Let's work some more problems!
Question
Evaluate the following:
Answer
- -5 + (3) - (-5) + (5 - (-2))
- 4 - (3 - 4) + (-2)
- 11 - 7 - (7 + 2)
Analysis
- -5 + (3) - (-5) + (5 - (-2)) = -5 + 3 + 5 + 7 = 10
- 4 - (3 - 4) + (-2) = 4 - (-1) + (-2) = 3
- 11 - 7 - (7 + 2) = 11 - 7 - 9 = -5
We start with the Order of Operations. Notice that in all of the practice problems, we do have brackets to deal with. We work those first, then do the remaining math from left to right.
Question 1:
-5 + (3) - (-5) + (5 - (-2))
The brackets around the 3 are extraneous - there's no operation in there to perform, so we can simply drop them.
The brackets around the -5 are to help clarify that we are going to subtract a negative number. Brackets are often used to help readers of the expression see that there is a negative term in them. There's no operation, so again nothing to do in the first step.
The bracket set in the last term, 5 - (-2), is showing that we'll add the result of the math inside the outer set of brackets. We can do this first. 5 - (-2) = 7.
All this gives:
-5 + (3) - (-5) + (5 - (-2)) = -5 + 3 - (-5) + (7)
Now let's go ahead and simplify the - (-5) term - just like with the 5 - (-2) above, we're subtracting a negative number - which means we are, in effect, adding a positive number. And so - (-5) = +5:
-5 + 3 - (-5) + (7) = -5 + 3 + 5 + 7
And now we do the math from left to right:
-5 + 3 + 5 + 7 = -2 + 5 + 7 = 3 + 7 = 10
Question 2:
4 - (3 - 4) + (-2)
We work the bracket first:
4 - (3 - 4) + (-2) = 4 - (-1) + (-2)
And now let's work the math from left to right:
4 - (-1) + (-2) = 5 + (-2) = 3
Question 3:
11 - 7 - (7 + 2)
Again, we work the brackets first:
11 - 7 - (7 + 2) = 11 - 7 - (9)
And now we work left to right:
11 - 7 - 9 = 4 - 9 = -5
Vocabulary used:
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Where might you have come from?
Fact-orials Index
Operations:
Operations with different kinds of numbers:
Where might we go?
Operations with different kinds of numbers:
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