GSEB Class 7 Maths Solutions Chapter 1 પૂર્ણાંક સંખ્યાઓ Exercise 1.1

Question 1. Following number line shows the temperature in degree Celsius (°C) at different places on a particular day.
(a) Observe this number line and write the temperature of the places marked on it.
(b) What is the temperature difference between the hottest and the coldest places among the above?
(c) What is the temperature difference between Lahulspiti and Srinagar?
(d) Can we say temperature of Srinagar and Shimla taken together is less than the temperature at Shimla? Is it also less than the temperature at Srinagar?
Answer:
(a) The temperatures are: Bangalore: \( 22^\circ\text{C} \), Ooty: \( 14^\circ\text{C} \), Shimla: \( 5^\circ\text{C} \), Srinagar: \( -2^\circ\text{C} \), Lahulspiti: \( -8^\circ\text{C} \).
(b) Hottest place is Bangalore (\( 22^\circ\text{C} \)) and coldest is Lahulspiti (\( -8^\circ\text{C} \)). Difference = \( 22^\circ\text{C} - (-8^\circ\text{C}) = 22^\circ\text{C} + 8^\circ\text{C} = 30^\circ\text{C} \).
(c) Difference = \( -2^\circ\text{C} - (-8^\circ\text{C}) = -2^\circ\text{C} + 8^\circ\text{C} = 6^\circ\text{C} \).
(d) Sum of Srinagar and Shimla = \( -2^\circ\text{C} + 5^\circ\text{C} = 3^\circ\text{C} \). Since \( 3^\circ\text{C} < 5^\circ\text{C} \), it is less than Shimla's temperature. However, \( 3^\circ\text{C} > -2^\circ\text{C} \), so it is not less than Srinagar's temperature.
In simple words: Read the values from the number line carefully. To find the difference, subtract the smaller number from the larger one.

Exam Tip: Always remember that subtracting a negative number is the same as adding a positive number.

Question 2. 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?
Answer: Total score = \( 25 + (-5) + (-10) + 15 + 10 = 25 - 5 - 10 + 15 + 10 = 35 \). Hence, Jack's total score is 35.
In simple words: Add all the positive scores together and subtract all the negative scores to get the final total.

Exam Tip: Grouping positive and negative numbers separately makes the addition much faster and reduces calculation errors.

Question 3. At Srinagar, temperature was – 5°C on Monday and then it dropped by 2°C on Tuesday. What was the temperature of Srinagar on Tuesday? On Wednesday, it rose by 4°C, then what was the temperature on this day?
Answer: Temperature on Monday = \( -5^\circ\text{C} \). Temperature on Tuesday = \( -5^\circ\text{C} - 2^\circ\text{C} = -7^\circ\text{C} \). Temperature on Wednesday = \( -7^\circ\text{C} + 4^\circ\text{C} = -3^\circ\text{C} \).
In simple words: When the temperature drops, subtract from the current value. When it rises, add to the current value.

Exam Tip: Be careful with negative numbers; dropping temperature means moving further left on the number line.

Question 4. A plane is flying at the height of 5000 m above the sea level. At a particular point, it is exactly above a submarine floating 1200 m below the sea level. What is the vertical distance between them?
Answer: Distance of plane from sea level = 5000 m. Distance of submarine from sea level = 1200 m. Total vertical distance = \( 5000\text{ m} + 1200\text{ m} = 6200\text{ m} \).
In simple words: Since one is above sea level and the other is below, add their distances to find the total gap between them.

Exam Tip: Visualize the sea level as zero; anything above is positive and anything below is negative, so the distance is the absolute difference.

Question 5. Mohan deposits ₹ 2000 in his bank account and withdraws ₹ 1642 from it, the next day. If withdrawal of 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.
Answer: The amount deposited is represented by a positive integer. Balance = \( ₹ 2000 - ₹ 1642 = ₹ 358 \).
In simple words: Deposits add to your balance, while withdrawals subtract from it.

Exam Tip: Always identify the sign convention (positive for deposit, negative for withdrawal) before performing the calculation.

Question 6. Rita goes 20 km towards east from a point A to the point B. From B she moves 30 km towards west along the same road. If the distance towards east is represented by a positive integer, then, how will you represent the distance travelled towards west? By which integer will you represent her final position from A?
Answer: Distance towards west is represented by a negative integer. Final position = \( +20\text{ km} - 30\text{ km} = -10\text{ km} \). Her final position is represented by -10.
In simple words: Moving in the opposite direction is like subtracting from the original distance.

Exam Tip: Use a number line to represent directions; east is positive and west is negative.

Question 7. In a magic square each row, column and diagonal have the same sum. Check which of the following is a magic square.
Answer:
(i) Sums: Rows: \( 0, 0, 0 \); Columns: \( 0, 0, 0 \); Diagonals: \( 0, -6 \). Since diagonals are not equal, it is not a magic square.
(ii) Sums: Rows: \( -9, -9, -9 \); Columns: \( -9, -9, -9 \); Diagonals: \( -9, -9 \). Since all sums are -9, it is a magic square.
In simple words: A magic square must have the same total for every row, every column, and both main diagonals.

Exam Tip: Check every single row, column, and diagonal; if even one sum is different, it is not a magic square.

Question 8. Verify a – (-b) = a + b for the following values of a and b.
(i) a = 21, b = 18
(ii) a = 118, b = 125
(iii) a = 75, b = 84
(iv) a = 28, b = 11
Answer:
(i) L.H.S = \( 21 - (-18) = 21 + 18 = 39 \); R.H.S = \( 21 + 18 = 39 \). Verified.
(ii) L.H.S = \( 118 - (-125) = 118 + 125 = 243 \); R.H.S = \( 118 + 125 = 243 \). Verified.
(iii) L.H.S = \( 75 - (-84) = 75 + 84 = 159 \); R.H.S = \( 75 + 84 = 159 \). Verified.
(iv) L.H.S = \( 28 - (-11) = 28 + 11 = 39 \); R.H.S = \( 28 + 11 = 39 \). Verified.
In simple words: Subtracting a negative number is the same as adding a positive number.

Exam Tip: Always show both L.H.S and R.H.S separately to clearly demonstrate that they are equal.

Question 9. Use the sign of >,< or = in the box to make the statements true.
(a) (- 8) + (- 4) ☐ ( – 8) – (- 4)
(b) (- 3) + 7 – (19) ☐ 15 – 8 + (- 9)
(c) 23 – 41 + 11 ☐ 23 – 41 – 11
(d) 39 + (- 24) – (15) ☐ 36 + (- 52) – (-36)
(e) – 231 + 79 + 51 ☐ – 399 + 159 + 81
Answer:
(a) \( -12 < -4 \)
(b) \( -15 < -2 \)
(c) \( -7 > -29 \)
(d) \( 0 < 20 \)
(e) \( -101 > -159 \)
In simple words: Solve both sides first, then compare the final numbers to see which is larger.

Exam Tip: Remember that for negative numbers, the one with the smaller absolute value is actually larger.

Question 10. A water tank has steps inside it. A monkey is sitting on the topmost step (i.e., the first step). The water level is at the ninth step.
(i) He jumps 3 steps down and then jumps back 2 steps up. In how many jumps will he reach the water level?
(ii) After drinking water, he wants to go back. For this, he jumps 4 steps up and then jumps back 2 steps down in every move. In how many jumps will he reach back the top step?
(iii) 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 part (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?
Answer:
(i) The monkey reaches the ninth step in 11 jumps.
(ii) The monkey reaches the top step in 5 jumps.
(iii) (a) \( -3 + 2 - 3 + 2 - 3 + 2 - 3 + 2 - 3 + 2 - 3 = -8 \). (b) \( 4 - 2 + 4 - 2 + 4 = 8 \). The sum 8 represents going up by 8 steps.
In simple words: Track the monkey's position step-by-step for each jump until he reaches the target.

Exam Tip: Drawing a small diagram or table helps keep track of the monkey's position after each jump.

Question 10. (i) He jumps 3 steps down and then jumps back 2 steps up. In how many jumps will he reach the water level?
Answer: The monkey is sitting on the top (i.e., the first step). The position of the monkey after the 1st jump is at the fourth step, 2nd jump is at the second step, 3rd jump is at the fifth step, 4th jump is at the third step, 5th jump is at the sixth step, 6th jump is at the fourth step, 7th jump is at the seventh step, 8th jump is at the fifth step, 9th jump is at the eighth step, 10th jump is at the sixth step, and the 11th jump is at the ninth step, which is the water level. Thus, the required number of jumps is 11.
In simple words: The monkey moves down three steps and up two steps repeatedly. By following this pattern, he reaches the ninth step on his eleventh jump.

Exam Tip: Keep track of the monkey's position after every single jump to avoid missing a step in the sequence.

Question 10. (ii) After drinking water, he wants to go back. For this, he jumps 4 steps up and then jumps back 2 steps down in every move. In how many jumps will he reach back the top step?
Answer: The monkey's position is at the water level (the ninth step). The position of the monkey after the 1st jump is at the fifth step, 2nd jump is at the seventh step, 3rd jump is at the third step, 4th jump is at the fifth step, and the 5th jump is at the first (top) step. Thus, the required number of jumps is 5.
In simple words: To get back to the top, the monkey jumps up four steps and down two steps. He reaches the top in just five jumps.

Exam Tip: Remember that the monkey starts from the ninth step for the return journey, so calculate the jumps accordingly.

Question 10. (iii) 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 part (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?
Answer: In case (i), the total number of steps = – 3 + 2 – 3 + 2 – 3 + 2 – 3 + 2 – 3 + 2 – 3 = – 8. In case (ii), the total number of steps = 4 – 2 + 4 – 2 + 4 = 8. Also, in (a), the sum (- 8) represents going down by 8 steps. Therefore, in (b), the sum (+ 8) will represent going up by 8 steps.
In simple words: Negative numbers show moving down towards the water, and positive numbers show moving up towards the top. A total of 8 means he moved up 8 steps.

Exam Tip: Always check the sign convention given in the question; here, down is negative and up is positive.