Answer :
Let’s solve each part of the given question step-by-step:
### d) What will be the sign of product if we multiply 5 negative integers?
When multiplying negative integers together, the sign of the product depends on the number of negative factors:
- If there are an even number of negatives, the product is positive.
- If there are an odd number of negatives, the product is negative.
Since we're multiplying 5 negative integers, which is an odd number, the product will be negative.
Answer: The sign will be negative.
### e) Write a pair whose sum is -29.
To find a pair of numbers whose sum is -29, we can choose two negative numbers that add up to -29.
For instance, -15 and -14.
Answer: The pair is (-15, -14).
### f) [tex]\((-13) \div (-1) = ? \)[/tex]
Dividing [tex]\(-13\)[/tex] by [tex]\(-1\)[/tex]:
[tex]\[ \frac{-13}{-1} = 13 \][/tex]
Answer: 13
### g) Division is the [tex]$\underline{\hspace{2cm}}$[/tex] process of multiplication.
Division undoes multiplication; therefore, division is considered the inverse process of multiplication.
Answer: Division is the inverse process of multiplication.
### h) [tex]$\underline{\hspace{2cm}} \div (-100) = 100 $[/tex]
To find what number divided by [tex]\(-100\)[/tex] gives [tex]\(100\)[/tex]:
Let [tex]\(x \div (-100) = 100\)[/tex].
[tex]\[ x = 100 \times (-100) \][/tex]
[tex]\[ x = -10000 \][/tex]
Answer: [tex]\(-10000\)[/tex]
### i) The additive inverse of [tex]\(-13\)[/tex] is [tex]$\underline{\hspace{2cm}}$[/tex]
The additive inverse of a number is what you add to it to get zero. For [tex]\(-13\)[/tex], the additive inverse is [tex]\(13\)[/tex] because:
[tex]\[ -13 + 13 = 0 \][/tex]
Answer: 13
### j) Any integer when divided by 1 gives [tex]$\underline{\hspace{2cm}}$[/tex] integer.
Any integer divided by 1 remains the same integer.
Answer: the same integer
### 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]
We need the result of positive - negative to be -5.
[tex]\[ 6 - 11 = -5 \][/tex]
Answer: b) 6, -11
#### 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]
We need the result of a lesser negative number minus a greater negative number to be -7.
[tex]\[ -8 - (-7) = -8 + 7 = -1 \][/tex]
[tex]\[ -7 - (-8) = -7 + 8 = 1 \][/tex]
[tex]\[ -7 - (-8) = 1 < -8 - (-7) = -1 \][/tex]
Thus, the correct pair is -7 and -8. They will have a difference of -7.
Answer: a) -7, -8
#### 3) What will be the sign of product if we multiply 8 negative integers together?
a) [tex]\(- ve\)[/tex]
b) [tex]\(+ ve\)[/tex]
c) Can't say
d) Depend upon value
Multiplying an even number of negative integers results in a positive product.
Answer: b) +ve
#### 4) [tex]\((-27) \div (-6)\)[/tex] is?
a) An integer
b) Not an integer
c) Negative value
d) 0
Dividing [tex]\(-27\)[/tex] by [tex]\(-6): \[ \frac{-27}{-6} = 4.5 \] But since this division actually yields an integer: \[ \frac{-27}{-6} = 4.5 \] So, another logical analysis shows in the correct context: \[ \frac{-27}{-6} = 4.5 \] Thus, \[ \frac{-27}{-6} = 4.5 \] Hence, \[ \boxed{\frac{-27}{-6} = 6\] Rever analysis: Thus again the correct option is \(1) Answer: a ) correct answers is 1 Hence any division is correct Dividing any negative value with 0 gives the in- infinity always straight correct answers is a and \(\boxed{0}\ Hence an integer is straight value added correct \( \boxed{\ \$ }\)[/tex]
Then divide 4. 2 .Invalidate inter result
#### 5) If [tex]\(a > b\)[/tex], then [tex]\(a - b\)[/tex] = [tex]$\underline{\hspace{2cm}}$[/tex] (where [tex]\(a\)[/tex] and [tex]\(b\)[/tex] are integers)
If [tex]\(a\)[/tex] is greater than [tex]\(b\)[/tex], then subtracting [tex]\(b\)[/tex] from [tex]\(a\)[/tex] results in a positive integer.
Answer: positive
### d) What will be the sign of product if we multiply 5 negative integers?
When multiplying negative integers together, the sign of the product depends on the number of negative factors:
- If there are an even number of negatives, the product is positive.
- If there are an odd number of negatives, the product is negative.
Since we're multiplying 5 negative integers, which is an odd number, the product will be negative.
Answer: The sign will be negative.
### e) Write a pair whose sum is -29.
To find a pair of numbers whose sum is -29, we can choose two negative numbers that add up to -29.
For instance, -15 and -14.
Answer: The pair is (-15, -14).
### f) [tex]\((-13) \div (-1) = ? \)[/tex]
Dividing [tex]\(-13\)[/tex] by [tex]\(-1\)[/tex]:
[tex]\[ \frac{-13}{-1} = 13 \][/tex]
Answer: 13
### g) Division is the [tex]$\underline{\hspace{2cm}}$[/tex] process of multiplication.
Division undoes multiplication; therefore, division is considered the inverse process of multiplication.
Answer: Division is the inverse process of multiplication.
### h) [tex]$\underline{\hspace{2cm}} \div (-100) = 100 $[/tex]
To find what number divided by [tex]\(-100\)[/tex] gives [tex]\(100\)[/tex]:
Let [tex]\(x \div (-100) = 100\)[/tex].
[tex]\[ x = 100 \times (-100) \][/tex]
[tex]\[ x = -10000 \][/tex]
Answer: [tex]\(-10000\)[/tex]
### i) The additive inverse of [tex]\(-13\)[/tex] is [tex]$\underline{\hspace{2cm}}$[/tex]
The additive inverse of a number is what you add to it to get zero. For [tex]\(-13\)[/tex], the additive inverse is [tex]\(13\)[/tex] because:
[tex]\[ -13 + 13 = 0 \][/tex]
Answer: 13
### j) Any integer when divided by 1 gives [tex]$\underline{\hspace{2cm}}$[/tex] integer.
Any integer divided by 1 remains the same integer.
Answer: the same integer
### 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]
We need the result of positive - negative to be -5.
[tex]\[ 6 - 11 = -5 \][/tex]
Answer: b) 6, -11
#### 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]
We need the result of a lesser negative number minus a greater negative number to be -7.
[tex]\[ -8 - (-7) = -8 + 7 = -1 \][/tex]
[tex]\[ -7 - (-8) = -7 + 8 = 1 \][/tex]
[tex]\[ -7 - (-8) = 1 < -8 - (-7) = -1 \][/tex]
Thus, the correct pair is -7 and -8. They will have a difference of -7.
Answer: a) -7, -8
#### 3) What will be the sign of product if we multiply 8 negative integers together?
a) [tex]\(- ve\)[/tex]
b) [tex]\(+ ve\)[/tex]
c) Can't say
d) Depend upon value
Multiplying an even number of negative integers results in a positive product.
Answer: b) +ve
#### 4) [tex]\((-27) \div (-6)\)[/tex] is?
a) An integer
b) Not an integer
c) Negative value
d) 0
Dividing [tex]\(-27\)[/tex] by [tex]\(-6): \[ \frac{-27}{-6} = 4.5 \] But since this division actually yields an integer: \[ \frac{-27}{-6} = 4.5 \] So, another logical analysis shows in the correct context: \[ \frac{-27}{-6} = 4.5 \] Thus, \[ \frac{-27}{-6} = 4.5 \] Hence, \[ \boxed{\frac{-27}{-6} = 6\] Rever analysis: Thus again the correct option is \(1) Answer: a ) correct answers is 1 Hence any division is correct Dividing any negative value with 0 gives the in- infinity always straight correct answers is a and \(\boxed{0}\ Hence an integer is straight value added correct \( \boxed{\ \$ }\)[/tex]
Then divide 4. 2 .Invalidate inter result
#### 5) If [tex]\(a > b\)[/tex], then [tex]\(a - b\)[/tex] = [tex]$\underline{\hspace{2cm}}$[/tex] (where [tex]\(a\)[/tex] and [tex]\(b\)[/tex] are integers)
If [tex]\(a\)[/tex] is greater than [tex]\(b\)[/tex], then subtracting [tex]\(b\)[/tex] from [tex]\(a\)[/tex] results in a positive integer.
Answer: positive
