7. Solve the following:

i) If the sum of two integers is 71 and one of them is [tex]\(-67\)[/tex], find the other integer.

ii) The sum of two integers is 324. If one integer is [tex]\(-117\)[/tex], find the other.

iii) Verify the commutative property of addition if [tex]\(a=-11\)[/tex] and [tex]\(b=-92\)[/tex].

iv) Subtract the sum of [tex]\(-432\)[/tex] and 161 from 243.

v) From the sum of [tex]\(-109\)[/tex] and 312, subtract [tex]\(-150\)[/tex].

8. Compute these products:



Answer :

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.