NCERT Solutions for Class 6 Maths

NCERT Solutions for Class 6 Maths Chapter 7 Fractions Ex 7.1 are part of NCERT Solutions for Class 6 Maths. Here we have given NCERT Solutions for Class 6 Maths Chapter 7 Fractions Ex 7.1.

• Fractions Class 6 Ex 7.2
• Fractions Class 6 Ex 7.3
• Fractions Class 6 Ex 7.4
• Fractions Class 6 Ex 7.5
• Fractions Class 6 Ex 7.6

Board	CBSE
Textbook	NCERT
Class	Class 6
Subject	Maths
Chapter	Chapter 7
Chapter Name	Fractions
Exercise	Ex 7.1
Number of Questions Solved	11
Category	NCERT Solutions

NCERT Solutions for Class 6 Maths Chapter 7 Fractions Ex 7.1

Question 1.
Write the fraction representing the shaded portion.



Solution :

Question 2.
Color the part according to the given fraction.

Solution :

Question 3.
Identify the error, if any

Solution :
Neither of the shaded portions represents the corresponding given fractions. 4.

Question 4.
What fraction of a day is 8 hours?
Solution :
1 day = 24 hours
∴ Required fraction = \(\frac { 8 }{ 24 }\)

Question 5.
What fraction of an hour is 40 minutes?
Solution :
1 hour = 60 minutes
∴ Required fraction = \(\frac { 40 }{ 60 }\)

Question 6.
Arya, Abhimanyu, and Vivek shared lunch. Arya brings two sandwiches, one made of vegetable and one of jam. The other two boys forgot to bring their lunch. Arya agreed to share his sandwiches so that each person will have an equal share of each sandwich.
(a) How can Arya divide his sandwiches so that each person has an equal share?
(b) What part of a sandwich will each boy receive?
Solution :
(a) Arya will divide each sandwich into three equal parts, and give one part of each sandwich to each one of them.
(b) Each boy will receive \(\frac { 1 }{ 3 }\) part of a sandwich.

Question 7.
Kanchan dyes dresses. She had to dye 30 dresses. She has so far finished 20 dresses. What fraction of dresses has she finished?
Solution :
She has finished \(\frac { 2 }{ 3 }\) fraction of the dresses.

Question 8.
Write the natural numbers from 2 to 12. What fraction of them are prime numbers?
Solution :
The natural numbers from 2 to 12 are 2, 3, 4,5,6, 7, 8, 9, 10, 11 and 12
Total number of natural numbers = 11
Out of these, the prime numbers are 2, 3, 5, 7, 11

Total number of these prime numbers = 5 5
∴ Required fraction = \(\frac { 5 }{ 11 }\).

Question 9.
Write the natural numbers from 102 to 113. What fraction of them are prime numbers?
Solution :
The natural numbers from 102 to 113 are
102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112 and 113
Total number of natural numbers =12
Out of these, the prime numbers are 103, 107, 109, 113.
Total number of these prime numbers = 4 . 4
∴ Required fraction = \(\frac { 4 }{ 12 }\).

Question 10.
What fraction of these circles have X’s in them?

Solution :
Total number of circles = 8
Number of circles which have X’s in them = 4
∴ Required fraction = \(\frac { 4 }{ 8 }\).

Question 11.
Kristin received a CD player for her birthday. She bought 3 CDs and received 5 others as gifts. What fraction of her total CDs did she buy and what fraction did she receive as gifts?
Solution :
Number of CDs bought = 3
Number of CDs received as gifts = 5
∴ Total number of CDs = 3 + 5 = 8
Fraction of her total CDs that she bought \(\frac { 3 }{ 8 }\) and, fraction of her total CDs that she received as gifts \(\frac { 5 }{ 8 }\).

 

We hope the NCERT Solutions for Class 6 Maths Chapter 7 Fractions Ex 7.1 help you. If you have any query regarding NCERT Solutions for Class 6 Maths Chapter 7 Fractions Ex 7.1, drop a comment below and we will get back to you at the earliest.

NCERT Solutions for Class 6 Maths Chapter 8 Decimals Ex 8.1 are part of NCERT Solutions for Class 6 Maths. Here we have given NCERT Solutions for Class 6 Maths Chapter 8 Decimals Ex 8.1.

• Decimals Class 6 Ex 8.2
• Decimals Class 6 Ex 8.3
• Decimals Class 6 Ex 8.4
• Decimals Class 6 Ex 8.5
• Decimals Class 6 Ex 8.6

Board	CBSE
Textbook	NCERT
Class	Class 6
Subject	Maths
Chapter	Chapter 8
Chapter Name	Decimals
Exercise	Ex 8.1
Number of Questions Solved	10
Category	NCERT Solutions

NCERT Solutions for Class 6 Maths Chapter 8 Decimals Ex 8.1

Question 1.
Write the following as numbers in the given table:
(a)

(b)

Hundreds (100)	Tens (10)	Ones (1)	Tenths (\(\frac { 1 }{ 10 } \))

Solution.

	Hundreds (100)	Tens (10)	Ones (1)	Tenths (\(\frac { 1 }{ 10 } \))
(a)	0	3	1	2
(b)	1	1	0	4

Question 2.
Write the following decimals in the place value table :
(a) 19.4
(b) 0.3
(c) 10.6
(d) 205.9
Solution.

	Hundreds	Tens	Ones	Tenths
(a)	0	1	9	4
(b)	0	0	0	3
(c)	0	1	0	6
(d)	2	0	5	9

Question 3.
Write each of the following as decimals:
(a) Seven-tenths
(b) Two tens and nine-tenths
(c) Fourteen point six
(d) One hundred and two ones
(e) Six hundred point eight
Solution.
(a) 7 tenths : \(\frac { 7 }{ 10 } \) =0.7.
(b) Two tens and nine-tenths = 20 + \(\frac { 9 }{ 10 } \)  =20.9
(c) Fourteen point six = 14.6
(d) One hundred and two-ones =100 + 2=102
(e) Six hundred point eight = 600.8

Question 4.
Write each of the following as decimals:
(a) \(\frac { 5 }{ 10 } \)
(b) 3 +\(\frac { 7 }{ 10 } \)
(c) 200+60+5+\(\frac { 1 }{ 10 } \)
(d) 70+\(\frac { 8 }{ 10 } \)
(e) 4 \(\frac { 2 }{ 10 } \)
(g) \(\frac { 3 }{ 2 } \)
(h) \(\frac { 2 }{ 5 } \)
(i) \(\frac { 12 }{ 5 } \)
(j) 3 \(\frac { 3 }{ 5 } \)
(k) 4\(\frac { 1 }{ 2 } \)
Solution.

Question 5.
Write the following decimals as fractions. Reduce the fractions to lowest form :
(a) 0.6
(b) 205
(c) 1.0
(d) 3.8
(e) 13.7
(f) 21.2
(g) 6.4
Solution.
(a)
 \(0.6=\frac { 6 }{ 10 } =\frac { 6\div 2 }{ 10\div 5 } \)
∵  H.C.F.(6,10) = 2
= \(\frac { 3 }{ 5 } \)

(b)
\(2.5=\frac { 25 }{ 10 } =\frac { 25\div 5 }{ 10\div 5 } \)
∵  H.C.F.(25,10) = 5
= \(\frac { 5 }{ 2 } \)

(c)
\(1.5=\frac { 10 }{ 10 } =\frac { 10\div 10 }{ 10\div 10 } \)
∵  H.C.F.(10,10) = 10
= \(\frac { 1 }{ 1 } \) =1

(d)
\(3.8 =\frac { 38 }{ 10 } =\frac { 38\div 2 }{ 10\div 2 } \)
∵  H.C.F.(38,10) = 2
= \(\frac { 19 }{ 5 } \)

(e)
\(13.7=\frac { 137 }{ 10 } \)

(f)
\( 21.2=\frac { 212 }{ 10 } =\frac { 212\div 2 }{ 10\div 5 } \)
∵  H.C.F.(212,10) = 5
= \(\frac { 106 }{ 5 } \)

(g)
\(6.4=\frac { 64 }{ 10 } =\frac { 64\div 2 }{ 10\div 5 } \)
∵  H.C.F.(64,10) = 2
= \(\frac { 32 }{ 5 } \)

Question 6.
Express the following as cm using decimals:
(a) 2 mm
(b) 30 mm
(c) 116 mm
(d) 4cm 2mm
(e) 11cm 52mm
(f) 83 mm
Solution.
(a)
\(2mm =\frac { 2 }{ 10 } \)
∵  \( 1mm =\frac { 1 }{ 10 } \)
= 0.2cm

(b)
\(30mm =\frac { 30 }{ 10 } \)
∵  \( 1mm =\frac { 1 }{ 10 } \)
= 3cm = 3.0cm

Question 7.
Between which two whole numbers on the number line are the given numbers lie? Which of these whole numbers is nearer the number?
(a) 0.8
(b) 5.1
(c) 2.6
(d) 6.4
(e) 9.0
(f) 4.9

Solution.
(a) 0.8. The number 0.8 is between the two whole numbers 0 and 1. The whole number 1 is nearer the number 0.8.

(b) 5.1. The number 5.1 is between the two whole numbers 5 and 6. The whole number 5 is nearer the number 5.1.

(c) 2.6. The number 2,6 is between the two whole numbers 2 and 3. The whole number 3 is nearer the number 2.6.

(d) 6.4 The number 6.4 is between the two whole numbers 6 and 7. The whole number 6 is nearer the number 6.4.

(e) 0. 9.0 itself is a whole number.

(f) 4.9. The number 4.9 is between the two whole numbers 4 and 5. The whole number 5 is nearer the number 4.9.

Question 8.
Show the following numbers on the number line:
(a) 2
(b) 1.9
(c) 1
(d) 2.5.
Solution.
(a) 0.2. We know that 0.2 is more than zero but less than one. There are 2-tenths in it. Divide the unit length between 0 and 1 into 10 equal parts and take 2 parts as shown below:

(b) 1.9. We know that 1.9 is more than one but less than two. There are 9-tenths in’it. Divide the unit length between 1 and 2 into 10 equal parts and take 9 parts as shown below:

(c) 1.1. We know that 1.1 is more than one but less than two. There is one-tenth in it. Divide the unit length between 1 and 2 into 10 equal parts and take 1 part as shown below:

(d) 2.5. We know that 2.5 is more than two but less than three. There are 5-tenths in it. Divide the unit length between 2 and 3 into 10 equal parts and take 5 parts as shown below :

Question 9.
Write the decimal number represented by the points A, B, C, D on the given number line :

Solution.
(i) A. The decimal number represented by the point A is 0.8 as the unit length between 0 and 1 has been divided into 10 equal parts and 8 parts have been taken.

(ii) B. The decimal number represented by the point B is 1.3 as the unit length between 1 and 2 has been divided into 10 equal parts and 3 parts have been taken.

(iii) C. The decimal number represented by the point C is 2.2 as the unit length between 2 and 3 has been divided into 10 equal parts and 2 parts have been taken.

(iv) D. The decimal number represented by the point D is 2.9 as the unit length between 2 and 3 has been divided into 10 equal parts and 9 parts have been taken.

Question 10.
(a) The length of Ramesh’s notebook is 9 cm 5 mm. What will be its length in cm?
(b) The length of a young gram plant is 65 mm. Express its length in cm.
Solution.
(a) Length of Ramesh’s notebook = 9 cm 5mm

 

We hope the NCERT Solutions for Class 6 Maths Chapter 8 Decimals Ex 8.1 help you. If you have any query regarding. NCERT Solutions for Class 6 Maths Chapter 8 Decimals Ex 8.1, drop a comment below and we will get back to you at the earliest.

NCERT Solutions for Class 6 Maths Chapter 6 Integers Ex 6.1 are part of NCERT Solutions for Class 6 Maths. Here we have given NCERT Solutions for Class 6 Maths Chapter 6 Integers Ex 6.1.

• Integers Class 6 Ex 6.2
• Integers Class 6 Ex 6.3

Board	CBSE
Textbook	NCERT
Class	Class 6
Subject	Maths
Chapter	Chapter 6
Chapter Name	Integers
Exercise	Ex 6.1
Number of Questions Solved	10
Category	NCERT Solutions

NCERT Solutions for Class 6 Maths Chapter 6 Integers Ex 6.1

Question 1.
Write opposite of the following:
(a) Increase in weight
(b) 30 km north
(c) 326 BC
(d) Loss of Rs. 700
(e) 100 m above sea level.
Solution.
(a) Decrease in weight
(b) 30 km south
(c) 326 AD
(d) Gain of Rs. 700
(e) 100 m below sea level

Question 2.
Represent the following numbers as integers with appropriate signs.
(a) An airplane is flying at a height two thousand meters above the ground.
(b) A submarine is moving at depth, eight hundred meters below the sea level.
(c) A deposit of rupees two hundred.
(d) Withdrawal of rupees seven hundred.
Solution.
(a) + 2000
(b) – 800
(c) + 200
(d) – 700.

Question 3.
Represent the following numbers on a number line:
(a) + 5
(b) -10
(c) + 8
(d) -7
Solution.

Question 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?
(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 p-decreasing order of value.
Solution.

(a) F
(b) negative integer
(c) B → + 4, E → 10
(d) E
(e) D, C, B, A, O, H, G, F, E.

Question 5.
Following is the list of temperatures of five places in India, on a particular day of the year.
Solution.

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 temperature 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 whose temperature are above 10°C.
Solution.
(a)

Place	Temperature
Siachin	10°C below 0°C	– 10°C
Shimla	2°C below 0°C	– 2°C
Ahmedabad	30°C above 0°C	+ 30°C
Delhi	20°C above 0°C	+ 20°C
Srinagar	5°C below 0°C	– 5°C

(b)

(c) Siachin is the coolest place.
(d) Ahmedabad and Delhi.

Question 6.
In each of the following pairs, which number is to the right of the other on the number line?
(a) 2, 9
(b) -3,-8
(c) 0,-1
(d) – 11, 10
(e) -6,6
(f) 1,- 100
Solution.
(a) 2, 9
The number 9 is to the right of the number 2.
(b) -3,-8
The number – 3 is to the right of the number -8.
(c) 0,-1
The number 0 is to the right of the number – 1.
(d) – 11,10
The number 10 is to the right of the number -11.
(e) -6, 6
The number 6 is to the right of the number – 6.
(f) 1, -100
The number 1 is to the right of the number – 100.

Question 7.
Write all the integers between the given pairs (write them in the increasing order)
(a) 0 and – 7
(b) -4 and 4
(c) – 8 and -15
(d) – 30 and – 23.
Solution.
(a) 0 and – 7
The integers between 0 and – 7 in increasing order are – 6, – 5, – 4, – 3, – 2 and – 1.
(b) – 4 and 4
The integers between – 4 and 4 in increasing order are – 3, – 2, – 1, 0, 1, 2 and 3.
(c) – 8 and – 15
The integers between – 8 and – 15 in increasing order are – 14, – 13, – 12, – 11, – 10 and – 9.
(d) – 30 and – 23
The integers between – 30 and – 23 in increasing order are – 29, – 28, – 27, – 26, – 25 and – 24.

Question 8.
(a) Write four negative integers greater than – 20.
(b) Write four negative integers less than -10.
Solution.
(a) Four negative integers greater than 20 are – 19, – 18, – 17 and – 16.
(b) Four negative integers less than – 10 and 11,- 12,- 13 and -14

Question 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- 50 on a number line.
(b) – 100 is to the right of – 50 on a number line.
(c) A smallest negative integer is – 1.
(d) – 26 is larger than -25
Solution.
(a) True (T)
(b) False (F); – 100 is to the left of – 50 on a number line.
(c) False (F); Greatest negative integer is – 1.
(d) False (F); – 26 is smaller than – 25.

Question 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 -l?
Solution.
(a) We will reach number 2.
(b) We will reach the number – 4.
(c) We should move in the left direction.
(d) We should move in the right direction

 

We hope the NCERT Solutions for Class 6 Maths Chapter 6 Integers Ex 6.1 help you. If you have any query regarding NCERT Solutions for Class 6 Maths Chapter 6 Integers Ex 6.1, drop a comment below and we will get back to you at the earliest.

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.1 are part of NCERT Solutions for Class 6 Maths. Here we have given NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.1.

• Understanding Elementary Shapes Class 6 Ex 5.2
• Understanding Elementary Shapes Class 6 Ex 5.3
• Understanding Elementary Shapes Class 6 Ex 5.4
• Understanding Elementary Shapes Class 6 Ex 5.5
• Understanding Elementary Shapes Class 6 Ex 5.6
• Understanding Elementary Shapes Class 6 Ex 5.7
• Understanding Elementary Shapes Class 6 Ex 5.8
• Understanding Elementary Shapes Class 6 Ex 5.9

Board	CBSE
Textbook	NCERT
Class	Class 6
Subject	Maths
Chapter	Chapter 5
Chapter Name	Understanding Elementary Shapes
Exercise	Ex 5.1
Number of Questions Solved	7
Category	NCERT Solutions

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.1

Question 1.
What is the disadvantage in comparing line segments by mere observation?
Solution :
Sometimes the difference in lengths betweenthe two line segments is not obvious. So, we are not always sure about our usual judgment.

Question 2.
Why is it better to use a divider than with a ruler, while measuring the length of a line segment?
Solution :
There may be errors due to the thickness of the ruler and angular viewing by using a ruler. These errors are eradicated by using a divider. So, it is better to use a divider, than a ruler, while measuring the length of a line segment.

Question 3.
Draw any line segment, say \(\overline { AB }\). Take any point C lying in between A and B. Measure the lengths of AB, BC and AC. Is AB = AC + CB? [Note : If A, B, C are any three points on a line such that AC + CB = AB, then we can be sure that C lies between A and B.]
Solution :

Length of AB = 7 cm
Length of BC = 3 cm
Length of AC = 4 cm
AC + CB = 4 cm + 3 cm = 7 cm
But AB = 7 cm
So, AB = AC A- CB.

Question 4.
If A, B, C are three points on a line such that AB = 5 cm, BC – 3 cm and AC – 8 cm, which one of them lies between the other two?

Solution :
AB + BC = AC, so, the point B lies between the point A and point C.

Question 5.
Verify, whether D is the mid-point of AG.
Solution :
AD = AB + BC + CD = 3 units
DG = OE + EF + FG = 3 units
∴ Yes ! D is the mid-point of AG.

Question 6.
If B is the mid-point of \(\overline { AC }\) and C is the mid-point of \(\overline { BD }\), where A, B, C, D lie on a straight line, say why AB = CD ?
Solution :

∴ B is the mid-point of \(\overline { AC }\)
∴ AB = BC …(1)
∴ C is the mid-point of \(\overline { BD }\)
∴ BC = CD … (2)
In view of (1) and (2), we get AB = CD.

Question 7.
Draw five triangles and measure their sides. Check in each case, if the sum of the lengths of any two sides is always less than the third side.
Solution :
(i) AB = 3.7 cm
BC = 3 cm
AC = 3.8 cm

Clearly, AB + BC > AC
BC + AC > AB
AC + AB > BC

(ii) AB = 3 cm
BC = 3 cm
CA = 3 cm

Clearly, AB + BC > AC
BC + AO AB
AC + AB > B C

(iii) AB = 4 cm
BC = 3 cm
AC = 5 cm

Clearly, AB + BC > AC
BC+ AC > AB
AC + AB > BC.

(iv) AB = 2 cm
BC = 2 cm
AC = 2.8 cm

Clearly, AB + BC > AC
BC + AC > AB
AC +AB> BC

(v) AB = 3 cm
BC = 4 cm
CA = 3 cm

Clearly, AB + BC > AC
BC + AC> AB
AC + AB> BC
In each case, we observe that the sum of the lengths of any two sides is always greater than the third side.

 

We hope the NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.1 help you. If you have any query regarding NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.1, drop a comment below and we will get back to you at the earliest.