NCERT Solutions For Class 6 Maths Chapter 6 Integers
Here at MentorAtHome, We provide NCERT Solutions For Class 6 Maths Chapter 6 Integers. NCERT solutions help students to improve their performance, and attain better results. In NCERT Solutions Class 6 Maths Chapter 6 there are 3 exerrcise.
NCERT Solutions For Class 6 Maths Chapter 6 Integers, will discuss about integer, types and its properties. NCERT Solutions For Class 6 Maths Chapter 6 is important for basic understanding.
NCERT Solutions For Class 6 Maths Chapter 6 Integers Exercises 6.1
Class 6th Maths Chapter 6 Solutions ex 6.1
Q.1. Write opposites of the following:
(a) Increase in weight
Ans:-
The opposite of an increase in weight is a decrease in weight
(b) 30 km north
Ans:-
The opposite of 30 km north is 30 km south
(c) 80 m east
Ans:-
The opposite of 80 m east is 80 m west
(d) Loss of Rs 700
Ans:-
The opposite of loss of Rs 700 is gain of Rs 700
(e) 100 m above sea level
Ans:-
The opposite of 100 m above sea level is 100 m below sea level
Q.2. Represent the following numbers as integers with appropriate signs.
(a) An aeroplane is flying at a height of two thousand metres above the ground.
Ans:- (+ 2000 m)
(b) A submarine is moving at a depth, eight hundred metres below sea level.
Ans:- (– 800 m)
(c) A deposit of rupees two hundred.
Ans:- (+ Rs 200)
(d) Withdrawal of rupees seven hundred.
Ans:-(– Rs 700)
Q.3. Represent the following numbers on a number line:
(a) + 5
Ans:-
(b) – 10
Ans:-
(c) + 8
Ans:-
(d) – 1
Ans:-
(e) – 6
Ans:-
Q.4. An 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?
(b) Is point G a negative integer or a positive integer?
(c) Write integers for points B and E.
(d) Which point marked on this number line has the least value?
(e) Arrange all the points in decreasing order of value.
Ans:-
(a) F represents -8
(b) G is a negative integer.
(c) B represents +4 and E represents – 10
(d) E has the least value of -10.
(e) Decreasing order of all the points are D, C, B, A, 0, H, G, F and E.
Q.5. Following is the list of temperatures of five places in India on a particular day of the year. Place Temperature
Siachin 10°C below 0°C ……………..
Shimla 2°C below 0°C ……………..
Ahmedabad 30°C above 0°C ……………..
Delhi 20°C above 0°C ……………..
Srinagar 5°C below 0°C ……………..
(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 name of the city against its temperature.
(c) Which is the coolest place?
(d) Write the names of the places where temperatures are above 10°C.
Ans:-
(a)
Siachin – 100 C
Shimla – 20 C
Ahmedabad + 300 C
Delhi + 200 C
Srinagar – 50 C
(b)
(c) Siachin is the coolest place with -10°C temperature.
(d) Ahmedabad and Delhi are the places where the temperatures are above 100C
(i) Delhi → 20°C
(ii) Ahmedabad → 30°C
Q.6. In each of the following pairs, which number is to the right of the other on the number line?
(a) 2, 9
Ans:-
9 is to the right of 2
(b) – 3, – 8
Ans:-
-3 is to the right of -8
(c) 0, – 1
Ans:
0 is to the right of – 1
(d) – 11, 10
Ans:
10 is to the right of -11
(e) – 6, 6
Ans:-
6 is to the right of -6
(f) 1, – 100
Ans:-
1 is to the right of -100.
Q.7. Write all the integers between the given pairs (write them in increasing order.)
(a) 0 and – 7
Ans:-
Integers between 0 and -7 are:
-6, -5, -4, -3, -2, -1
(b) – 4 and 4
Ans:-
Integers between -4 and 4 are:
-3, -2, -1, 0, 1, 2, 3
(c) – 8 and – 15
Ans:-
Integers between -8 and -15 are:
-14, -13, -12, -11, -10, -9
(d) – 30 and – 23
Ans:-
Integers between -30 and -23 are:
-29, -28, -27, -26, -25, -24
8. (a) Write four negative integers greater than – 20.
Ans:-
Four negative integers greater than – 20 are – 19, – 18, – 17, – 16.
(b) Write four integers less than – 10.
Ans:-
(b) Four negative integers less than – 10 are: – 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.
Ans:-
True as (-8 > -10)
(b) – 100 is to the right of – 50 on a number line.
Ans:
False (F); Correction: -100 is to the left of -50 on a number line.
(c) Smallest negative integer is – 1.
Ans:-
False (F); Correction: There is no smallest negative integer.
(d) – 26 is greater than – 25.
Ans:-
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.
(b) Which number will we reach if we move 5 numbers to the left of 1.
(c) If we are at – 8 on the number line, in which direction should we move to reach – 13?
(d) If we are at – 6 on the number line, in which direction should we move to reach – 1?
Ans:-
(a)
If we move 4 numbers to the right of -2, we will reach 2
(b)
If we move 5 numbers to the left of 1, we will reach at -4
(c)
-13 lies to the left of -8 on the number line. Hence, we should move in the left direction
(d)
-1 lies to the right of -6 on the number line. So, we should move in the right direction.
NCERT Solutions For Class 6 Maths Chapter 6 Integers Exercises 6.2
NCERT Class 6 Maths Chapter 6 Solutions ex 6.2
Q.1. Using the number line write the integer which is:
(a) 3 more than 5
Ans:-
Moving right 3 steps from 5, we reach 8.
Hence, 3 more than 5 = 8.
(b) 5 more than –5
Ans:-
Moving right 5 steps from -5 we reach 0.
Hence, 5 more than -5 = 0
(c) 6 less than 2
Ans:-
Moving left 6 steps from 2, we reach -4.
Hence, 6 less than 2 = -4
(d) 3 less than –2
Ans:-
Moving left 3 steps from -2, we reach -5.
Q.2. Use the number line and add the following integers:
(a) 9 + (–6)
Ans:-
9 + (–6) = +3
(b) 5 + (–11)
Ans:-
5 + (–11) = -6
(c) (–1) + (–7)
Ans:-
(–1) + (–7) = -8
(d) (–5) + 10
Ans:-
(–5) + 10 = +5
(e) (–1) + (–2) + (–3)
Ans:-
(–1) + (–2) + (–3) = -6
(f) (–2) + 8 + (–4)
Ans:-
(–2) + 8 + (–4) = +2
Q.3. Add without using number line:
(a) 11 + (–7)
Ans:-
11 + (–7) = +4
(b) (–13) + (+18)
Ans:-
(–13) + (+18) = +5
(c) (–10) + (+19)
Ans:-
(–10) + (+19) = +9
(d) (–250) + (+150)
Ans:-
(–250) + (+150) = -100
(e) (–380) + (–270)
Ans:-
(–380) + (–270) = -650
(f) (–217) + (–100)
Ans:-
(–217) + (–100) = -317
Q.4. Find the sum of:
(a) 137 and – 354
Ans:-
(137) + ( -354)
= (137) + (-137) + (-217)
= (137) + (-137) = 0
= 0 + (-217) = -217
(b) – 52 and 52
Ans:-
(-52) + (+52) = 0
(c) – 312, 39 and 192
Ans:-
-312, 39 and 192
(-312) + (+ 39) + (+192)
= (-231) + (- 81) + [(+39) + (+192)]
= (-231) + (-81) + (+ 231)
= (-231) + (+ 231) = 0
= 0 + (- 81) = – 81
(d) – 50, – 200 and 300
Ans:-
– 50, -200 and 300
(-50) + (-200) + (+ 300)
= (-50) + [(-200) + (+200)]+ (+100)
= (-50) + 0 + (+100)
= (-50) + (+100)
= [(-50) + (+50)] + (+ 50)
= 0 + (+ 50) = 50 [ ∵ (-a) + (+ a) = 0]
Q.5. Find the sum:
(a) (–7) + (–9) + 4 + 16
Ans:-
(- 7) + (-9) + 4 + 16
= (-7) + (-9) + 4 + (+ 7) + (+ 9)
= (-7) + (+7) + (-9) + (+9) + 4
= 0 + 0 + 4 = 4 [∵ (-a) + (a) = 0]
(b) (37) + (–2) + (–65) + (–8)
Ans:-
(37) + (-2) + (-65) + (-8)
= (+37) + (-75)
= (+37) + (-37) + (-38)
= 0 + (-38) = (-38) [∵ (-a) + (+a) = 0]
NCERT Solutions For Class 6 Maths Chapter 6 Integers Exercises 6.3
Ch 6 class 6 maths solutions ex 6.3
Q.1. Find
(a) 35 – (20)
Ans:-
35 – (20) = (15 + 20) – (20)
= 15 + (20 – 20)
= 15 + 0 = 15 [(+a) + (-a) = 0]
(b) 72 – (90)
Ans:
72 – (90) = 72 – (72 + 18)
= 72 – 72 – 18
= 0 – 18 = – 18 [a + (- a) = 0]
(c) (-15) – (-18)
Ans:-
(- 15) – (- 18)
= (- 15) + (additive inverse of – 18)
= (-15 + 18) = 3
(d) (-20) – (13)
Ans:-
(- 20) – (13) = – [20 + 13] = – 33
(e) 23 – (-12)
Ans:-
23 – (- 12)
= 23 + (additive inverse of – 12)
= (23 + 12) = 35
(f) (-32) – (-40)
Ans:-
(-32) – (- 40)
= (-32) + (additive inverse of – 40)
= (-32 + 40) = 8
NCERT Class 6 Maths Chapter 6 Solutions ex 6.3 Q2
Q.2. Fill in the blanks with >, < or = sign.
(a) (–3) + (–6) ______ (–3) – (–6)
Ans:-
(-3) + (-6) = – [3 + 6] = – 9
(-3) – (-6) = (-3) + 6 = 3
Here, – 9 < 3
Therefore (- 3) + (- 6) < (- 3) – (- 6)
(b) (–21) – (–10) _____ (–31) + (–11)
Ans:-
(-21) – (-10) = (-21) + 10 = -11
(-31) + (-11) = – (31 + 11) = – 42
Here, -42 < -11 or -11 > -42
∴ (-21) , -(-10) >(-31)+ (-11)
(c) 45 – (– 11) ______ 57 + (– 4)
Ans:-
45 – (-11) = 45 + 11 = 56
57 + (-4) = 57 -4 = 53
Here, 56 >53
∴ 45 – (-11) > 57 + ( -4)
(d) (–25) – (–42) _____ (– 42) – (–25)
Ans:-
(-25) – (-42) = -25 + 42 = 17
(-42) – (-25) = -42 + 25 = -17
Here, 17 > -17
∴ (-25) – (-42) > (-42) – (-25).
NCERT Class 6 Maths Chapter 6 Solutions ex 6.3 Q3
Q.3. Fill in the blanks.
(a) (–8) + _____ = 0
Ans:-
(-8) + (additive inverse of -8) = 0
= (-8) + (8) = 0
∴ Value of blank is 8
(b) 13 + _____ = 0
Ans:-
13 + (additive inverse of 13) = 0
= 13 + (-13) = 0
∴ Value of blank is – 13
(c) 12 + (–12) = ____
Ans:-
12 + (-12) = 0
= -12 is additive inverse of 12
∴ The Value of blank is 0
(d) (–4) + ____ = –12
Ans:-
(-4) + (-8) = -[4 + 8] = -12
∴ Value of blank is -8.
(e) ____ – 15 = – 10
Ans:
(+5) – 15 = (5 – 15) = -10
∴ Value of blank is +5.
NCERT Class 6 Maths Chapter 6 Solutions ex 6.3 Q4
Q.4. Find
(a) (–7) – 8 – (–25)
Ans:-
(-7) – 8 – (-25)
= (-7) – 8 + 25
[-25 is Additive inverse of 25]
= -7 + 17 = -7 + 7 +10
[∵ (-a) + (+a) = 0]
= 0 + 10 = 10.
(b) (–13) + 32 – 8 – 1
Ans:-
(-13) + 32 – 8 – 1
= (-13) + (13) + 19 – (8 + 1)
= 0 + 19 – 9
= 19 – 9 = 10 + 9 – 9 [∵ (-a) + (+a) = 0]
= 10 + 0 = 10.
(c) (–7) + (–8) + (–90)
Ans:-
(-7) + (-8) + (-90) = – (7 + 8) + (-90)
= -15 + (-90)
= -(15 + 90)
= -105.
(d) 50 – (–40) – (–2)
Ans:-
50 – (-40) – (-2)
= 50 – [- 40 – 2]
= 50 – (-42)
= 50 + 42
= 92.
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| NCERT Solutions for Class 6 Science | Class 6 Maths Chapter 6 Solutions |
NCERT Solutions For Class 6 Maths Chapter 6 interger are based on NCERT Books. You can download ncert book for class 6 maths chapter 6. Ch 6 class 6 maths solutions are desing by our subject expert team.
What We Learn?
- We have seen that there are times when we need to use numbers with a negative
sign. This is when we want to go below zero on the number line. These are
called negative numbers. Some examples of their use can be in temperature scale,
water level in lake or river, level of oil in tank etc. They are also used to denote
debit account or outstanding dues.
- The collection of numbers…, – 4, – 3, – 2, – 1, 0, 1, 2, 3, 4, … is called integers.
So, – 1, – 2, – 3, – 4, … called negative numbers are negative integers and 1, 2, 3, 4,
… called positive numbers are the positive integers. - We have also seen how one more than given number gives a successor and one less
than given number gives predecessor. - We observe that
(a) When we have the same sign, add and put the same sign.
(i) When two positive integers are added, we get a positive integer
[e.g. (+ 3) + ( + 2) = + 5].
(ii) When two negative integers are added, we get a negative integer
[e.g. (–2) + ( – 1) = – 3].
(b) When one positive and one negative integers are added we subtract them as
whole numbers by considering the numbers without their sign and then put the
sign of the bigger number with the subtraction obtained. The bigger integer is
decided by ignoring the signs of the integers [e.g. (+4) + (–3) = + 1 and (–4) +
( + 3) = – 1].
(c) The subtraction of an integer is the same as the addition of its additive inverse. - We have shown how addition and subtraction of integers can also be shown on a
number line.