Fill in the blanks:
i {(-13) + 27} + (-41) = (-13) + {27 + (...)}
ii (-26) + {(-49) + (-83)} = {(-26) + (-49)} + (...)
iii 53+(-37) = (-37)+ (...)
iv (-68) + (-76) = (...) + (-68)
v (-72)+ (...) =-72
vi -(-83)=….
vii (-60)-(...) = -59
viii (-31)-+-(...) = -40

Answer

Let's solve the question step by step:

### Question:
Fill in the blanks:
1. {(-13) + 27} + (-41) = (-13) + {27 + (...)}

### Step 1: Solve the left side of the equation
Calculate the expression inside the curly brackets:
\[ (-13) + 27 = 14 \]
So, we rewrite the left side:
\[ 14 + (-41) \]

### Step 2: Calculate \(14 + (-41)\)
This can be simplified as:
\[ 14 - 41 = -27 \]
Thus, the left side becomes:
\[ -27 \]

### Step 3: Rewrite the right side
Now, we rewrite the right side of the equation:
\[ (-13) + {27 + (...)} = -27 \]

### Step 4: Isolate the blank
To find the value that fills the blank, we need:
\[ (-13) + (27 + x) = -27 \]
Where \(x\) is the value we need to find.

### Step 5: Solve for \(x\)
First, isolate \(27 + x\):
\[ 27 + x = -27 + 13 \]
\[ 27 + x = -14 \]
Now, subtract 27 from both sides:
\[ x = -14 - 27 \]
\[ x = -41 \]

### Conclusion for Part i:
The blank in the first part is:
\[ -41 \]

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### Part ii:
2. (-26) + {(-49) + (-83)} = {(-26) + (-49)} + (...)

### Step 1: Solve the left side
Calculate:
\[ (-49) + (-83) = -49 - 83 = -132 \]
So, the left side becomes:
\[ -26 + (-132) = -26 - 132 = -158 \]

### Step 2: Rewrite the right side
Now, we rewrite the right side:
\[ {(-26) + (-49)} + x = -158 \]

### Step 3: Calculate \((-26) + (-49)\)
\[ -26 - 49 = -75 \]
Thus, we have:
\[ -75 + x = -158 \]

### Step 4: Solve for \(x\)
Isolate \(x\):
\[ x = -158 + 75 \]
\[ x = -83 \]

### Conclusion for Part ii:
The blank in the second part is:
\[ -83 \]

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### Part iii:
3. 53 + (-37) = (-37) + (...)

### Step 1: Calculate the left side
\[ 53 + (-37) = 53 - 37 = 16 \]

### Step 2: Rewrite the right side
We have:
\[ (-37) + x = 16 \]

### Step 3: Solve for \(x\)
Isolate \(x\):
\[ x = 16 + 37 \]
\[ x = 53 \]

### Conclusion for Part iii:
The blank in the third part is:
\[ 53 \]

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### Part iv:
4. (-68) + (-76) = (...) + (-68)

### Step 1: Calculate the left side
\[ -68 - 76 = -144 \]

### Step 2: Rewrite the right side
We have:
\[ x + (-68) = -144 \]

### Step 3: Solve for \(x\)
Isolate \(x\):
\[ x = -144 + 68 \]
\[ x = -76 \]

### Conclusion for Part iv:
The blank in the fourth part is:
\[ -76 \]

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### Part v:
5. (-72) + (...) = -72

### Step 1: Isolate the blank
Let \(x\) be the blank:
\[ -72 + x = -72 \]

### Step 2: Solve for \(x\)
\[ x = -72 + 72 \]
\[ x = 0 \]

### Conclusion for Part v:
The blank in the fifth part is:
\[ 0 \]

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### Part vi:
6. -(-83) = ...

### Step 1: Simplify
The negative of a negative is positive:
\[ -(-83) = 83 \]

### Conclusion for Part vi:
The answer is:
\[ 83 \]

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### Part vii:
7. (-60) - (...) = -59

### Step 1: Isolate the blank
Let \(x\) be the blank:
\[ -60 - x = -59 \]

### Step 2: Solve for \(x\)
Rearranging gives:
\[ -x = -59 + 60 \]
\[ -x = 1 \]
Thus,
\[ x = -1 \]

### Conclusion for Part vii:
The blank in the seventh part is:
\[ -1 \]

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### Part viii:
8. (-31) - - (...) = -40

### Step 1: Rewrite
This can be rewritten as:
\[ -31 + x = -40 \]

### Step 2: Solve for \(x\)
Isolate \(x\):
\[ x = -40 + 31 \]
\[ x = -9 \]

### Conclusion for Part viii:
The blank in the eighth part is:
\[ -9 \]

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