1. Following number line shows the temperature in degree celsius (e) at different places on a particular day. Observe this number line and write the temperature of the places marked on it.

Solution:-


The temperature of five cities can be determined by observing the number line.


These are as follows


Labulspiti is -8°C


Srinagar is -2°C


• Shimla is 5'C Ooty is 14°C


Bengaluru is 22°C


2.What is the temperature difference between the hottest and the coldest places among the above?

Explanation:


To find the temperature difference between the hottest and the coldest places among the cities


listed, we can subtract the temperature of the coldest city from the temperature of the hottest city.


The coldest city on the list is Lahulspiti with a temperature of -8°C,


and the hottest city is Bengaluru with a temperature of 22°C.


Therefore, the temperature difference between the hottest and coldest places is:


22°C -(-8°C) = 34°C


The temperature difference between the hottest and coldest places is 30°C.


3.What is the temperature difference between Lahulspiti and Srinagar?

Explanation:


To find the temperature difference between Lahulspiti and Srinagar, we can subtract the


temperature of Srinagar from the temperature of Labulspiti.


The temperature of Lahulspiti is -8°C, and the temperature of Srinagar is -2°C.


Therefore, the temperature difference between Lahulspiti and Srinagar is:


-8°C-(-2°C)=-6°C


The temperature difference between Lahulspiti and Srinagar is 6 degrees Celsius (-6°C).


4.Can we say the temperature of Srinagar and Shimla, taken together, is less than the temperature in Shimla? Is it also less than the temperature in Srinagar?

Explanation:


To determine this, we need to find the average temperature of Srinagar and Shimla.


The temperature of Srinagar is -2°C, and the temperature of Shimla is 5ºC.


The average temperature of Srinagar and Shimla is:


(-2°C+5°C)/2=1.5°C


The average temperature of Srinagar and Shimla is 1.5°C.


Therefore, we can say that the temperature of Srinagar and Shimla, taken together, is less than the temperature in Bengaluru (which has a temperature of 22°C).

However, we cannot say for certain whether it is less than the temperature in Shimla or less than the temperature in Srinagar, as the average temperature of Srinagar and Shimla (15°C) falls between the temperature of Srinagar (-2°C) and the temperature of Shimla (5°C).


5.In a quiz, positive marks are given for correct answers and negative marks are given for incorrect answers. If Jack's scores in five successive rounds were 25,-5,-10, 15 and 10, what was his total at the end?

Explanation:


To find Jack's total score, we need to add up his scores for each round.


For the first round, Jack scored 25 points.


For the second round, Jack scored -5 points because he got an incorrect answer and lost points


For the third round. Jack scored -10 points for getting another incorrect answer


For the fourth round, Jack scored 15 points for a correct answer.


For the fifth and final round, Jack scored 10 points for another correct answer.


To find Jack's total score, we can add up his scores for each round


25-5-10+15+10=35


Therefore, Jack's total score at the end of the five rounds is 35.


6. At Srinagar temperature was -5°C on Monday, and then it dropped by 2°C on Tuesday. What was the temperature in Srinagar on Tuesday? On Wednesday, it rose by 4°C. What was the temperature on this day?

Explanation:


The temperature at Srinagar on Monday was -5°C.


On Tuesday, the temperature dropped by 2°C. We can find the temperature on Tuesday by


subtracting 2 from -5:


3°C -2°C=-7C


Therefore, the temperature at Srinagar on Tuesday was -7°C.


adding 4 to -7:


On Wednesday, the temperature rose by 4°C. We can find the temperature on Wednesday by


-7°C+4°C=-3°C


Therefore, the temperature at Srinagar on Wednesday was -3°C.


7. A plane is flying at the height of 5000 m above sea level. At a particular point, it is exactly above a submarine flouting 1200 m below sea level. What is the vertical distance between them?

Solution:-


The vertical distance between the plane and the submarine is the sum of their altitudes from sen level.

Since the plane is flying 5000 m above sea level and the submarine is floating 1200 m below sea level, the vertical distance between them is

5000 m + 1200 m = 6200 m

Therefore, the vertical distance between the plane and the submarine is 6200 meters.


8. Mohan deposits ₹ 2,000 in his bank account and withdraws 1,642 from it the next day. If the withdrawal of the amount from the account is represented by a negative integer, then how will you represent the amount deposited? Find the balance in Mohan's account after the withdrawal.

Explanation:


If the withdrawal of the amount from Mohan's account is represented by a negative integer, then the amount deposited will be represented by a positive integer.

Mohan deposited 2,000 in his bank account, so the amount deposited can be represented by the positive integer +2000.

Mohan withdrew 71,642 from his account, which can he represented by the negative integer 1642

To find the balance in Mohan account after the withdrawal, we need to subtract the amount withdrawn from the amount deposited:

Balance = Amount deposited - Amount withdrawn

Balance = +2000-(-1642)

Balance= +2000+1642

Balance= 3,642


Therefore, the balance in Mohan's account after the withdrawal is 3,6-42 6.


9. Rita goes 20 km towards the east from point A to point B. From B, she moves 30 km towards the west along the same road. If the distance towards the east is represented by a positive integer, then how will you represent the distance travelled towards the west? By which integer will you represent her final position from A?

Explanation:

East

A positive number will be used to indicate the distance travelled in the direction of the east, and a negative integer will be used to represent the distance travelled in the direction of the west Rita travels 20 kilometers (km) in the direction of the east to get from point A to point B, hence

the positive integer +20 can be used to indicate the castern distance.

integer -30. To represent Rita's final position from A, we need to add the distances travelled towards the east

and towards the west:

From point B. Rita moves 30 km towards the west along the same road. This means that she has traveled 30 km in the opposite direction to the east, which can be represented by the negative

Final position from A Distance towards the east-Distance towards the west

Final position from A+20-(-30)

Final position from A+20+30

Final position from A =+50

Therefore. Rita's final position from A can be represented by the positive imeger +50. 


10. In a magic square, each row, column and diagonal have the same sum. Check which of the following is a magic square.


3-1


1-10


0


-5-2


7


4


-3-2


0


3


4-7

(1)

Explanation:


For square (1), we first find the sum of each row, column, and diagonal:


Row 1:5+(-1)+(-4)=0


Row 2:-5+(-2)+7=0


Row 3:03+(-3)=0


Column 1:5+(-5)+0=0


Column 2 (-1)+(-2)+3=0)


• Column 3: (-4)+7+(-3)=0)


Diagonal 1:5+(-2)+(-3)=0


Diagonal 2: (-4)+(-2)+0=-6


We can see that all rows, columns, and diagonal 1 have a sum of 0, which is not equal to the sum of diagonal 2 (-6). Therefore, square (i) is not a magic square.


For square (ii), we find the sum of each row, column, and diagonal:


Row 1:1-10)+0=-9


Row 2: (-4)+(-3)+(-2)=-9


Row 3: (6)+4+(-7)=-9


Column 1:1+(-4) + (-6) = -9.


.Column 2: (-10)+1-3)+4=-9


Column 3:0)+(-2)+(-7)=-9


Diagonal 1:1+(-3)+(-7)=-9


Diagonal 2:0+(-3)+(-6)=-9


We can see that all rows, columns, and diagonals have a sum of 9. Therefore, square (ii) is a magic square.


11. Verify a-b)=a+b for the following values of a and b.

(i) a 21,b=18

(ii) = 118, b = 125

(iii) a=75.b=84

(iv) a = 28, b = 11

(v) a=21.b=18

Explanation:

LHS: (-b)=21-(-18)=21+18=39


RHS:+b=21+ 18-39


LHS RHS, so the statement is true for these values. (ii) a 118,b=125


LHS: a-(-b) = 118-(-125)=118+125=243


RHS: a+b=118+ 125=243


LHS RHS. 50 the statement is true for these values.


(iii) n = 75,b=84


LHS: a-(-b) 75-(-84)=75+84-159


RHS: a+b=75+84-159


LHS RHS, so the statement is true for these values.


(iv) a=28, h=11.


LHS: a-(-b) = 28-(-11)=28+11=39 RIS: a+b=28+11=39


LHS = RHS, so the statement is true for these values.


12. Use the sign of >, < or = in the box to make the statements true (a) (-8) + (-4) [1 (-8)-1-4)

(b) (-3)+7-(19) 15-8+(-9) (c) 23-41+11 | | 23-41-11 (d) 39+(-24) (15) 36+ (-52) (36)

Explanation:


(-8)+(-4)=-12


(-8)-(-4)=-8+4=4


Since 12 is less than -4, we use the < sign.


(b) (-3)+7-(19) > 15-8+(-9)


(-3)+7-(19) -15 15-8+(-9)--2


Since 15 is greater than 2, we use the sign, (c) 23-41+11 <23-41-11


23-41+11--7


23-41-11-29


Since -7 is greater than -29, we use the sign. (d) 39+(-24)-(15)>36+(-52)-(36)


39+(-24)-(15) 0


36+(-52)-1-36)=20


Since 0 is less than 20, we use the < sign.


13. A water tank has steps inside it. A monkey is sitting on the topmost step (Le... the first step). The water level is at the ninth step. He Jumps 3 steps down and then jumps back 2 steps up. In how many jumps will he reach the water level?

Explanation:


Assuming that descending steps are denoted by positive integers and ascending steps by negative integers, the monkey begins its ascent from the first step.


After the first jump, the monkey is on step 4 (1+3).

Subsequently, the monkey descends two steps, landing on step 2 (4-(2)) after the second jump.


For the third jump, the monkey climbs three steps to reach step 5.


After the fourth jump, the monkey descends two steps to land on step 3 (5+(-2)).


The fifth jump sees the monkey climh three steps to reach step 6.


After the sixth jump, the monkey descends two steps to land on step 4 (6+ (-2)).


For the seventh jump. the monkey climbs three steps to reach step 7.


After the eighth jump, the monkey descends two steps to land on step 5 (7+(-2)).


The ninth jump sees the monkey climbs three steps to reach step B


After the tenth jump, the monkey descends two steps to land on step 6 (8+(-2)).


For the eleventh and final jump, the monkey climbs three steps to reach step 9.


Thus, the monkey required eleven jumps to reach the water level, ie, the ninth step (


14. After drinking water, he wants to go back. For this, he jumps 4 steps up and then jumps back 2 steps down with every move. In how many jumps will he reach back to the top step?

Explanation: 

Assuming that ascending steps are denoted by positive integers and descending steps by negative integers, the monkey begins its descent from the ninth step after drinking water.

To reach back to the top step, the monkey needs to climb 8 steps from the current position on the ninth step. Since the monkey jumps 4 steps up and then jumps back 2 steps down with every move, the monkey climbs a net of 2 steps with every two jumps. So, the monkey needs to make 4 jumps of 2 moves each (ie., 8 moves in total) to climb the 8 steps required to reach the top step.

Therefore, the monkey will reach back to the top step in 4 jumps of 2 moves each, which is a total of 8 moves.


15.If the number of steps moved down is represented by negative integers, and the number of steps moved up by positive integers, represent his moves in parts (i) and (ii) by completing the following: (a)-3+2-...-8 (b) 4-2+...-8. In (a), the sum (-8) represents going down by eight steps. So, what will the sum 8 in (b) represent?

Explanation:


In part (1), the monkey's moves can be represented as follows:


First jump.-3 (moves down by 3 steps)


Second jump: +2 (moves up by 2 steps)


Third jump: -2 (moves down by 2 steps)


Fourth jump: +3 (moves up by 3 steps) Fifth jump: -2 (moves down by 2 steps)


Sixth jump: +3 (moves up by 3 steps)


Seventh jump: -2 (moves down by 2 steps) Eighth jump: +3 (moves up by 3 steps)


Ninth jump: -2 (moves down by 2 steps) Eleventh jump: -2 (moves down by 2 steps) To find the sum of these moves, we can simply add up all the numbers:


Tenth jump +3 (moves up by 3 steps)


(-3)+2+(-2)+3+(-2)+3+(-2)+3+(-2)+3+(-2)=-8

In qurt (ii), the monkey's moves can be represented as follows:


First jump: +4 (moves up by 4 steps)


Second jump: -2 (moves down by 2 steps:


Third jump: +4 (moves up by 4 steps)


Fourth jump: -2 (moves down by 2 steps)


Fifth jump: +4 (moves up by 4 steps)


Sixth jump: -2 (moves down by 2 steps)


Seventh jump: +4 (moves up by 4 steps)


Eighth jump: -2 (moves down by 2 steps) To find the sum of these moves, we can again add up all the numbers:


4+(-2)+4+(-2)+4+(-2)+4+(-2)=8

Here, the sum 8 represents the total number of steps that the monkey moves up, which is the number of steps required to reach the topmost step from the ninth step.


16. Write down a pair of integers whose:

  1. sum is -7

      (b) the difference is-10

      (c) sum is 0

Explanation:

There are infinitely many pairs of integers whose sam is -7. for examples:


2+(-5)=-7


0+(-7)=-7


3+(-10)=-77


(b) the difference is-10


Explanation:


There are infinitely many pairs of integers whose difference is -10. for examples:


-3-4-15)-10


8-18-10.


0-(-10)=-10


13-23=-10


(c) sum is 0

Explanation:


There are infinitely many pairs of integers whose sum is 0. for examples:


3+3=0


-7+7=0


0+0=0


4+(-4)-0


17.  Write a pair of negative integers whose difference gives 8

Explanation:

 A pair of negative integers whose difference gives 8 is -12 und -4.


We can verify that their difference is indeed 8.


-12-(-4)=-12+4=-8


And the absolute value of their difference is 8.


18. Write a negative integer and a positive integer whose sum is -5.

Explanation:


8+3=3


Adding a negative integer (-8) and a positive integer (3) whose absolute values add up to 5, the


sum will be -5.


19. Write a negative integer and a positive integer whose difference is - 3.

Explanation:

One possible solution would be; -5-2-3 Subtracting a positive integer (2) from a negative integer (-5), the difference will be -3.


20. In a quiz, team A scored-40, 10,0 and team B scored 10,0,-40 in three successive rounds. Which team scored more? Can we say that we can add integers in any order?

Solution:-


From the given scores, we can calculate the total score for each team as follows:


Team A: 40+ 10+0=-30


Team B: 100-40--30


Both teams have the same total score of 30, so both teams has scored the same.


Regarding the second question, we cannot add integers in any order. The order of the integers matters when we are adding or subtracting them. For example, 1+2+3 is not the same as 3+2 +1. However, we can say that we can change the grouping of the integers while adding or subtracting them. This is known as the associative property of addition. For example. (1+2)+3


is the same as 1+ 12+3.


21. Fill in the blanks to make the following statements true.

 (-5)+(-8)=(-8)+()

Explanation:


Let us assume the missing integer be x, then we can set up the equation as follows:-


(-5)+(-8)=(-8)+(0)


Simplifying the left-hand side, we get:


-5-8=-13


Substituting this value into the equation, we get:


By adding 8 to both sides of the equation, we get


-13+8x


Simplifying the left-hand side, we get:


5=x


So the missing integer is-5, and we can substitute it into the equation to get


(-5)+(-8)=(-8)+(-5)


Explanation:


Let us assume the missing integer be x.

Then, =-53+x=-53


By sending 53 from LHS to RHS, it becomes-53


X-53


Now, substitute the x value in the blank place.


-53+(-53)=-106 [This equation is in the form of the Associative Law of Addition]



22.[13+ (-12)]+.........) = 13+ [-12)+(-7)]

Solution:-


Let us assume the missing integer be x.


Then.


=113+(-12))+(x)=13+ (-12)+(-7)1


= [13-12+(x) = 13 +1-12-7]


=[1]+(x)=13+1-19]


=1+(x)=13-19


=1+(x)=-6


By sending I from LHS to REIS, it becomes-1.


Now, substitute the s value in the blank place.


=113+(-12)]+(-7)=13+(-12)+(-7))... [This equation is in the form of Associative Property of Addition


23. (-4)+115+(-3)=1-4+15]+...........

Explanation:


Let's assume that the missing integer is x. Then we can write the equation as:


113+(-12) x 13+(-12)+(-7)


We can simplify the left-hand side by performing the addition inside the brackets first:


from both sides:

To solve for x, we need to isolate it on one side of the equation. We can do this by subtracting


Simplifying


Therefore, the missing integer is -7, and we can write the completed equation as:

113+(-12) (-7) - 13+ (-12)+(-7)


24. Find each of the following products: 3x (-1)


Explanation:


In this case, we are multiplying 3 and -1, which have different signs (positive and negative), so their product is negative. Specifically:


3x(-1)=-(381)


Now we can multiply the absolute values of 3 and 1, which are both 3.


Therefore, the product of 3 and -1 is-3-


25. (-1) x 225

Solution:-


we are multiplying -1 by 225. Since -1 is negative and 225 is positive, their product will be


negative. We can find the product by simply multiplying the absolute values of the integers, and then


adding the negative sign:


(-1) x 225=-225


Therefore, the product of (-1) and 225 is -225.


26.(-21) x (-30)

Explanation:


To find the product, we can simply multiply the absolute values of the integers and then add the positive sign:


(-21)x(-30)=630


Therefore, the product of (-21) and (-30) is 630.


27. (-316) x (-1)

Solution:


As we know the product of any number and -1 is the opposite of that number.


=-(316)


Therefore, the product of (-316) and (-1) is-316.


28. (-15) x0x-18)

Solution:


By the rule of multiplication of integers.


=(-15)x0x(-18)


Any number multiplied by 0 is equal to 0. Therefore,


=0


Therefore, the product of (-15),0, and (-18) is 0.


(1) (-12)x(-11) x (10) Solution:-


By the rule of multiplication of integers,


=(-12) (-11) x 10


When multiplying three integers, we can do it in any order. Therefore,


10x (-12) x (-11)


10 x 132 (-x


= 1320

Therefore, the product of (-12).(-11), and 10 is 1320.


29. 9x (-3)x(-6)

Solution:


By the rule of Multiplication of integers.


= 9x (-3)x(-6)


First, multiply the two numbers having the same sign.


9x18x ==+)]


= 162


Therefore, the product of 9. (-3), and (-6) is 162.


30. (-18) x (-5) x (-4)

Solution:-


By the rule of Multiplication of integers,


=(-18) x (-5) x (-4)


Multiply the three numbers having the same sign,


Therefore, the product of (-18), (-5), and (-4) is 360,


31. (-3)x(-6)x(-2)x(-1)

Solution:


By the rule of Multiplication of integers,


=(-3)x(-6)*(-2)x(-1)


= 36 x (-1)


-36


Therefore, (-3) x (-6) x (-2)x(-1)=-36.


32. Verify the following:

 18 x (7+(-3)] = [ 18 x 7] + [18 (-3)]

Explanation:


From the given equation, 18x17+(-3)=118x71 +18 x (-3))


We need to simplify both sides of the equation and show that they are equal. Starting with the left-hand side


18x17+(-3))


We simplify the expression inside the brackets first, since the minus sign in front of the 3 means that we need to subtract 3 from 7:


= 18 x 17-3]


18x4

-72


Now, lets simplify the right-hand side of the equation


[18x7]+[18 x (-3)1


Multiplying 18 by 7 gives


= 126


Multiplying 18 by -3 gives:


=-54


Adding these two values together.


=126+(-54)


=72


As we can see, the left-hand side and the right-hand side both simplify to 72, which means that


18x (7+(-3)=118x7]+118x (-3))


is true. Therefore, we have verified the statement.


33. (-21) x [(-4)+(-6)] = [(-21) x (-4))+(-21) (-6))

Explanation:

Starting with the left-hand side of the equation:


(-21)x((-4)+(-6)]


First, we simplify the expression inside the parentheses by adding the two terms:


Next, we multiply-21 by-10.


210


So the left-hand side simplifies to 210


Now, let's simplify the right hand side of the equation:


1-21)x(-4)+(-21) x (-60


We can use the distributive property of multiplication over addition to simplify this expression:


(84)+(126)


Ackling these two terms, we get:


210


So the right-hand side simplifies to 210 as well.


Since both sides of the equation simplify to the same value (210), we can verify that the equation


is true:


(-21)x-4)+(-6)=(-21)x(-4)+(-21) (-6))


is true.


34.For any integer a, what is (-1) x a equal to?

Explanation:


For any integer a. (-1) x a is equal to the additive inverse of a, which means the opposite of a.


In other words, (-1) x ama


This is because multiplying any number by -1 simply negates the value of the number, making it

the opposite of what it was before.


35. Determine the integer whose product with (-1) is -22

Explanation:-

Lets be the integer whose product with (-1) is -22. Then we have:


(-1) xx=-22


Multiplying both sides by (-1), we get:


(-1)*(-1) xx=(-1) x (-22)


Simplifying the left-hand side using the fact that (-1) x (-1)=1, we get:


x=22


Therefore, the integer whose product with (-1) is -22 is 22.


36. Starting from (-1) x 5, write various products showing some pattern to show (-1)x(-1)=1.


Explanation:


The various products are


Starting from (-1) x 5, we can use the distributive property of multiplication to find other products that show the pattern we're looking for:


(-11x5=-5


(-1)x(-5)=5


(-1)x(-1)x(-5)=(-1)x5=-5


Continuing in this way, we see that every time we multiply by (-1), the sign of the product flips. So when we multiply three (1)'s together, the signs cancel out and we're left with a positive


product:


Therefore, we have shown that (-1) x (-1) = 1.


37. Find the product using suitable properties: (a) 26 x (48)+(-48) x (-36)

Explanation:


The given equation is in the form of the Distributive Law of Multiplication over Addition =ax(b+c)=(axh)+(axc) Let. a48, b26.c -361


Now


=26x-48)+(-48)x(36)


=-48 x (26+(-36)


=-48 x (26-36) =-48 × (-10)


480 (x=+) (b) 8 x 53 x (-125)


Explanation:


The given equation is in the form of the Commutative Law of Multiplication. We can use the distributive property of multiplication over addition to simplify this expression.

26x(48)+(-48) × (36)


=(26+(-48))x(-48) // factor out-48 using distributive property


= (26-48) x (48) // simplify the addition inside the purentheses


= (-22) × (--48) // simplify further


Now we can use the commutative and associative properties of multiplication to rearrange and group the factors in a convenient way:


(-22)x(-48)


=(-1) x 22 x (-1) x 48


=(-1)x(-1) x 22 x 48)


= 22 x 48


1056


Therefore,


26 × (48)+(-48) x (-36) = 1056.


(c) 15 x (-25) x (-4)x(-10)


Explanation:


We can use the commutative and associative properties of multiplication to simplify the expression:


15x(-25)*(-4)*(-10)


15x-1)x(-25) x (-4)x(-1)x(-10)


=(15x-1x-1)x(-25x-4x-10)


= 15 x 1x (250)


=-3750


Therefore, 15 x (-25)(-4)x-10)=-3750.


38. (-17) x (-29)

Explanation:


To find the product of (-17) and (-29), we can use the commutative and associative properties of


multiplication as follows:


(-17)x(-29)=(-29) x (17)


We can also use the fact that the product of two negative numbers is positive:


(-17) x (-29) 17 x 29


So now we just need to multiply 17 and 29:


17 x 29-493


Therefore, (-17) x (-29)=493,


(h) (-57)x(-19)+57


Explanation:


We can use the distributive property of multiplication over addition to simplify this expression31/52


(-57) (-19)+57=(-57) x (-19)+57 x 1


Now we can factor out 57:


= 57 × (1-19 x(-1))


=57 × (1+19)


=57x20


1140


Therefore, (-57) x (-19)+57=1140,


39. A certain freezing process requires that room temperature be lowered from 40°C at the rate of 5°C every hour. What will be the room temperature 1) hours after the process begins?

Explanation:


Initial room temperature = 40°C rate at which temperature decreases 5°C/hour


then temperature after 1 hour is given by.


40°C -5°C = 35°C


After 2 hours, the temperature will be:


35°C -3°C = 30°C We can continue this pattern to find the temperature after 10 hours


Temperature after 3 hours 37°C -3°C 25°C


Temperature after 4 hours 25°C -5°C 20°C Temperature after 5 hours 20°C-3°C 15°C


Temperature after 6 hours 15°C -5°C 10°C.


Temperature after 7 hours 10°C-5°C 5°C


Temperature after 8 hours SC-S°C=0°C Temperature after 9 hours PC-5°C -5°C

Temperature after 10 hours = -5°C -5°C -10°C


Therefore, the room temperature 10 hours after the process begins will be-10°C


40.Heena gets two correct and five incorrect answers out of seven questions she attempts. What is her score?

Explanation:


Heena attempted 7 questions and got 2 correct and 5 incorrect answers. Each correct answer is worth 5 marks, and each incorrect answer deducts 2 marks from her score. The questions that she did not attempt will not affect her score. Therefore, Heena's score can be calculated as:


2 correct answers x 5 marks per correct answer = 10 marks


33/52


5 incorrect answers x (-2) marks per incorrect answer = -10 marks


Total score 10-10=0) marks


Therefore, Heena's score is 0 marks.


Question &. A cement company earns a profit of 28 per bag of white cement sold and a loss of


41. Evaluate each of the following.

(-30)+10.

Explanation:


(-30)+10


When we divide a negative number by a positive number, the result is always negative.


(-30)+10=-3


Therefore, (-30)-10-3.


42. 50+(-5)

Explanation:


To evaluate 50+(-5), we need to perform the division operation.


Dividing 50 by a negative number, in this case. 5. results in a negative quotient.


So, 50+(-5)=-10.


Therefore, the value of the expression 50+1-5) is -10.


43. (-36)+(-9)

Explanation:


To evaluate (-36) (-9), we need to perform the division operation.


Dividing a negative number by another negative number results in a positive quotient


So, (-36)+(-9)=4


Therefore, the value of the expression (36) + (-9) is 4


44. (-49) + (49) 

Explanation:


To evaluate (49)+(49), we need to perform the division operation.


Dividing a negative number by a positive number results in a negative number.


So, (-49)+(49)=-1


Therefore, the value of the expression (49) - (49) is -1.


45. 13+ ((-2)+1) 

Explanation:


To evaluate 13+ [(-2)+1], we need to perform the addition operation inside the parentheses first, and then perform the division operation.


(-2)+1=-1, so we can substitute this back into the original expression to get:


13-(-1)


Dividing by -1 is the same as multiplying by -1, which changes the sign of the quotient.


So, 13(-2)+11=-13,


Therefore, the value of the expression 13+ [(-2)+1) is-13.)


(D) 0+(-12) Explanation:


To evaluate 0+(-12), we need to perform the division operation.


Dividing by a negative number, in this case, -12, results in 0.


So, 0+(-12)=0.


Therefore, the value of the expression ()+(-12) is 0.



46. Evaluate each of the following. (-30)+10.


Explanation:


 (-30)+10


When we divide a negative number by a positive number, the result is always negative.


(-30)+10=-3


Therefore, (-30)-10-3.


47. 50+(-5) 

Explanation:


To evaluate 50+(-5), we need to perform the division operation.


Dividing 50 by a negative number, in this case. 5. results in a negative quotient.


So, 50+(-5)=-10.


Therefore, the value of the expression 50+1-5) is -10.


48. Write five pairs of integers (a, b) such that a+b=-3. One such pair is (6,-2

Explanation:

These are five pairs of integers (a, b) such that a+b=-3


1. (-9,3) because (9)+3=-3

2. (-15.5) because (-15)+5=-3

3. (248) because 24+ (-8)=-3

4. (60,-20) because 60+(-20)=-3 5. (-27.9) because (-27)+9=-3


49. The temperature at 12 noon was 10°C above zero. If it decreases at the rate of 2°C per hour until midnight, at what time would the temperature be 8°C below zero? What would be the temperature at midnight?

Explanation:


The temperature at 12 noon was 100€ above zero. It decreases at the rate of 20C/hour until


midnight.


Let's first find out how many hours it takes for the temperature to decrease by 186C (106C +


SoC) since we want to find the time at which the temperature will be SoC below zero.


The decrease in temperature per hour is 2oC, and we want to know the time it takes to decrease


the temperature by 180C, so


Time = Decrease in temperature - Decrease per hour


Time = 18+2 Time=9


So it will take 9 hours for the temperature to decrease by 180C. If it starts at 12 noon, it will


reach SoC below zero at 9 pm (12+9=21).


The temperature decreases by 20C per hour, so from 12 noon to midnight, it decreases by


Temperature decrease Decrease per hour x Number of hours


Temperature decrease = 2x 12 Temperature decrease = 24


The temperature was initially 100C above zero, so to find the temperature at midnight, we need to subtract 100C from the decrease in temperature:


Temperature at midnight - Initial temperature - Temperature decrease Temperature at midnight-10-24 Temperature at midnight=-14


Therefore, the temperature at midnight would be-140C.


50. In a class test, (+3) marks are given for every correct answer and (-2) marks are given for every incorrect answer and no marks for not attempting any question. Radhika scored 20 marks. If she has got 12 correct answers, how many questions has she attempted incorrectly? 

Explanation:


Let's denote the number of questions Radhika attempted with "x". We know that she got 12


correct answers, so the number of incorrect answers she attempted is "x-12"


According to the given scoring system. Radhika got (+3) marks for every correct answer, which


gives her a total of 3 x 12=36 marks.


For every incorrect answer, she got (-2) marks, which means she lost 2 x (x-12)=2x-24 marks


She got a total of 20 marks, so we can write the equation:


36-(2x-24)=20


Simplifying and solving for "x":


x=16


So Radhika attempted a total of 16 questions and answered (12) correctly. The number of questions she answered incorrectly is:


16-12-4


Therefore, Radhika attempted 4 questions incorrectly.


51. An elevator descends into a mine shaft at the rate of 6 m/min. If the descent starts from 10 m above the ground level, how long will it take to reach - 350 m

Explanation:


The elevator is descending at a rate of 6 m/min. Let's take the time taken to reach a depth of -350 m as "t" minutes.


According to question: At the start of the descent, the elevator is at a height of 10 m above the ground level. So, the total


distance the elevator needs to travel is: Total distance = height of starting point - depth of endpoint


Total distance=10+350 Total distance = 360 m


We know that the speed of the elevator is 6 m/min. Therefore, we can write the equation:


Total distance = speed x time


360=6t


So, it will take 60 minutes for the elevator to reach a depth of 350 m.


Therefore, the elevator will take 60 minutes or 1 hour to reach a depth of -350 m.