Class 6 Maths Chapter 10 Extra Questions The Other Side of Zero
Class 6 Maths The Other Side of Zero Extra Questions
NCERT Class 6 Maths Chapter 10 The Other Side of Zero Extra Questions and Answers
Question 1.
State whether the following statements are True or False:
(a) The smallest natural number is zero.
(b) Zero is not an integer as it is neither positive nor negative.
(c) The sum of two negative integers is always smaller than both the integers.
(d) Since 5 > 3, therefore, -5 > -3.
Solution:
(a) False, the smallest natural number is 1.
(b) False, zero is an integer because integers are the collection of whole numbers and negative of counting numbers.
(c) True, (-1) + (-10) = (-11); -11 < -10 and -11 < -1. (d) False, since 5 > 3, so -5 < -3.
Question 2.
Fill in the blanks to make the following statements true:
(a) On the number line, -15 is to the ____ of zero.
(b) On the number line, 10 is to the ____ of zero.
(c) The additive inverse of -1 is ____.
(d) (-11) + (-2) + (-1) = ____.
Solution:
(a) On the number line, -15 is to the left of zero.
(b) On the number line, 10 is to the right of zero.
(c) The additive inverse of -1 is +1 or 1.
(d) (-11) + (-2) + (-1) = -14
Question 3.
Write 5 integers which are less than -100 but greater than -150.
Solution:
Here, -100 > -150 and difference -100 – (-150)
= -100 + 150 = 50
So, there lie (50 – 1) = 49 integers between -100 and -150.
Thus, we can write any five integers out of-101, -102, -103, …,-148,-149.
Question 4.
If profit is considered as positive, state the following as profit:
(a) Profit of ₹ 90
(b) Loss of ₹ 36.
Solution:
(a) ∵ Profit is considered as positive.
∵ Profit of ₹ 90 is a positive quantity.
⇒ Profit = ₹ (+90).
(b) ∵ Profit is considered as positive.
But loss is considered as negative.
∵ Loss of ₹ 36 is a negative quantity.
⇒ Loss of ₹ 36 = Profit of ₹(-36)
Question 5.
If depth is considered as positive, express the following as depth:
(a) 25 metres deep
(b) 45 metres height.
Solution:
(a) ∵ Depth is considered as positive.
∴ 25 metres deep is positive quantity.
⇒ 25 metres deep = (+25) metres depth.
(b) ∵ Depth is considered as positive.
∴ 45 metres height is negative depth.
⇒ 45 metres height = (-45) metres depth.
Question 6.
Using a number line, write an appropriate symbol ‘>’ or ‘<’ in each of the following boxes:
(i) -1 ___ 0
(ii) 0 ___ -2
(iii) -5 ___ -2
(iv) 4 ___ -5
Solution:
(i) Since (-1) is on the left of 0 on the number line, i.e. (-1) is less than 0,
∴ -1 < 0
(ii) Since, -2 is on the left of 0 on the number line, i.e. 0 is greater than -2,
∴ 0 > (-2)
(iii) Since, -5 is on the left of-2 on the number line, i.e. -5 is less than -2,
∴ -5 < -2
(iv) Since, 4 is on the right of-5 on the number line, i.e. 4 is greater than (-5),
∴ 4 > (-5)
Question 7.
Indicate the integer on the number line which is:
(i) 4 less than -1
(ii) 5 more than -2
Solution:
We know that the numbers goes on decreasing as we move towards left.
(i) 4 less than (-1) means moving towards left by 4 steps from (-1). We reach at (-5). A
We represent it on the number line as shown in this figure.
(ii) To represent 5 more than (-2), we start from (-2) and move five steps to the right and reach at 3.
Question 8.
Check whether the following are true.
(i) 3 + (0 + 9) = (3 + 0) + 9
(ii) 34 + {90 + (-11)} = (34 + 90) + (-11)
Solution:
(i) LHS = 3 +(0 + 9) = 3 + 9 = 12
RHS = (3 + 0)+ 9 = 3 + 9 = 12
∴ LHS = RHS
(ii) LHS = 34 + {90 + (-11)} = 34 + {90 – 11}
= 34 + 79 = 113
RHS = (34 + 90) + (-11) = 124 + (-11)
= 124 – 11 = 113
∴ LHS = RHS
Question 9.
Evaluate the following:
(i) 79 – 68 + 28 – (-32)
(ii) 153 + 218- {29 – (367)}
Solution:
(i) 79 – 68 + 28 – (-32) = 79-68 + 28 + 32
= (79 + 28 + 32) – 68
= 139 – 68
= 71
(ii) 153 + 218 – {29 – (367)} = 153 + 218 – {29 – 367}
= 153 + 218 – (-338)
= 153 + 218 + 338
= 709.
Question 10.
Fill in the blanks using <, = or >.
(a) (-11)+ (-15) ____ 11 + 15
(b) (-71) + (+9) ___ (-81) + (-9)
(c) (-101) ____ (-102)
(d) 1 + 2 + 3 ___ (-1) + (-2) + (-3)
Solution:
(a) (-11)+ (-15) = -26 and 11 + 15 = 26
Since, – 26 < 26, so (-11) + (-15) < 11 + 15
(b) (-71) + (+9) = – 62 and (-81) + (-9) = -90
Since, -62 > -90, so (-71) + (+9) > (-81) + (-9)
(c) Since, 101 < 102, so -101 > -102
(d) 1 + 2 + 3 = 6 and (-1) + (-2) + (-3) = -6
Since, 6 > -6, so 1 + 2 + 3 > (-1) + (-2) + (-3)
Question 11.
Complete the grid to make the required border sum.
Solution:
We can complete the grid as shown below.
