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Each option: 1 Mark
(a) We first move to the right of 0 by 5 steps reaching 5. Then we move 3 steps to the left of 5 reaching 2.

We get, $(+5)+(-3)=2$
(b)We want to know an integer which is 5 less than 3 for that we need to start from 3 and move to the left by 5 steps and obtain –2 as shown below:

(c)We want to know the integer which is 4 more than –1. So, we start from –1 and proceed 4 steps to the right of –1 to reach 3 as shown below:

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Each option: 1 Mark
(a) a = 12, b = −4, c = 2
a$÷$ (b$+$ c) = 12$÷$ (− 4$+$ 2) = 12$÷$ (−2)
= −6
(a$÷$ b)$+$ (a$÷$ c) = [12$÷$ (−4)]$+$ [12$÷$ 2] = −3$+$ 6 = 3
Hence, a$÷$ (b$+$ c) ≠ (a$÷$ b)$+$ (a$÷$ c)
(b) a = −10, b = 1, c = 1
a$÷$ (b$+$ c) = (−10)$÷$ (1$+$ 1) = (−10)$÷$ 2
= −5
(a$÷$ b)$+$ (a$÷$ c) = [(−10)$÷$ 1]$+$ [(−10)$÷$ 1]
= − 10 − 10 = −20
Hence, a$÷$ (b$+$ c) ≠ (a$÷$ b)$+$ (a$÷$ c)

:
Each option:1.5 Marks
As per the question
Marks obtained for 1 right answer = +3
Marks obtained for 1 wrong answer = −2
(i) Marks scored by Radhika = 20
Marks obtained for 12 correct answers = 12 $\times$ 3 = 36
Marks obtained for incorrect answers = Total score − Marks obtained for 12 correct answers
= 20 − 36 = −16
Marks obtained for 1 wrong answer = −2
Thus, number of incorrect answers
= (−16) $÷$ (−2) = 8
Therefore, she had answered 8 questions incorrectly.
(ii) Marks scored by Mohini = −5
Marks obtained for 7 correct answers
= 7 $\times$ 3 = 21
Marks obtained for incorrect answers = Total score − Marks obtained for 12 correct answers
= − 5 − 21 = −26
Marks obtained for 1 wrong answer = −2
Thus, number of incorrect answers
= (−26) $÷$ (−2) = 13
Therefore, she had answered 13 questions incorrectly.

:
Steps: 2 Marks
Result: 2 Marks
Upward movement is taken as positive while downward movement is taken as negative. Hence, from the question we can conclude that helicopter is moving downward. So, the distance of helipad from the helicopter will be negative integers.
$=-1500m+600m$
$=-900m$.
Given that the speed of the helicopter is 50 meters per second.
Total distance to be covered = 900 m
Time taken by the helicopter to reach the helipad = 900 $÷$ 50 =18 seconds
Hence, the helicopter will reach the helipad in 18 seconds.

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Definition: 1 Mark
Example: 1 Mark
The word "commutative" comes from "commute" or "move around", so the Commutative Property is the one that refers to moving stuff around.
So, if we add any number of integersin any order the result will be the same.
For addition, the rule is "a + b = b + a".
Example
2 + 3 = 3 + 2 = 5.

:
As we know that the product of two negative integers is always positive. Hence, when we multiply 12 negative integers, we can treat these 12 integers like 6 pairs of negative integers. Each pair will give us a positive integer. Hence the overall multiplewill be a positive integer.

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Each option: 2 Marks
(a) 26 $\times$ (−48) + (−48)$\times$ (−36)
= (−48)$\times$ 26 + (−48)$\times$ (−36)
($\because$ (b$\times$ a = a$\times$ b))
= (−48) [26 − 36] (a$\times$ b + a$\times$ c) = a (b + c)
= (−48)$\times$ (−10) = 480
(b) 15$\times$ (−25)$\times$ (−4)$\times$ (−10)
= 15$\times$ [(−25)$\times$ (−4)]$\times$ (−10)
= 15$\times$ [100]$\times$ (−10)
= 15$\times$ (−1000) = −15000

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Concept: 1 Mark
Result: 1 Mark
The result will be anegative integer as multiplication of one negative and one positive integer willresult in a negative integer.
(a $÷$ b) = + integer
$(+)\times (-)=(-)$ integer

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Calculations: 1 Mark
Steps: 2 Marks
Result: 1 Mark
Given that
An elevator descends into a mine shaft at the rate of 6 m/min.
The descent starts from10m above the ground level.
Now, the distance descended is denoted by a negative integer.
Initial height = +10 m
Final depth = −350 m
Total distance to be descended by the elevator = (−350) − (+10) = −360 m
Time taken by the elevator to descend −6 m = 1 min
Thus, time taken by the elevator to descend −360 m = (−360) $÷$ (−6)
= 60 minutes = 1 hour
Hence it will take 1 hour to reach -350m.

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Each part: 1.5 Marks
(i) Multiplication of even no. of negative integers gives a positive integer whereas multiple of odd no. of negative integers gives a negative integer.
(a) We have multiplication of three negative integers. So, the product will be negative integers.
$(-2)\times (-3)\times (-4)=6\times (-4)=(-24)$
(b) We have multiplication of two negative integers and one positive integer. So, the product will be positive integers.
$2\times (-3)\times (-4)=12\times 2=24$
(c) $\frac{2}{6}\times (-3)\times \frac{4}{10}$
$=\frac{1}{3}\times -3\times \frac{2}{5}$
$=\frac{-2}{5}$
(ii)(a) $-12<-4$
(b) $-15<-2$
(c) $-7>-29$