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Question 213739: I would like to know how do you subtract negative rational numbers such as problems like these -49 - (-54) = ; i am having prblems with questions like these so please help me and maybe you can give me a little bit of extra practice!
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! RULE NUMBER 1
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Adding a negative number is the same as subtracting a positive number.
Example:
+ (-5) = - (+5) = - 5
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RULE NUMBER 2
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Subtracting a negative number is the same as adding a positive number.
Example:
- (-5) = + (+5) = + 5
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-5 always shows the sign of the operand.
+5 seldom shows the sign of the operand unless you want to make it explicitly clear that the number is positive. Not showing the sign makes it implicitly clear that the number is positive. You see 5; you recognize it as +5.
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operands and operators sometimes get confused because of this.
if you see + 5, is it addition or is it simply the positive number 5.
if you see - 5, is it subtraction or is it simply the negative 5.
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You get the hang of it after awhile, but it can be confusing sometimes.
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If you have to add a lot of numbers together and some of them are negative and some of them are positive, then do the following:
1. Add all the positive numbers together.
2. Add all the negative numbers together.
3. Subtract the smaller number from the larger number.
4. Give the sign of the larger number to the result.
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Example:
Add these numbers together:
5
-50
-30
-20
35
21
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1. Add all the positive number together.
you get: 5 + 35 + 21 = 61
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2. Add all the negative numbers together.
you get: (-50) + (-30) + (-20) = -100
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3. Subtract the smaller number from the larger number as if both numbers were positive.
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100 - 61 = 39
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4. Give the sign of the larger number to the result.
sign of the larger number is negative so the result = -39
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YOUR PROBLEM
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-49 - (-54) = ???
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This becomes:
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-49 + 54 (rule number 2)
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Now you're adding two numbers together but they have different signs.
Subtract the smaller number from the larger number as if they were both positive.
You get 54 - 49 = 5
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Give the sign of the larger number to the result.
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The larger number is 54 which is the same as +54 so the result is +5 which is shown as 5.
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EXAMPLE 1
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100 - (-50) = ???
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Subtraction is indicated by the first minus sign.
Subtracting a negative number is the same as adding a positive number (rule number 2).
This becomes:
100 + 50 = 150
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EXAMPLE 2
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(-100) - (-50) = ???
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Same problem as before only the first 100 is negative.
subtraction is indicated.
- (-50) is the same as + 50
problem becomes:
(-100) + 50
you are adding a negative number and a positive number together.
subtract the smaller number from the larger number as if they were both positive to get 100 - 50 = 50
give the sign of the larger number to the result to get (-50)
(-100) + 50 = (-50)
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EXAMPLE 3
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(-5) + (-5) = ???
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You are adding a negative number which is the same as subtracting a positive number (rule number 1)
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(-5) - 5
You are adding two negative numbers together.
You add them together as if they were positive and then give the negative sign to the result.
5 + 5 = 10
result is -10.
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EXAMPLE 4
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(-5) - (-5) = ???
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You are subtracting a negative number which is the same as adding a positive number (rule number 2)
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Your problem becomes:
(-5) + 5
Now you adding two numbers together with different signs.
You subtract the smaller number from the larger number and give the sign of the larger number to the result.
Only problem is these numbers are equal.
since they are equal, the result is 0 without a sign. 0 is not a negative number and not really a positive number either. it's just 0. When some problems state that negative numbers are not allowed, 0 is usually allowed along with the positive numbers, so it is more closely tied to positive numbers than to negative numbers.
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Your answer is 0.
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EXAMPLE 5
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5 + (-5) = ???
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Adding a negative number is the same as subtracting a positive number (rule number 1) so the problem becomes:
5 - 5 = ???
and the answer is 0.
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