Let's solve each part of the given question step-by-step:
### i) If the sum of two integers is 71 and one of them is (-67), find the other integer.
We are given:
[tex]\[
\text{Sum} = 71
\][/tex]
[tex]\[
\text{One integer} = -67
\][/tex]
To find the other integer, subtract -67 from 71:
[tex]\[
\text{Other integer} = 71 - (-67) = 71 + 67 = 138
\][/tex]
Thus, the other integer is 138.
### ii) The sum of two integers is 324. If one integer is (-117), find the other.
We are given:
[tex]\[
\text{Sum} = 324
\][/tex]
[tex]\[
\text{One integer} = -117
\][/tex]
To find the other integer, subtract -117 from 324:
[tex]\[
\text{Other integer} = 324 - (-117) = 324 + 117 = 441
\][/tex]
Thus, the other integer is 441.
### iii) Verify the commutative property of addition if [tex]\( a = -11 \)[/tex] and [tex]\( b = -92 \)[/tex].
The commutative property of addition states that the order in which two numbers are added does not change their sum:
[tex]\[
a + b = b + a
\][/tex]
Substitute [tex]\( a = -11 \)[/tex] and [tex]\( b = -92 \)[/tex]:
[tex]\[
-11 + (-92) = -103
\][/tex]
[tex]\[
-92 + (-11) = -103
\][/tex]
Both expressions give the same result, [tex]\(-103\)[/tex], verifying the commutative property.
### iv) Subtract the sum of -432 and 161 from 243.
First, find the sum of [tex]\(-432\)[/tex] and [tex]\(161\)[/tex]:
[tex]\[
-432 + 161 = -271
\][/tex]
Now, subtract this sum from 243:
[tex]\[
243 - (-271) = 243 + 271 = 514
\][/tex]
Thus, the result is 514.
### v) From the sum of -109 and 312, subtract -150.
First, find the sum of [tex]\(-109\)[/tex] and [tex]\(312\)[/tex]:
[tex]\[
-109 + 312 = 203
\][/tex]
Now, subtract [tex]\(-150\)[/tex] from this sum:
[tex]\[
203 - (-150) = 203 + 150 = 353
\][/tex]
Thus, the result is 353.
### Summary
The results for each part are:
i) The other integer is 138.
ii) The other integer is 441.
iii) The commutative property is verified since [tex]\(-11 + (-92) = -103\)[/tex] and [tex]\(-92 + (-11) = -103\)[/tex].
iv) The result is 514.
v) The result is 353.
