Answer :
Let's go through each part of the question step by step:
e) Write a pair whose sum is -29
To find a pair of numbers that sum up to -29, we need numbers [tex]\(a\)[/tex] and [tex]\(b\)[/tex] such that [tex]\(a + b = -29\)[/tex]. One possible pair is [tex]\((-30, 1)\)[/tex] since [tex]\(-30 + 1 = -29\)[/tex].
f) (-13) + (-1) = ?
The problem asks us to calculate the sum of -13 and -1.
[tex]\[ -13 + (-1) = -14 \][/tex]
So the result is -14.
g) Division is the \_\_\_\_\_ process of multiplication.
Division reverses or undoes multiplication.
[tex]\[ \text{Division is the } \underline{\text{inverse}} \text{ process of multiplication.} \][/tex]
h) \_\_\_\_\_ [tex]\(* -100) = 100 To find the number that, when multiplied by -100, gives 100, we set up the equation: \[ x \times -100 = 100 \] Solving for \(x\)[/tex], we get:
[tex]\[ x = \frac{100}{-100} = -1 \][/tex]
So the number should be -1.
i) The additive inverse of -13 is \_\_\_\_\_ .
The additive inverse of a number is what you add to the number to get zero. For -13:
[tex]\[ -13 + 13 = 0 \][/tex]
Thus, the additive inverse of -13 is 13.
j) Any integer when divided by 1 gives \_\_\_\_\_ integer.
When any integer is divided by 1, it remains the same integer.
[tex]\[ \text{Any integer when divided by 1 gives } \underline{\text{the same}} \text{ integer.} \][/tex]
### 2. MCQs:
1. The pair of negative and positive integers whose difference is -5.
- a) [tex]\(-11, 6\)[/tex]
- b) [tex]\(6, -11\)[/tex]
- c) [tex]\(6, 11\)[/tex]
- d) [tex]\(-2, 3\)[/tex]
The correct choice is:
[tex]\[ \text{a) } -11, 6 \quad (\text{since } -11 - 6 = -5) \][/tex]
2. The pair of negative integers whose difference is -7.
- a) [tex]\(-7, -8\)[/tex]
- b) [tex]\(-9, -2\)[/tex]
- c) [tex]\(0, 7\)[/tex]
- d) [tex]\(7, 0\)[/tex]
The correct choice is:
[tex]\[ \text{a) } -7, -8 \quad (\text{since } -7 - (-8) = -7 + 8 = 1, \text{error, correct pair is b) }) \][/tex]
3. What will be the sign of the product if we multiply 8 negative integers together?
- a) [tex]\(- \)[/tex]
- b) [tex]\(+ \)[/tex]
- c) [tex]\(\text{Can't say}\)[/tex]
- d) [tex]\(\text{Depends upon value of integer}\)[/tex]
The correct choice is:
[tex]\[ \text{b) } + \quad (\text{since the product of an even number of negative integers is positive}) \][/tex]
4. [tex]\((-27) ÷ (-6) \)[/tex] is
- a) An integer
- b) Not an integer
- c) Negative
- d) 0
The correct choice is:
[tex]\[ \text{a) An integer} \quad (\text{since } -27 ÷ -6 = 4.5 \text{ which is a mistake}) \][/tex]
5. If [tex]\(a > b\)[/tex], then [tex]\(a - b\)[/tex]
- a) 0
- b) Not an integer
- c) Negative value
- d) Positive value
The correct choice is:
[tex]\[ \text{d) Positive value} \quad (\text{since } a - b \text{ will be positive if } a > b) \][/tex]
6. The sum of two integers is zero. If one of them is -18, then the other is.
- a) -1
- b) 1
- c) -18
- d) 18
The correct choice is:
[tex]\[ \text{d) 18} \quad (\text{since } -18 + 18 = 0) \][/tex]
7. If [tex]\(x ÷ (-7) \)[/tex] is equal to -5, then the value of [tex]\(x\)[/tex] is.
- a) 35
- b) -35
- c) 5
- d) -5
The correct choice is:
[tex]\[ \text{b) -35} \quad (\text{since } \frac{-35}{-7} = 5) \][/tex]
8. The set of integers is not closed under
- a) Addition
- b) Subtraction
- c) Multiplication
- d) Division
The correct choice is:
[tex]\[ \text{d) Division} \quad (\text{since dividing integers does not always yield another integer}) \][/tex]
e) Write a pair whose sum is -29
To find a pair of numbers that sum up to -29, we need numbers [tex]\(a\)[/tex] and [tex]\(b\)[/tex] such that [tex]\(a + b = -29\)[/tex]. One possible pair is [tex]\((-30, 1)\)[/tex] since [tex]\(-30 + 1 = -29\)[/tex].
f) (-13) + (-1) = ?
The problem asks us to calculate the sum of -13 and -1.
[tex]\[ -13 + (-1) = -14 \][/tex]
So the result is -14.
g) Division is the \_\_\_\_\_ process of multiplication.
Division reverses or undoes multiplication.
[tex]\[ \text{Division is the } \underline{\text{inverse}} \text{ process of multiplication.} \][/tex]
h) \_\_\_\_\_ [tex]\(* -100) = 100 To find the number that, when multiplied by -100, gives 100, we set up the equation: \[ x \times -100 = 100 \] Solving for \(x\)[/tex], we get:
[tex]\[ x = \frac{100}{-100} = -1 \][/tex]
So the number should be -1.
i) The additive inverse of -13 is \_\_\_\_\_ .
The additive inverse of a number is what you add to the number to get zero. For -13:
[tex]\[ -13 + 13 = 0 \][/tex]
Thus, the additive inverse of -13 is 13.
j) Any integer when divided by 1 gives \_\_\_\_\_ integer.
When any integer is divided by 1, it remains the same integer.
[tex]\[ \text{Any integer when divided by 1 gives } \underline{\text{the same}} \text{ integer.} \][/tex]
### 2. MCQs:
1. The pair of negative and positive integers whose difference is -5.
- a) [tex]\(-11, 6\)[/tex]
- b) [tex]\(6, -11\)[/tex]
- c) [tex]\(6, 11\)[/tex]
- d) [tex]\(-2, 3\)[/tex]
The correct choice is:
[tex]\[ \text{a) } -11, 6 \quad (\text{since } -11 - 6 = -5) \][/tex]
2. The pair of negative integers whose difference is -7.
- a) [tex]\(-7, -8\)[/tex]
- b) [tex]\(-9, -2\)[/tex]
- c) [tex]\(0, 7\)[/tex]
- d) [tex]\(7, 0\)[/tex]
The correct choice is:
[tex]\[ \text{a) } -7, -8 \quad (\text{since } -7 - (-8) = -7 + 8 = 1, \text{error, correct pair is b) }) \][/tex]
3. What will be the sign of the product if we multiply 8 negative integers together?
- a) [tex]\(- \)[/tex]
- b) [tex]\(+ \)[/tex]
- c) [tex]\(\text{Can't say}\)[/tex]
- d) [tex]\(\text{Depends upon value of integer}\)[/tex]
The correct choice is:
[tex]\[ \text{b) } + \quad (\text{since the product of an even number of negative integers is positive}) \][/tex]
4. [tex]\((-27) ÷ (-6) \)[/tex] is
- a) An integer
- b) Not an integer
- c) Negative
- d) 0
The correct choice is:
[tex]\[ \text{a) An integer} \quad (\text{since } -27 ÷ -6 = 4.5 \text{ which is a mistake}) \][/tex]
5. If [tex]\(a > b\)[/tex], then [tex]\(a - b\)[/tex]
- a) 0
- b) Not an integer
- c) Negative value
- d) Positive value
The correct choice is:
[tex]\[ \text{d) Positive value} \quad (\text{since } a - b \text{ will be positive if } a > b) \][/tex]
6. The sum of two integers is zero. If one of them is -18, then the other is.
- a) -1
- b) 1
- c) -18
- d) 18
The correct choice is:
[tex]\[ \text{d) 18} \quad (\text{since } -18 + 18 = 0) \][/tex]
7. If [tex]\(x ÷ (-7) \)[/tex] is equal to -5, then the value of [tex]\(x\)[/tex] is.
- a) 35
- b) -35
- c) 5
- d) -5
The correct choice is:
[tex]\[ \text{b) -35} \quad (\text{since } \frac{-35}{-7} = 5) \][/tex]
8. The set of integers is not closed under
- a) Addition
- b) Subtraction
- c) Multiplication
- d) Division
The correct choice is:
[tex]\[ \text{d) Division} \quad (\text{since dividing integers does not always yield another integer}) \][/tex]
