Exercise 6.1
1. Write opposites of the following:
(a) Increase in weight
Solution: Decrease in weight
Solution: Decrease in weight
(b) 30 km North
Solution: 30 km South
Solution: 30 km South
(c) 326 BC
Solution: 326 AD
Solution: 326 AD
(d) Loss of ₹700
Solution: Profit of ₹700
Solution: Profit of ₹700
(e) 100 m above sea level.
Solution: 100 m below sea level.
Solution: 100 m below sea level.
2. Represent the following numbers as integers with appropriate signs.
(a) An aeroplane is flying at a height two thousand metre above the ground.
Solution: +2000 m
Solution: +2000 m
(b) A submarine is moving at a depth, eight hundred metre below the sea level.
Solution: -800 m
Solution: -800 m
(c) A deposit of rupees two hundred.
Solution: + ₹200
Solution: + ₹200
(d) Withdrawal of rupees seven hundred.
Solution: – ₹700
Solution: – ₹700
3. Represent the following numbers on a number line:
(a) +5
(b) -10
(c) +8
(d) -1
(e) -6
4. Adjacent figure is a vertical number line, representing integers. Observe it and locate the following points:
(a) If point D is +8, then which point is -8?
Solution: Point F represents -8.
Solution: Point F represents -8.
(b) Is point G a negative integer or a positive integer?
Solution: G is a negative integer (as it is below 0).
Solution: G is a negative integer (as it is below 0).
(c) Write integers for points B and E.
Solution: B represents +4 and E represents – 10.
Solution: B represents +4 and E represents – 10.
(d) Which point marked on this number line has the least value?
Solution: Point E has the least value of -10.
Solution: Point E has the least value of -10.
(e) Arrange all the points in decreasing order of value.
Solution: Decreasing order of all the points are: D, C, B, A, O, H, G, F and E.
Solution: Decreasing order of all the points are: D, C, B, A, O, H, G, F and E.
5. Following is the list of temperatures of five places in India on a particular day of the year.
(a) Write the temperatures of these places in the form of integers in the blank column.
(b) Following is the number line representing the temperature in degree Celsius.
Plot the points on the number line corresponding to their temperatures.
(c) Which is the coolest place?
Solution: Siachen is the coolest place with -10°C temperature.
Solution: Siachen is the coolest place with -10°C temperature.
(d) Write the names of the places where temperatures are above 10°C.
Solution: (i) Delhi → 20°C, (ii) Ahmedabad → 30°C.
Solution: (i) Delhi → 20°C, (ii) Ahmedabad → 30°C.
6. In each of the following pairs, which number is to the right of the other on the number line?
(a) 2, 9 → 9 is to the right of 2
(b) -3, -8 → -3 is to the right of -8
(c) 0, -1 → 0 is to the right of – 1
(d) -11, 10 → 10 is to the right of -11
(e) -6, 6 → 6 is to the right of -6
(f) 1, -100 → 1 is to the right of -100
7. Write all the integers between the given pairs (write them in the increasing order):
(a) 0 and -7
Solution: -6, -5, -4, -3, -2, -1.
Solution: -6, -5, -4, -3, -2, -1.
(b) -4 and 4
Solution: -3, -2, -1, 0, 1, 2, 3.
Solution: -3, -2, -1, 0, 1, 2, 3.
(c) -8 and -15
Solution: -14, -13, -12, -11, -10, -9.
Solution: -14, -13, -12, -11, -10, -9.
(d) -30 and -23
Solution: -29, -28, -27, -26, -25, -24.
Solution: -29, -28, -27, -26, -25, -24.
8. (a) Write four negative integers greater than -20. (b) Write four negative integers less than – 10.
(a) Write four negative integers greater than -20.
Solution: -19, -18, -17, -16.
Solution: -19, -18, -17, -16.
(b) Write four negative integers less than -10.
Solution: -11, -12, -13, -14.
Solution: -11, -12, -13, -14.
9. For the following statements, write True (T) or False (F). If the statement is false, correct the statement.
(a) – 8 is to the right of – 10 on a number line.
Solution: True (T)
Solution: True (T)
(b) – 100 is to the right of -50 on a number line.
Solution: False (F). Correction: -100 is to the left of -50.
Solution: False (F). Correction: -100 is to the left of -50.
(c) Smallest negative integer is – 1
Solution: False (F). Correction: There is no smallest negative integer.
Solution: False (F). Correction: There is no smallest negative integer.
(d) – 26 is greater than – 25.
Solution: False (F). Correction: -26 is smaller than -25.
Solution: False (F). Correction: -26 is smaller than -25.
10. Draw a number line and answer the following:
(a) Which number will we reach if we move 4 numbers to the right of -2?
Solution: We will reach 2.
(b) Which number will we reach if we move 5 numbers to the left of 1?
Solution: We will reach -4.
(c) If we are at -8 on the number line, in which direction should we move to reach -13?
Solution: We should move to the Left.
(d) If we are at -6 on the number line, in which direction should we move to reach -1?
Solution: We should move to the Right.