Exercise 2.1 - Chapter 2 Integers Term 3 6th Maths Guide Samacheer Kalvi Solutions - SaraNextGen [2024-2025]

Updated By SaraNextGen

On April 24, 2024, 11:35 AM

Question $1 .$
Fill in the blanks.
(i) The potable water available at $100 \mathrm{~m}$ below the ground level is denoted as ___$\mathrm{m}$.
Hint: Below ground level - negative; ground level $-0 ;$ above ground level - positive. 
(ii) A swimmer dives to a depth of 7 feet from the ground into the swimming pool. The integer that represents this, is $\quad$ feet.
Hint: Below ground level $-$ negative numbers.
(iii) $-46$ is to the of $-35$ on the number line.
Hint: $-46<-35$ integers from $-5$ to $+5$ (both inclusive).
(iv) There are integers from $-5$ to $+5$ (both inclusive).

(v) _____is an integer which is neither positive nor negative.

Solutions:
(i) $-100$
(ii) $-7$
(iii) Left
(iv) 11
(v) 0
 

Question 2 .
Say True or False.
(i) Each of the integers $-18,6,-12,0$ is greater than $-20$.
(ii) $-1$ is to the right of 0 .
(iii) $-10$ and 10 are at equal distance from 1 .
(iv) All negative integers are greater than zero.
(v) All whole numbers are integers.

Solution:

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

Question $3 .$
Mark the numbers $4,-3,6,-1$ and $-5$ on the number line.
Solution:

Question $4 .$
On the number line, which number is
i) 4 units to the right of-7?
ii) 5 units to the left of 3 ?
Solution:

(i) $-3$ is 4 units to the right of $-7$
(ii) $-2$ is 5 units to the left of 3

Question $5 .$
Find the opposite of the following numbers.
(i) 44
(ii) $-19$
(iii) 0
(iv) $-312$
(v) 789
Solution:
(i) Opposite of 44 is $-44$
(ii) Opposite of- 19 is $+19$ or 19
(iii) Opposite of 0 is 0
(iv) Opposite of- 312 is $+312$ or 312
(v) Opposite of 789 is $-789$.
 

Question $6 .$
If $15 \mathrm{~km}$ east of a place is denoted as $+15 \mathrm{~km}$, what is the integer that represents $15 \mathrm{~km}$ west of it?
Solution:
Opposite of east is west.
$\therefore$ If $15 \mathrm{~km}$ east is $+15 \mathrm{~km}$, then $15 \mathrm{~km}$ west is $-15 \mathrm{~km}$.

Question 7.

From the following number lines, identify the correct and the wrong representations with reason?

Solution:
(i) This representation is wrong. Because the numbers are not continuously marked as $-6,-5,-4,-3,-2,-1$, $0,1,2,3,4,5,6$,
(ii) This is the correct representation of Integers
(iii) The representation is wrong. $-2$ is misplaced in the number line.
(iv) This representation is correct as the numbers are marked at equal intervals in the correct order.
(v) Here negative integers are marked wrongly to the left of 0

Question 8 .
Write all the integers between the given numbers.
(a) 7 and 10
(b) $-5$ and 4
(c) $-3$ and 3
(d) $-5$ and 0
Solution:

Question $9 .$
Put the appropriate signs as $<,>$ or $=$ in the box?
i) $-7 \square 8$
ii) $-8 \square-7$
iii) $-999 \square-1000$
iv) $-111 \square-111 \quad$ v) $0 \square-200$

Solution:

Question 10 .
Arrange the following integers in ascending order.
i) $-11,12,-13,14,-15,16,-17,18,-19,-20$
ii) $-28,6,-5,-40,8,0,12,-1,4,22$
iii) $-100,10,-1000,100,0,-1,1000,1,-10$
Solution:
(i) $-11,12,-13,14,-15,16,-17,18,-19,-20$
- First separating the positive integers $12,14,16,18$ and the negative integers $-11,-13,-15,-17,-19,-20$.
- Then arranging the positive integers in ascending order we get $12,14,16,18$ and negative integers in ascending order as $-20,-19,-17,-15,-13,-114$
- Now the ascending order: $-20,-19,-17,-15,-13,-11,12,14,16,18 .$
(ii) $-28,6,-5,-40,8,0,12,-1,4,22$
- Positive integers are $6,8,12,4,22$ Negative integers are $-28,-5,-40,-1$
- Arranging the positive integers in ascending order we get $4,6,8,12,22$ and the negative integers in ascending order $-40,-28,-5,-1$
- The number 0 is neither positive nor negative and stand in the middle.
- In ascending order : $-40,-28,-5,-1,0,4,6,8,12,22$
(iii) $-100,10,-1000,100,0,-1,1000,1,-10$
- Separating positive integers $10,100,1000,1$ and negative integers $-100,-1000,-1,-10$.
- Now the positive integers in ascending order $1,10,100,1000$ and the negative integers in ascending order. $-1000,-100,-10,-1$

- Also ' 0 ' stand in the middle as its is neither positive nor negative.
- $\therefore$ The numbers in ascending order: $-1000,-100,-10,-1,0,1,10,100,1000$.

Question $11 .$
Arrange the following integers in descending order.
i) $14,27,15,-14,-9,0,11,-17$
ii) $-99,-120,65,-46,78,400,-600$
iii) $111,-222,333,-444,555,-666,7777,-888$
Solution:
(i) $14,27,15,-14,-9,0,11,-17$
- Separating the positive integers $14,27,15,11$ and negative integers $-14,-9,-17$
- Arranging in descending order we get the positive integers $27,15,14,11$ and the negative integers $-9$, $-14,-17 .$
- ' 0 ' is neither positive nor negative and so it stand in middle.
- $\therefore$ The numbers in descending order: $27,15,14,11,0,-9,-14,-17$
(ii) $-99,-120,65,-46,78,400,-600$
- Separating the positive integers $65,78,400$ and negative integers $-99,-120,-46,-600$
- Arranging the positive integers in descending order as $400,78,65$ and the negative integers in descending order $-46,-99,-120,-600$.
- The numbers in descending order : $400,78,65,-46,-99,-120,-600$.
(iii) $111,-222,333,-444,555,-666,7777,-888$
- Separating the positive integers $111,333,555,7777$ and negative integers $-222,-444,-666,-888$
- Arranging the positive integers in descending order as $7777,555,333,111$ and negative integers in descending order as $-222,-444,-666,-888$
- The numbers in descending order: $7777,555,333,111,-222,-444,-666,-888$

Objective Type Questions
Question 12 .
There are positive integers from $-5$ to 6 .
(a) 5
(b) 6
(c) 7
(d) 11
Solution:
(b) 6

Question $13 .$
The opposite of 20 units to the left of 0 is
(a) 20
(b) 0
(c) $-20$
(d) 40
Solution:
(a) 20

Question $14 .$
One unit to the right of $-7$ is
(a) $+1$
(b) $-8$
(c) $-7$
(d) $-6$
Solution:
(d) $-6$

Question $15 .$
3 units to the left of 1 is
(a) $-4$
(b) $-3$
(c) $-2$
(d) 3
Solution:
(c) $-2$

Question $16 .$
The number which determines marking the position of any number to its opposite on a number line is?
(a) $-1$
(b) 0
(c) 1
(d) 10
Solution:
(b) 0