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Q1. Fill in the blanks with appropriate symbols ‘>' or ‘<' (i) -9 ___ -15 (ii) -10 ___ 10 (iii) 0 ___ 3 (iv) -28 ____ 17

Solution

(i) -9 > -15 (ii) -10 < 10 (iii) 0 < 3 (iv) -28 < 17

Q2. If a = -9, b = -6. Show that (a - b) ≠  (b - a)

Solution

(a - b) = -9 - (-6) = -9 + 6 = -3 (b - a) = -6 - (-9) = -6 + 9 = 3 Here, -3 ≠ 3 So, a - b ≠ b - a

Q3. The sum of two integers is 65 and one of them is -31. Find the integer which is 12 more than the other integer?

Solution

Sum of two integers is 65 and one of them is -31. Let the other integer be a Then, a + (-31) = 65   ....(Given) a - 31 = 65 Thus, a = 65 + 31 = 96 Now, the required integer is 12 more than 96. Thus, required integer = 96 + 12 = 108

Q4. A cooling machine requires that room temperature to be lowered from 50^oC at the rate of 5^oC every hour. What will be the room temperature after 8 hours of starting the process?

Solution

Room temperature at the beginning of the process = 50^oC Rate of lowering the temperature = 5^oC every hour Temperature lowered after 8 hours= 5 × 8 = 40^oC Room temperature after 8 hours = 50^oC - 40^oC = 10^oC

Q5. Which is the smaller integer in each of the following: (i) 6, -7 (ii) -13, -27 (iii) -26, 17 (iv) 0, -1

Solution

(i) -7 (ii) -27 (iii) -26 (iv) -1

Q6. Find the value of the following expression using suitable property: 725 × (-35) + (-725) x 65

Solution

725 × (-35) + (-725) × 65= 725 × (-35) - 725 × 65= 725 x (-35 - 65)         [Using distributive property] = 725 × (-100) = -72500

Q7. Write an integer to represent each situation: (i) 10 degrees above zero (ii) a loss of 16 dollars (iii) a gain of 5 points (iv) 8 steps backward

Solution

(i) +10 (ii) -16 (iii) +5 (iv) -8

Q8. A scientist cools two samples of bacteria to see effect of temperature on two samples. He cools one sample to -53^oC and the other to -42^oC in the laboratory. Which sample is colder and by how much?

Solution

The temperature to which first sample is cooled = -53^oCThe temperature to which second sample is cooled = -42^oCSince -53^oC < -42^oC                So the first sample is colder than the second one.                                                        And, temperature difference = -53 - (-42) = -53 + 42 = -11°C                                                   

Q9. Find 36 - (-64) and (-64) - 36. Are these equal?

Solution

36 - (-64) = 36 + 64 = 100 -64 - 36 = -100 Since, 100 ≠ -100, they are not equal.

Q10. Multiply (-251) × 97 by using suitable property.

Solution

For simplification, write 97 as 100 - 3 Thus, -251 x (100 - 3) Now, by using distributive property of multiplication over subtraction, we get = (-251 × 100) - (-251 × 3) = -25100 + 753 = -24347

Q11. Find the sign of the product, if we multiply 7 negative and 4 positive integers.

Solution

When 7 negative integers are multiplied, the result is a negative integer as we are multiplying odd number of negative integers. When 4 positive integers are multiplied, the result is a positive integer as we are multiplying even number of positive integers. Multiplication of a negative and a positive integer is negative. So, result is a negative integer.

Q12. In a competitive exam, containing 24 questions, 5 marks are awarded for every correct answer and (-2) marks are awarded for every incorrect answer. There are 0 marks for questions not attempted. Raveena attempted 16 correct and 8 incorrect answers. Find her score in an exam?

Solution

Marks for the correct answer = 5 Marks for the incorrect answer = -2 Marks for the questions not attempted = 0 Marks for 16 correct answers = 16 × 5 = 80 Marks for the 8 incorrect answers = -2 × 8 = -16 Total marks awarded to Raveena = 80 + (-16) = 80 - 16 = 64

Q13. Verify: (-10) ×[16 + (-36)] = [(-10)×16] + [(-10) × (-36)]

Solution

(-10) ×[16 + (-36)] = [(-10)×16] + [(-10) × (-36)] L.H.S. = (-10) × [16 + (-36)] = -10 × [16 - 36]  = -10 × [-20] = 200 R.H.S. = [(-10) × 16] + [(-10) × (-36)] = -160 + 360 = 200   Hence, L.H.S. = R.H.S.

Q14. What will you get on subtracting -134 from the sum of 38 and -87?

Solution

Sum of 38 and -87 = 38 + (-87) = 38 - 87 = -49 Subtracting (-134) from -49, we get -49 - (-134) = -49 + 134 = 85

Q15. Simplify {-13 - (-27)} + {-25 - (-40)}

Solution

{-13 - (-27)} + {-25 - (-40)} = {-13 + 27} + {-25 + 40} = {14} + {15} = 14 + 15 = 29

Q16. If a = -8, b = -7, c = 6, then verify that (a + b) + c = a + (b + c).

Solution

Given: a = -8, b = -7, c = 6 (a+ b) + c = [(-8) + (-7)] + 6 = -15 + 6 = -9a + (b + c) = (-8) + [(-7) + 6] = -8 - 1 = -9 Hence, (a + b) + c = a + (b + c).

Q17. Verify: (-25) x {(-9) - (-4)} = (-25) x (-9) - (-25) x (-4)

Solution

L.H.S. = (-25) x {(-9) - (-4)} = (-25) x {-9 + 4} = (-25) x (-5) = 125 R.H.S. = (-25) x (-9) - (-25) x (-4) = 225 - 100 = 125 Hence, L.H.S. = R.H.S.

Q18. Write the opposite of each of the following: (i) Going 7 m to the East (ii) 10 km above sea level 

Solution

(i) Going 7 m to the West (ii) 10 km below sea level

Q19. A cloud is at a height of 4000 m above the sea level. At a particular point, it is exactly above a submarine which is floating 2400 m below the sea level. What is the vertical distance between them?

Solution

Height above sea level = +4000 m Distance below sea level = -2400 m Distance in Between =4000 - (-2400) = 4000 + 2400 = 6400 m Thus, the vertical distance between cloud and submarine is 6400 m.

Q20. What is the arrangement of integers -7, -10, 0, -11, 14, 24 in ascending order?

Solution

-7, -10, 0, -11, 14, 24 Ascending order means arranging the numbers from smallest to highest.Smallest number is the highest negative number, which is -11.Then the highest negative number from the remaining numbers is -10 followed by -7.0 is greater than negative numbers and smaller than positive numbers.Among two positive numbers, 14 is smaller than 24.So the arrangement in ascending order is -11, -10, -7, 0, 14, 24.                 

Q21. A Chemical is unstable at room temperature, so it is kept in a refrigerator at -38^oC. Once removed from the fridge, its temperature rises at a rate of 4^oC per minute. Assuming a bottle of the chemical was exactly -38^oC when removed from the fridge, what will its temperature be five minutes after removal from the fridge?

Solution

The temperature at which the chemical is stored = -38^oC        The rate of rise of temperature after the sample is removed from refrigeration= 4^oC per minute                                                        Rise in temperature after 5 minutes = 4x5 = 20^oC                         Net temperature of the chemical after 5 minutes = -38 + 20                                                                              =  -18^oC

Q22. Simplify : (-25 - 26) - (35 - 40)

Solution

(-25 - 26) - (35 - 40) = (-51) - (-5) = -51 + 5 = -46

Q23. Find the sign of the product, if we multiply 5 negative and 6 positive integers?

Solution

When 5 negative integers are multiplied, the result is a negative integer as we are multiplying odd number of negative integers.When 6 positive integers are multiplied, the result is obviously positive integer.Multiplication of a negative and a positive integer is negative.So, result is a negative integer.

Q24. In a building, there are 9 floors above ground and 4 floors below the ground. An elevator starts ascending from the second floor below the ground. If the elevator reaches each floor in 3 minutes, where would it be 15 minutes after the start? (Assume that elevator stops at each floor)

Solution

Number of floors above the ground level = 9Number of floors below the ground level = 4The floor from which the elevator starts ascending = -2 floorRate of ascending = 3 minutes per floor                Number of floors covered in 15 minutes = 15 /3 = 5 floors    Now, starting form -2 floors, 5 floors covered would be(-2) + 5 = 3 floors from the ground level.Thus, elevator will be above 3 floors from the ground after 15 minutes of the start.

Q25. What is the arrangement of integers -30, -25, -15, -5, 0, 5 in descending order?

Solution

Descending order means arranging the numbers from greatest to smallest.Greatest number is the highest positive number which is 5.Then the highest number from the remaining numbers is 0.Now, the greatest integer is the least negative number from the remaining integers which is -5 followed by -15, -25 and -30. Thus, the arrangement in descending order is 5, 0, -5, -15, -25, -30.

Q26. Multiply (-51) × 197 by using suitable property

Solution

For simplification, write 97 as 100 - 3Thus, -51 x (100 - 3)Now, by using distributive property of multiplication over subtraction, we get= (-51 × 100) - (-51 × 3)= -5100 + 153= -4947

Q27. Find the value of the following expression using suitable property:725 × (105) + (-725) x 55

Solution

725 × (105) + (-725) × 55= 725 × 105 - 725 × 55= 725 x (105 - 55)         [Using distributive property]= 725 × (50)= 36250

Q28. In three rounds of a quiz, Reena scored -10, 5 and 25. Find her final score.

Solution

Final score of Rena = -10 + 5 + 25 = -5 + 25 = 20

Q29. An electrical company earns a profit of Rs. 80 on every color TV and loss of Rs 60 on every refrigerator. The Company sold 5000 pieces of color TV and 4000 pieces of refrigerator in a month. What is its profit or loss?

Solution

Money earned on each color TV = Rs. 80 Money loosed on each refrigerator = Rs. 60 Total money earned on selling 5000 color TV = 5000 × 80 = Rs. 400000 Total money loosed on selling 4000 refrigerators = 4000 × 60 = Rs. 240000 Since money earned on selling color TV is more, the company makes a profit. Total money earned = 400000 + (-240000) = Rs. 160000

Q30. Write true or false: (i) -8 lies to the right of 0 on number line. (ii) 9 > -9. (iii) 0 is an integer. (iv) -1 is the smallest negative integer.

Solution

(i) False (ii) True (iii) True (iv) False