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Selina Concise Mathematics Class 7 ICSE Solutions Chapter 3 Fractions (Including Problems)

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 3 Fractions (Including Problems)

Fractions Exercise 3A – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Classify, each fraction given below, as decimal or vulgar fraction, proper or improper fraction and mixed fraction :

Solution:

Question 2.
Express the following improper fractions as mixed fractions :

Solution:

Question 3.
Express the following mixed fractions as improper fractions :

Solution:

Question 4.
Reduce the given fractions to lowest terms

Solution:

Question 5.
State : true or false

Solution:

Question 6.
Distinguish each of the following fractions, given below, as a simple fraction or a complex fraction :

Solution:

Fractions Exercise 3B – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
For each pair, given below, state whether it forms like fractions or unlike fractions :

Solution:

Question 2.
Convert given fractions into fractions with equal denominators :

Solution:

Question 3.
Convert given fractions into fractions with equal numerators :

Solution:

Question 4.
Put the given fractions in ascending order by making denominators equal :

Solution:

Question 5.
Arrange the given fractions in descending order by making numerators equal :

Solution:

Question 6.
Find the greater fraction :


Solution:

Question 7.
Insert one fraction between :

Solution:

Question 8.
Insert three fractions between

Solution:

Question 9.
Insert two fractions between

Solution:

Fractions Exercise 3C – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Reduce to a single fraction :


Solution:

Question 2.
Simplify :

Solution:

Question 3.
Subtract :

Solution:

Question 4.
Find the value of

Solution:

Question 5.
Simplify and reduce to a simple fraction :


Solution:

Question 6.
A bought 3 \(\frac { 3 }{ 4 }\) kg of wheat and 2 \(\frac { 1 }{ 2 }\) kg of rice. Find the total weight of wheat and rice bought.
Solution:

Question 7.
Which is greater,\(\frac { 3 }{ 5 }\) or \(\frac { 7 }{ 10 }\) and by how much?
Solution:

Question 8.
What number should be added to 8 \(\frac { 2 }{ 3 }\) to 12 \(\frac { 5 }{ 6 }\)
Solution:

Question 9.
What should be subtracted from 8\(\frac { 3 }{ 4 }\) to get 2 \(\frac { 2 }{ 3 }\)
Solution:

Question 10.
A field is 16 \(\frac { 1 }{ 2 }\) m long and 12 \(\frac { 2 }{ 5 }\) m wide. Find the perimeter of the field.
Solution:

Question 11.
Sugar costs ₹37 \(\frac { 1 }{ 2 }\)per kg. Find the cost of 8\(\frac { 3 }{ 4 }\) kg sugar.
Solution:

Question 12.
A motor cycle runs 31\(\frac { 1 }{ 4 }\) km consuming 1 litre of petrol. How much distance will it run consuming 1\(\frac { 3 }{ 5 }\) liter of petrol?
Solution:

Question 13.
A rectangular park has length = 23 \(\frac { 2 }{ 3 }\) m and breadth = 16 \(\frac { 2 }{ 3 }\) m. Find the area of the park.
Solution:

Question 14.
Each of 40 identical boxes weighs 4 \(\frac { 4 }{ 5 }\) kg Find the total weight of all the boxes.
Solution:

Question 15.
Out of 24 kg of wheat, \(\frac { 5 }{ 6 }\) th of wheat is consumed. Find, how much wheat is still left?
Solution:

Question 16.
A rod of length 2 \(\frac { 2 }{ 5 }\) metre is divided into five equal parts. Find the length of each part so obtained.
Solution:

Question 17.
IfA = 3\(\frac { 3 }{ 8 }\) and B = 6\(\frac { 5 }{ 8 }\) find :
(i) A+B
(ii) B A
Solution:

Question 18.
Cost of 3 \(\frac { 5 }{ 7 }\) litres of oil is ₹83 \(\frac { 1 }{ 2 }\). Find the
cost of one litre oil.
Solution:

Question 19.
The product of two numbers is 20 \(\frac { 5 }{ 7 }\). If one of these numbers is 6 \(\frac { 2 }{ 3 }\), find the other.
Solution:

Question 20.
By what number should 5 \(\frac { 5 }{ 6 }\) be multiplied 1 to get 3\(\frac { 1 }{ 3 }\) ?
Solution:

Fractions Exercise 3D – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Simplify
Solution:

Question 2.

Solution:

Question 3.

Solution:

Question 4.

Solution:

Question 5.

Solution:

Question 6.

Solution:

Question 7.

Solution:

Question 8.

Solution:

Question 9.

Solution:

Question 10.

Solution:

Question 11.

Solution:

Fractions Exercise 3E – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
A line AB is of length 6 cm. Another line CD is of length 15 cm. What fraction is :
(i) The length of AB to that of CD ?
(ii) \(\frac { 1 }{ 2 }\) the length of AB to that of \(\frac { 1 }{ 3 }\) of CD ?
(iii) \(\frac { 1 }{ 5 }\) of CD to that of AB ?
Solution:

Question 2.
Subtract \(\frac { 2 }{ 7 }\) – \(\frac { 5 }{ 21 }\) from the sum of \(\frac { 3 }{ 4 }\) , \(\frac { 5 }{ 7 }\) and \(\frac { 7 }{ 12 }\)
Solution:

Question 3.
From a sack of potatoes weighing 120 kg, a merchant sells portions weighing 6 kg, 5\(\frac { 1 }{ 4 }\) kg, 9\(\frac { 1 }{ 2 }\) kg and 9\(\frac { 3 }{ 4 }\) kg respectively.
(i) How many kg did he sell ?
(ii) How many kg are still left in the sack ?
Solution:

Question 4.
If a boy works for six consecutive days for 8 hours, 7\(\frac { 1 }{ 2 }\) hours, 8\(\frac { 1 }{ 4 }\) hours, 6 \(\frac { 1 }{ 4 }\)4 3hours, 6\(\frac { 3 }{ 4 }\) hours and 7 hours respectively. How much money will he earn at the rate of Rs. 36 per hour ?
Solution:

Question 5.
A student bought 4 \(\frac { 1 }{ 3 }\) m of yellow ribbon, 6 \(\frac { 1 }{ 6 }\) m of red ribbon and 3\(\frac { 2 }{ 9 }\) m of blue ribbon for decorating a room. How many metres of ribbon did he buy ?
Solution:

Question 6.
In a business, Ram and Deepak invest \(\frac { 3 }{ 5 }\) and \(\frac { 2 }{ 5 }\) of the total investment. IfRs. 40,000 is the total investment, calculate the amount invested by each ?
Solution:

Question 7.
Geeta had 30 problems for home work. She worked out \(\frac { 2 }{ 5 }\) of them. How many problems were still left to be worked out by her ?
Solution:

Question 8.
A picture was marked at Rs. 90. It was sold at \(\frac { 3 }{ 4 }\) of its marked price. What was the sale price ?
Solution:

Question 9.
Mani had sent fifteen parcels of oranges. What was the total weight of the parcels, if each weighed 10\(\frac { 1 }{ 2 }\) kg ?Solution:

Question 10.
A rope is 25\(\frac { 1 }{ 2 }\) m long. How many pieces , 1 \(\frac { 1 }{ 2 }\) each of length can be cut out from it?Solution:

Question 11.
The heights of two vertical poles, above the earth’s surface, are 14 \(\frac { 1 }{ 4 }\) m and 22 \(\frac { 1 }{ 3 }\) respectively. How much higher is the second pole as compared with the height of the first pole ?
Solution:

Question 12.
Vijay weighed 65\(\frac { 1 }{ 2 }\) kg. He gained 1\(\frac { 2 }{ 5 }\) kg during the first week, 1 \(\frac { 1 }{ 4 }\) kg during the second week, but lost \(\frac { 5 }{ 16 }\) kg during the 16 third week. What was his weight after the third week ?
Solution:

Question 13.
A man spends \(\frac { 2 }{ 5 }\) of his salary on food and \(\frac { 3 }{ 10 }\) on house rent, electricity, etc. What fraction of his salary is still left with him ?
Solution:

Question 14.
A man spends \(\frac { 2 }{ 5 }\) of his salary on food and \(\frac { 3 }{ 10 }\) of the remaining on house rent, electricity, etc. What fraction of his salary is still left with him ?
Solution:

Question 15.
Shyam bought a refrigerator for Rs. 5000. He paid \(\frac { 1 }{ 10 }\) of the price in cash and the rest in 12 equal monthly instalments. How much had he to pay each month ?
Solution:

Question 16.
A lamp post has half of its length in mud, and \(\frac { 1 }{ 3 }\) of its length in water.
(i) What fraction of its length is above the water ?
(ii) If 3\(\frac { 1 }{ 3 }\) m of the lamp post is above the water, find the whole length of the lamp post.
Solution:

Question 17.
I spent \(\frac { 3 }{ 5 }\) of my savings and still have Rs. 2,000 left. What were my savings ?
Solution:

Question 18.
In a school, \(\frac { 4 }{ 5 }\) of the children are boys. If the number of girls is 200, find the number of boys.
Solution:

Question 19.
If \(\frac { 4 }{ 5 }\) of an estate is worth Rs. 42,000, find the worth of whole estate. Also, find the value of \(\frac { 3 }{ 7 }\) of it.
Solution:

Question 20.
After going \(\frac { 3 }{ 4 }\) of my journey, I find that I have covered 16 km. How much Journey is still left ?
Solution:

Question 21.
When Krishna travelled 25 km, he found that \(\frac { 3 }{ 5 }\) of his journey was still left. What was the length of the whole journey.
Solution:

Question 22.
From a piece of land, one-third is bought by Rajesh and one-third of remaining is bought by Manoj. If 600 m² land is still left unsold, find the total area of the piece of land.
Solution:

Question 23.
A boy spent \(\frac { 3 }{ 5 }\) of his money on buying 1 cloth and \(\frac { 1 }{ 4 }\) of the remaining on buying shoes. If initially he has ?2,400; how much did he spend on shoes?
Solution:

Question 24.
A boy spent \(\frac { 3 }{ 5 }\) of his money on buying cloth and \(\frac { 1 }{ 4 }\) of his money on buying shoes. If initially he has ?2,400; how much did he spend on shoes?
Solution:

Selina Concise Mathematics Class 7 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 33 Data Handling (Including Pictograph and Bar Graph)

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 33 Data Handling (Including Pictograph and Bar Graph)

Data Handling Exercise 33A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Marks scored by 30 students of class VI are as given below :
38, 46, 33, 45, 63, 53, 40, 85, 52, 75, 60, 73, 62, 22, 69, 43, 45, 33, 47, 41, 29, 43, 37, 49, 83, 44, 55, 22, 35 and 45. State :
(i) the highest marks scored.
(ii) the lowest marks scored.
(iii) the range of marks.
Solution:

Question 2.
For the following raw data, form a discrete frequency distribution :
30,32,32, 28,34,34,32,30,30,32,32,34,30,32,32. 28,32,30, 28,30,32,32,30,28 and 30.
Solution:

Question 3.
Define :
(i) data
(ii) frequency of an observation.
Solution:

Question 4.
Rearranage the following raw data in descending order :
5.3, 5.2, 5.1, 5.7, 5.6, 6.0, 5.5, 5.9, 5.8, 6.1, 5.5, 5.8, 5.7, 5.9 and 5.4. Then write the :
(i) highest value
(ii) lowest value
(iii) range of values
Solution:

Question 5.
Represent the following data in the form of a frequency distribution :
52, 56, 72, 68, 52, 68, 52, 68, 52, 60, 56, 72, 56, 60, 64, 56, 48, 48, 64 and 64.
Solution:

Question 6.
In a study of number of accidents per day, the observations for 30 days were obtained as follows :

Solution:

Question 7.
The following data represents the weekly wages (in ₹) of 15 workers in a factory : 900, 850, 800, 850, 800, 750, 950, 900, 950, 800, 750, 900, 750, 800 and 850.
Prepare a frequency distribution table. Now find,
(i) how many workers are getting less than ₹850 per week?
(ii) how many workers are getting more than ₹800 per week?
Solution:

Question 8.
Using the data, given below, construct a frequency distribution table : 9, 17, 12, 20, 9, 18, 25, 17, 19, 9, 12, 9, 12, 18, 17, 19, 20, 25, 9 and 12. Now answer the following :
(i) How many numbers are less than 19?
(ii) How many numbers are more than 20?
(iii) Which of the numbers, given above, is occurring most frequently?
Solution:

Question 9.
Using the following data, construct a frequency distribution table : 46, 44, 42, 54, 52, 60, 50, 58, 56, 62, 50, 56, 54, 58 and 48.
Now answer the following :
(i) What is the range of the numbers?
(ii) How many numbers are greater than 50?
(iii) How many numbers are between 40 and 50?
Solution:

Data Handling Exercise 33B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
The sale of vehicles, in a particular city, during the first six months of the year 2016 is shown below :

vehicles sold
Draw a pictograph to represent the above data.
Solution:

Question 2.


Solution:

Question 3.
The following pictograph shows the number of watches manufactured by a factory, in a particular weeks.


Find
(i) on which day were the least number of w atches manufactured?
(ii) total number of watches manufatured in the whole week?
Solution:

Question 4.
The number or animals in five villages are as follows :

Prepare a pitctograph of these animals using one symbol to represent 20 animals.
Solution:

Question 5.
The following pictograph shows different subject books which are kept in a school library.

Taking symbol of one book = 50 books, find :
(i) how many History books are there in the library ?
(ii) how many Science books are there in the library ?
(iii) which books are maximum in number ?
Solution:

Data Handling Exercise 33C – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
The following table gives the number of students in class VI in a school during academic years 2011-2012 to 2015-2016.

Represent the above data by a bar graph.
Solution:

Question 2.
The attendence of a particular class for the six days of a week are as given below :

Draw a suitable graph.
Solution:

Question 3.
The total number of students present in class VI B, for the six days in a week were as given below. Draw a suitable bar graph.

Solution:

Question 4.
The following table shows the population of a particular city at different years :

Represent the above information with the help of a suitable bar graph.
Solution:

Question 5.
In a survey of 300 families of a colony, the number of children in each family was recorded and the data has been represented by the bar graph, given below :

Read the graph carefully and answer the following questions :
(i) How many families have 2 children each?
(ii) How many families have no child?
(iii) What percentage of families have 4 children?
Solution:

Question 6.
Use the data, given in the following table, to draw’ a bar graph

Out of A, B, C, D, E and F
(i) Which has the maximum value.
(ii) Which is greater A + D or B + E.
Solution:

Question 7.
The bar graph drawn below shows the number of tickets sold during a fair by 6 students A, B, C, D, E and F.

Using the Bar graph, answer the following questions :
(i) Who sold the least number of tickets?
(ii) Who sold the maximum number of tickets?
(iii) How many tickets were sold by A, B and C taken together?
(iv) How many tickets were sold by D, E and F taken together?
(v) What is the average number of tickets sold per student?
Solution:

Question 8.
The following bar graph shows the number of children, in various classes, in a school in Delhi.

Using the given bar graph, find :
(i) the number of children in each class.
(ii) the total number of children from Class 6 to Class 8.
(iii) how many more children there are in Class 5 compared to Class 6 ?
(iv) the total number of children from Class 1 to Class 8.
(v) the average number of children in a class.
Solution:

Question 9.
The column graph, given above, shows the number of patients, examined by Dr. V.K. Bansal, on different days of a particular week.
Use the graph to answer the following:
(i) On which day were the maximum number of patients examined?
(ii) On which day were the least number of patients examined?
(iii) On which days were an equal number or patients examined?
(iv) What is the total number of patients examined in the week?
Solution:

Question 10.
A student spends his pocket money on various items, as given below :
Books : Rs. 380, Postage : Rs. 30, Cosmetics : Rs. 240, Stationary : Rs. 220 and Entertainment: Rs. 120.
Draw a bar graph to represent his expenses.
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 15 Decimal Fractions

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 15 Decimal Fractions

Decimal Fractions Exercise 15A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Write the number of decimal places in each of the following :
(i) 7.03
(ii) 0.509
(iii) 146.2
(iv) 0.0065
(v) 8.03207
Solution:

Question 2.
Convert the given unlike decimal fractions into like decimal fractions:
(i) 1.36, 239.8 and 47.008
(ii) 507.0752, 8.52073 and 0.808
(iii) 459.22, 7.03093 and 0.200037
Solution:

Question 3.
Change each of following fractions to a decimal fraction :

Solution:

Question 4.
Convert into a decimal fraction :

Solution:

Question 5.
Change the given decimals fractions to fractions in their lowest terms :
(i) 0.05
(ii) 3.95
(iii) 4.005
(iv) 0.876
(v) 50.06
(vi) 0.01075
(vii) 4.8806
Solution:

Decimal Fractions Exercise 15B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Add the following :
(i) 0.243, 2.47 and 3.009
(ii) 0.0736, 0.6095 and 0.9107
(iii) 1.01, 257 and 0.200
(iv) 18, 200.35, 11.72 and 2.3
(v) 0.586, 0.0586 and 0.00586
Solution:

Question 2.
Find the value of :
(i) 6.8 – 2.64
(ii) 2 – 1.0304
(iii) 0.1 – 0.08
(iv) 0.83 – 0.342
Solution:

Question 3.
Subtract :
(i) 0.43 from 0.97
(ii) 2.008 from 22.1058
(iii) 0.18 from 0.6
(iv) 1.002 from 17
(v) 83 from 92.05
Solution:

Question 4.
Simplify :
(i) 3.5 – 2.43 + 0.075
(ii) 7.84 + 0.3 – 4.016
(iii) 2.987 – 1.25 – 0.54
(iv) 52.9 – 231.666 + 204
(v) 8.57 – 6.4432 – 1.70 + 0.683
Solution:

Question 5.
From the sum of 75.75 and 4.9 subtract 28.465.
Solution:

Question 6.
Subtract the sum of 8.14 and 12.9 from 32.7.
Solution:

Question 7.
Subtract the sum of 34.27 and 159.8 from the sum of 20.937 and 200.6.
Solution:

Question 8.
From the sum of 2.43 and 4.349 subtract the sum of 0.8 and 3.15.
Solution:

Question 9.
By how much does the sum of 18.0495 and 34.9644 exceed the sum of 7.6752 and 24.876?
Solution:

Question 10.
What least number must be added to 89.376 to get 1000?
Solution:

Decimal Fractions Exercise 15C – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Multiply :
(i) 5.6 and 8
(ii) 38.46 and 9
(iii) 0.943 and 62
(iv) 0.0453 and 35
(v) 7.5 and 2.5
(vi) 4.23 and 0.8
(vii) 83.54 and 0.07
(viii) 0.636 and 1.83
(ix) 6.4564 and 1000
(x) 0.076 and 100
Solution:

Question 2.
Evaluate :
(i) 0.0008 x 26
(ii) 0.038 x 95
(iii) 1.2 x 2.4 x 3.6
(iv) 0.9 x 1.8 x 0.27
(v) 1.5 x 1.5 x 1.5
(vi) 0.025 x 0.025
(vii) 0.2 x 0.002 x 0.001
Solution:

Question 3.
Multiply each of the following numbers by 10, 100 and 1000 :
(i) 3.9
(ii) 2.89
(in) 0.0829
(iv) 40.3
(v) 0.3725
Solution:

Question 4.
Evaluate :
(i) 8.64 ÷ 8
(ii) 0.0072 ÷ 6
(iii) 20.64 ÷ 16
(iv) 1.602 ÷ 15
(v) 13.08 ÷ 4
(vi) 3.204 ÷ 9
(vii) 3.024 ÷ 12
(viii) 5.15 ÷ 5
(ix) 3 ÷ 5
Solution:

Question 5.
Divide each of the following numbers by 10,100 and 1000 :
(i) 49.79
(ii) 0.923
(iii) 0.0704
Solution:

Question 6.
Evaluate :
(i) 9.4 ÷ 0.47
(ii) 6.3 ÷ 0.09
(iii) 2.88 ÷ 1.2
(iv) 8.64 ÷ 1.6
(v) 37.188 ÷ 3.6
(vi) 16.5 ÷ 0.15
(vii) 3.2 ÷ 0.005
(viii) 3.24 ÷ 0.0016
Solution:

Question 7.
Fill in the blanks with 10,100,1000, or 10000 etc.:
(i) 7.85 x ………….. = 78.5
(ii) 0.442 x ………. = 442
(in) 0.0924 x ………… = 9.24
(iv) 0.00187 x …………. = 18-7
(v) 2.6 x …………. = 2600
(vi) 0.08 x ………… = 80
(vii) 96.7 ÷ ………….. = 0.967
(viii) 5.2 ÷ ……………. = 0.52
(ix) 33.15 ÷ ……………….. = 0.03315
(x) 0.7 ÷ ………… = 0.007
(xi) 0.00672 x ……… = 67.2
Solution:

Question 8.
Evaluate :
(i) 9.32 – 28.54 ÷ 10
(ii) 0.234 x 10 + 62.8
(iii) 3.06 x 100 – 889.4 ÷ 100
(iv) 2.86 x 7.5 + 45.4 ÷ 0.2
(v) 97.82 x 0.03 – 0.54 ÷ 0.3
Solution:

Decimal Fractions Exercise 15D – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Express in paise :
(i) Rs. 8.40
(ii) Rs. 0.97
(iii) Rs. 0.09
(iv) Rs. 62.35
Solution:

Question 2.
Express in rupees :
(i) 55 P
(ii) 8 P
(iii) 695 P
(iv) 3279 P
Solution:

Question 3.
Express in centimetre (cm) :
(i) 6 m
(ii) 8.54 m
(iii) 3.08 m
(iv) 0.87 m
(v) 0.03 m
(vi) 25.04 m
Solution:

Question 4.
Express in metre (m) :
(i) 250 cm
(ii) 2328 cm
(iii) 86 cm
(iv) 4 cm
(v) 107 cm
Solution:

Question 5.
Express in gramme (gm) :
(i) 6 kg
(ii) 5.543 kg
(iii) 0.078 kg
(iv) 3.62 kg
(v) 4.5 kg
Solution:

Question 6.
Express in kilogramme (kg) :
(i) 7000 gm
(ii) 6839 gm
(iii) 445 gm
(iv) 8 gm
(iv) 93 gm
(vi) 13545 gm
Solution:

Question 7.
Add (giving answer in rupees) :
(i) Rs. 5.37 and Rs. 12
(ii) Rs. 24.03 and 532 paise
(iii) 73 paise and Rs. 208
(iv) 8 paise and Rs. 1536
Solution:

Question 8.
Subtract :
(i) Rs. 35.74 from Rs. 63.22
(ii) 286 paise from Rs. 7.02
(iii) Rs. 0.55 from 121 paise
Solution:

Question 9.
Add (giving answer in metre) :
(i) 2.4 m and 1.78 m
(ii) 848 cm and 2.9 m
(iii) 0.93 m and 64 cm
Solution:

 

Question 10.
Subtract (giving answer in metre) :
(i) 5.03 m from 19.6 m
(ii) 428 cm from 1033 m
(iii) 0.84 m from 122 cm
Solution:

Question 11.
Add (giving answer in kg) :
(i) 2.06 kg and 57.864 kg
(ii) 778 gm and 1.939 kg
(iii) 0.065 kg and 4023 gm
Solution:

Question 12.
Subtract (giving answer in kg) :
(i) 9.462 kg from 15.6 kg
(ii) 4317 gm from 23 kg
(iii) 0.798 kg from 4169 gm
Solution:

Decimal Fractions Exercise 15E – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
The cost of a fountain pen is Rs. 13.25. Find the cost of 8 such pens.
Solution:

Question 2.
The cost of 25 identical articles is Rs. 218.25. Find the cost of one article.
Solution:

Question 3.
The length of an iron rod is 10.32 m. The rod is divided into 4 pieces of equal lengths. Find the length of each piece.
Solution:

Question 4.
What will be the total length of cloth required to make 5 shirts, if 2.15 m of cloth is needed for each shirt?
Solution:

Question 5.
Find the distance walked by a boy in 1\(\frac { 1 }{ 2 }\) hours, if he walks at 2.150 km every hour.
Solution:

Question 6.
83 note-books are sold at Rs. 15.25 each. Find the total money (in rupees) obtained by selling these note-books.
Solution:

Question 7.
If length of one bed-cover is 2.1 m, find the total length of 17 bed-covers.
Solution:

Question 8.
A piece of rope is 10 m 67 cm long. Another rope is 16 m 32 cm long. By how much is the second rope longer than the first one?
Solution:

Question 9.
12 cakes of soap together weigh 5 kg and 604 gm. Find the weight of
(i) One cake in both kg and gramme
(ii) 5 cakes in kg.
Solution:

Question 10.
Three strings of lengths 50 m 75 cm; 68 m 58 cm and 121 m 3 cm, respectively, are joined together to get a single string of greatest length, And the length of the single string obtained.
If this single string is then divided into 12 equal pieces ; find the length of each piece.
Solution:

Decimal Fractions Revision Exercise – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Write th& following decimal numbers in ascending order of value
(i) 5.054, 5.250, 5.245 and 5.0543
(ii) 62.443, 62.434, 62.344 and 62.444
Solution:

Question 2.
What number added to 0.805 gives 1?
Solution:

Question 3.
What must be subtracted from 3 to get 2.462?
Solution:

Question 4.
By how much should 83.407 be decreased to get 27.78?
Solution:

Question 5.
Two articles weigh 32.674 kg and 40.038 kg respectively. Find :
(i) the total weight of both the articles.
(ii) the difference in the weights of both the articles.
Solution:

Question 6.
By how much does the sum of 34.07 and 15.239 exceed the sum of 16.40 and 27.08?
Solution:

Question 7.
The cost of 1 kg of fruit is Rs. 27.50. What is the cost of 3.6 kg of fruit?
Solution:

Question 8.
Evaluate :
(i) 0.8 x 0.8 x 0.8
(ii) 0.8 ÷ 0.8 x 0.8
(iii) 0.8 x 0.8 ÷ 0.8
(iv) 0.8 ÷ 0.8 of 0.8
(v) 0.8 of 0.8 ÷ 0.8
Solution:

Question 9.
Evaluate :
(i) 3.5 x (4.2 + 2.6)
(ii) 3.5 x 4.2 + 3.5 x 2.6
Are (i) and (ii) equal ?
Solution:

Question 10.
Evaluate :
(i) (3.87 – 2.09) x 2.4
(ii) 3.87 x 2.4 – 2.09 x 2.4
Are (i) and (ii) equal ?
Solution:

Question 11.
A 4.85 m long pole is divided into 5 equal parts. Find the length of each part.
Solution:

Question 12.
A car can run 16.8 km consuming one litre of petrol. How many kilometres will it run on 3.7 litres of petrol ?
Solution:

Question 13.
A certain amount of money is distributed among 28 persons. If each person gets Rs. 62.45 and Rs. 5.78 is left, find the original amount of money.
Solution:

Question 14.
Complete the following table :

Solution:

Question 15.
The difference between two numbers is 47.364. If the smaller number is 31.855 ; find the bigger one.
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 32 Perimeter and Area of Plane Figures

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 32 Perimeter and Area of Plane Figures

Perimeter and Area of Plane Figures Exercise 32A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
What do you understand by a plane closed figure?
Solution:

Question 2.
The interior of a figure is called region of the figure. Is this statement true ?
Solution:

Question 3.
Find the perimeter of each of the following closed figures :
Solution:

Question 4.
Find the perimeter of a rectangle whose:
(i) length = 40 cm and breadth = 35 cm
(ii) length = 10 m and breadth = 8 m
(iii) length = 8 m and breadth = 80 cm
(iv) length = 3.6 m and breadth = 2.4 m
Solution:

Question 5.
If P denotes perimeter of a rectangle, l denotes its length and b denotes its breadth, find :
(i) l, if P = 38cm and b = 7cm
(ii) b, if P = 3.2m and l = 100 cm
(iii) P, if l = 2 m and b = 75cm
Solution:

Question 6.
Find the perimeter of a square whose each side is 1.6 m.
Solution:

Question 7.
Find the side of the square whose pe-rimeter is 5 m.
Solution:

Question 8.
A square field has each side 70 m whereas a rectangular field has length = 50 m and breadth = 40 m. Which of the two fields has greater perimeter and by how much?
Solution:

Question 9.
A rectangular field has length = 160m and breadth = 120 m. Find :
(i) the perimeter of the field.
(ii) the length of fence required to enclose the field.
(iii) the cost of fencing the field at the rate of ? 80 per metre.
Solution:

Question 10.
Each side of a square plot of land is 55 m. Find the cost of fencing the plot at the rate of ₹32 per metre.
Solution:

Question 11.
Each side of a square field is 70 cm. How much distance will a boy walk in order to make ?
(i) one complete round of this field?
(ii) 8 complete rounds of this field?
Solution:

Question 12.
A school playground is rectangular in shape with length = 120 m and breadth = 90 m. Some school boys run along the boundary of the play-ground and make 15 complete rounds in 45 minutes. How much distance they run during this period.
Solution:

Question 13.
Mohit makes 8 full rounds of a rect-angular field with length = 120 m and breadth = 75 m.
John makes 10 full rounds of a square field with each side 100 in. Find who covers larger distance and by how much?
Solution:

Question 14.
The length of a rectangle is twice of its breadth. If its perimeter is 60 cm, find its length.
Solution:

Question 15.
Find the perimeter of :
(i) an equilateral triangle of side 9.8 cm.
(ii) an isosceles triangle with each equal side = 13 cm and the third side = 10 cm.
(iii) a regular pentagon of side 8.2 cm.
(iv) a regular hexagon of side 6.5 cm.
Solution:

Question 16.
An equilateral triangle and d square have an equal perimeter. If the side of the triangle is 9.6 cm; what is the length of the side of the square?
Solution:

Question 17.
A rectangle with length = 18 cm and breadth = 12 cm has same perimeter as that of a regular pentagon. Find the side of the pentagon.
Solution:

Question 18.
A regular pentagon of each side 12 cm has same perimeter as that of a regular hexagon. Find the length of each side of the hexagon.
Solution:

Question 19.
Each side of a square is 45 cm and a rectangle has length 50 cm. If the perimeters of both (square and rectangle) are same, find the breadth of the rectangle.
Solution:

Question 20.
A wire is bent in the form of an equilateral triangle of each side 20 cm. If the same wire is bent in the form of a square, find the side of the square.
Solution:

Perimeter and Area of Plane Figures Exercise 32B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Find the area of a rectangle whose :
(i) length = 15 cm breadth = 6.4 cm
(ii) Length = 8.5 m breadth = 5 m
(iii) Length = 3.6 m breadth = 90 cm
(iv) Length = 24 cm breadth =180 mm
Solution:

Question 2.
Find the area of a square, whose each side is :
(i) 7.2 cm
(ii) 4.5 m
(iii) 4.1 cm
Solution:

Question 3.
If A denotes area of a rectangle, l represents its length and b represents its breadth, find :
(i) l, if A = 48 cm² and b = 6 cm
(ii) b, if A = 88 m² and l = 8m
Solution:

Question 4.
Each side of a square is 3.6 cm; find its
(i) perimeter
(ii) area.
Solution:

Question 5.
The perimeter of a square is 60 m, find :
(i) its each side its area
(ii) its new area obtained on increasing
(iii) each of its sides by 2 m.
Solution:

Question 6.
Each side of a square is 7 m. If its each side be increased by 3 m, what will be the increase in its area.
Solution:

Question 7.
The perimeter of a square field is numerically equal to its area. Find each side of the square.
Solution:

Question 8.
A rectangular piece of paper has area = 24 cm² and length = 5 cm. Find its perimeter.
Solution:

Question 9.
Find the perimeter of a rectangle whose area = 2600 m² and breadth = 50 m.
Solution:

Question 10.
What will happen to the area of a rectangle, if its length and breadth both are trebled?
Solution:

Question 11.
Length of a rectangle is 30 m and its breadth is 20 m. Find the increase in its area if its length is increased by 10 m and its breadth is doubled.
Solution:

Question 12.
The side of a square field is 16 m. What will be increase in its area, if:
(i) each of its sides is increased by 4 m
(ii) each of its sides is doubled.
Solution:

Question 13.
Each rectangular tile is 40 cm long and 30 cm wide. How many tiles will be required to cover the floor of a room with length = 4.8 m and breadth = 2.4 m.
Solution:

Question 14.
Each side of a square tile is 60 cm. How many tiles will be required to cover the floor of a hall with length = 50 m and breadth = 36 m.
Solution:

Question 15.
The perimeter of a square plot = 360 m. Find :
(i) its area.
(ii) cost of fencing its boundary at the rate of ₹ 40 per metre.
(iii) cost of levelling the plot at ₹60 per square metre.
Solution:

Question 16.
The perimeter of a rectangular field is 500 m and its length = 150 m. Find:
(i) its breadth,
(ii) its area.
(iii) cost of ploughing the field at the rate of ₹1.20 per square metre.
Solution:

Question 17.
The cost of flooring a hall of ₹64 per square metre is ₹2,048. If the breadth of the hall is 5m, find :
(i) its length.
(ii) its perimeter.
(iii) cost of fixing a border of very small width along its boundary at the rate of ₹60 per square metre.
Solution:

Question 18.
The length of a rectangle is three times its breadth. If the area of the rectangle is 1875 sq. cm, find its perimeter.
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions

Fractions Exercise 14A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
For each expression, given below, write a fraction :
(i) 2 out of 7 = ………..
(ii) 5 out of 17 = ………..
(iii) three-fifths = ………
Solution:

Question 2.
Fill in the blanks :


Solution:

Question 3.
From the following fractions, separate :
(i) Proper fractions
(ii)Improper fractions :

Solution:

Question 4.
Change the following mixed fractions to improper fractions :

Solution:

Question 5.
Change the following improper fractions to mixed fractions :

Solution:

Question 6.
Change the following groups of fractions to like fractions :

Solution:

Fractions Exercise 14B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Reduce the given fractions to their lowest terms :

Solution:

Question 2.
State, whether true or false?

Solution:

Question 3.
Which fraction is greater?

Solution:
<

Question 4.
Which fraction is smaller ?

Solution:

Question 5.
Arrange the given fractions in descending order of magnitude :

Solution:
<

Question 6.
Arrange the given fractions in ascending order of magnitude :

Solution:

Question 7.
I bought one dozen bananas and ate five of them. What fraction of the total number of bananas was left ?
Solution:

Question 8.
Insert the symbol ‘=’ or ‘>’ or ‘<’ between each of the pairs of fractions, given below :

Solution:

Question 9.
Out of 50 identical articles, 36 are broken. Find the fraction of :
(i) The total number of articles and the articles broken.
(ii) The remaining articles and total number of articles.
Solution:

Fractions Exercise 14C – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Add the following fractions :

Solution:

Question 2.
Simplify :

Solution:

Fractions Exercise 14D – Selina Concise Mathematics Class 6 ICSE Solutions

Point to Remember :
BODMAS :- While simplifying an expressions we can involve six operation in following orders.
B Stands for “BRACKET”
O Stands for “OF”
D Stands for “DIVISION”
M Stands for “MULTIPLICATION”
A Stands for “ADDITION”
S Stands for “SUBTRACTION”

Question 1.
Simplify :

Solution:

Question 2.
Simplify :

Solution:

Question 3.
Simplify :

Solution:

Question 4.
Simplify :


Solution:

Question 5.
Simplify :


Solution:

Fractions Exercise 14E – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
From a rope of 10\(\frac { 1 }{ 2 }\) m long, 4\(\frac { 5 }{ 8 }\) m is cut off. Find the length of the remaining rope.
Solution:

Question 2.
A piece of cloth is 5 metre long. After washing, it shrinks by \(\frac { 1 }{ 25 }\) of its length. What is the length of the cloth after washing?
Solution:

Question 3.
I bought wheat worth Rs. 12\(\frac { 1 }{ 2 }\), rice worth Rs. 25\(\frac { 3 }{ 4 }\) and vegetables worth Rs. 10\(\frac { 1 }{ 4 }\). If I gave a hundred-rupee note to the shopkeeper ; how much did he return to me
Solution:

Question 4.
Out of 500 oranges in a box, \(\frac { 3 }{ 25 }\) are rotten and \(\frac { 1 }{ 5 }\) are kept for some guests. How many oranges are left in the box?
Solution:

Question 5.
An ornament piece is made of gold and copper. Its total weight is 96g. If \(\frac { 1 }{ 12 }\) of the ornament hi copper, find the weight of gold in it.
Solution:

Question 6.
A girl did half of some work on Monday and one-third of it on Tuesday. How much will she have to do on Wednesday in order to complete the work?
Solution:

Question 7.
A man spends \(\frac { 3 }{ 8 }\) of his money and 8 still has Rs. 720 left with him. How much money did he have at first?
Solution:

Question 8.
In a school, \(\frac { 4 }{ 5 }\) of the students are boys, and the number of girls is 100. Find the number of boys.
Solution:

Question 9.
After finishing \(\frac { 3 }{ 4 }\) of my journey, I find that 12 km of my journey is covered. How much distance is still left to be covered?
Solution:

Question 10.
When Ajit travelled 15 km, he found that one-fourth of his journey was still left. What was the full length of the journey?
Solution:

Question 11.
In a particular month, a man earns Rs. 7,200. Out of this income, he spends \(\frac { 3 }{ 10 }\) on food, \(\frac { 1 }{ 4 }\) on house rent, \(\frac { 1 }{ 10 }\) on insurance and \(\frac { 2 }{ 25 }\) on holidays. How much did he save in that month ?
Solution:

Fractions Revision Exercise – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.

Solution:

Question 2.

Solution:

Question 3.
Evaluate :

Solution:

Question 4.
Mr. Mehra gave one-third of his money to his son, one-fifth of his money to his daughter and the remaining amount to his wife. If his wife got Rs. 91,000, how much money did Mr. Mehra have originally?
Solution:

Question 5.
A sum of Rs. 84,000 is divided among three persons A, B and C. If A gets one-fourth of it and B gets one-fifth of it; how much did C get?
Solution:

Question 6.
In one hour Rohit walks 3\(\frac { 2 }{ 5 }\) km. How much distance will he cover in 2\(\frac { 1 }{ 2 }\) hours?
Solution:

Question 7.
An 84 m long string is cut into pieces each of length 5\(\frac { 1 }{ 4 }\) m. How many pieces are obtained?
Solution:

Question 8.
In buying a ready made shirt-two-fifths of my pocket money is spent If Rs. 540 is still left with me, find :
(i) The money I had before I bought the shirt.
(ii) The emit of the shirt
Solution:

Question 9.
Mohan leaves Rs. 1,20,000 to his wife and three children such that two-fifths of this money is given to his wife and the remaining is distributed equally among the children. Find, how much each child gets?
Solution:

Question 10.
Simplify :

Solution:

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 31 Recognition of Solids

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 31 Recognition of Solids

Recognition of Solids Exercise 31 – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Identify the nets which can be used to form cubes :

Solution:

Question 2.
Draw at least three different nets for making cube.
Solution:

Question 3.
The dimensions of a cuboid are 6 cm, 4 cm and 3 cm. Draw two different types of oblique sketches for this cuboid.
Solution:

Question 4.
Two cubes, each with 3 cm edge, are placed side by side to form a cuboid. For this cuboid, draw :
(i) an oblique sketch
(ii) an isometric sketch.
Solution:

Question 5.
The figure, given below, shows shadows of some 3D objects, when seen under the lamp of an overhead projector :

In each case, name the object.
Solution:

Question 6.
Look at the solids, drawn below, and fill the given chart.


Solution:

P. Q. Using Euler’s formula, find the values of a, b, c and d.

Solution:

P.Q. Using an isometric dot paper, draw :
(i) a cube with each edge 3 cm.
(ii) a cuboid measuring 5 cm x 4 cm x 3 cm.
Solution:

Question 7.
Dice are cubes with dot or dots on each face. Opposite faces of a die always have a total of seven on them.
Below are given two nets to make dice (cube), the numbers inserted in each square indicate the number of dots in it.

Insert suitable numbers in each blank so that numbers in opposite faces of the die have a total of seven dots.
Solution:

Question 8.
The following figure represents mets of some solids. Name the solids.

Solution:

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 10 Simple Interest

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 10 Simple Interest

Simple Interest Exercise 10 – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Find the S.I. and amount on :
(i) Rs. 150 for 4 years at 5% per year.
(ii) Rs. 350 for 3\(\frac {1 }{ 2 }\) years at 8% p.a.
(iii) Rs. 620 for 4 months at 8 p. per rupee per month.
(iv) Rs. 3,380 for 30 months at 4 \(\frac { 1 }{ 2 }\) % p.a.
(v) 600 from July 12 to Dec. 5 at 10% p.a.
(vi) Rs. 850 from 10th March to 3rd August at 2 \(\frac { 1 }{ 2 }\) % p.a.
(vii) Rs. 225 for 3 years 9 months at 16% p.a.
Solution:

Question 2.
On what sum of money does the S.I. for 10 years at 5% become Rs. 1,600 ?
Solution:

Question 3.
Find the time in which Rs. 2,000 will amount to Rs. 2,330 at 11% p.a. ?
Solution:

Question 4.
In what time will a sum of money double it self at 8% p.a ?
Solution:

Question 5.
In how many years will be ₹870 amount to ₹1,044, the rate of interest being 2\(\frac { 1 }{ 2 }\) % p.a ?
Solution:

Question 6.
Find the rate percent if the S.I. on ₹275 is 2 years is ₹22.
Solution:

Question 7.
Find the sum which will amount to ₹700 in 5 years at 8% rate p.a.
Solution:

Question 8.
What is the rate of interest, if ₹3,750 amounts to ₹4,650 in 4 years ?
Solution:

Question 9.
In 4 years, ₹6,000 amount to ₹8,000. In what time will ₹525 amount to ₹700 at the same rate ?
Solution:

Question 10.
The interest on a sum of money at the end of 2\(\frac { 1 }{ 2 }\) years is \(\frac { 4 }{ 5 }\) of the sum. What is the rate percent ?
Solution:

Question 11.
What sum of money lent out at 5% for 3 years will produce the same interest as Rs. 900 lent out at 4% for 5 years ?
Solution:

Question 12.
A sum of Rs. 1,780 become Rs. 2,136 in 4 years,
Find :
(i) the rate of interest.
(ii) the sum that will become Rs. 810 in 7 years at the same rate of interest ?
Solution:

Question 13.
A sum amounts to Rs. 2,652 in 6 years at 5% p.a. simple interest.
Find :
(i) the sum
(ii) the time in which the same sum will double itself at the same rate of interest.
Solution:

Question 14.
P and Q invest Rs. 36,000 and Rs. 25,000 respectively at the same rate of interest per year. If at the end of 4 years, P gets Rs. 3,080 more interest than Q; find the rate of interest.
Solution:

Question 15.
A sum of money is lent for 5 years at R% simple interest per annum. If the interest earned be one-fourth of the money lent, find the value of R.
Solution:

Question 16.
The simple interest earned on a certain sum in 5 years is 30% of the sum. Find the rate of interest.
Solution:

Selina Concise Mathematics Class 7 ICSE Solutions

Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers

Rational Numbers Exercise 2A – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Write down a rational number whose numerator is the largest number of two digits and denominator is the smallest number of four digits.

Solution:

Question 2.
Write the numerator of each of the following rational numbers:

Solution:

Question 3.
Write the denominator of each of the following rational numbers:

Solution:

Question 4.
Write down a rational number numerator (-5) x (-4) and denominator (28 – 27) x (8 – 5).

Solution:

Question 5.

Solution:

Question 6.
Separate positive and negative rational numbers from the following :

Solution:

Question 7.
Find three rational numbers equivalent to

Solution:

Question 8.
Which of the following are not rational numbers :

Solution:

Question 9.
Express each of the following integers as a rational number with denominator 7 :
(i) 5
(ii) -8
(iii) 0
(iv) -16
(v) 7
Solution:

Question 10.
Express \(\frac { 3 }{ 5 }\) as a rational number with denominator:
Solution:

Question 11.
Express \(\frac { 4 }{ 7 }\) as a rational number with numerator :
Solution:

Question 12.
Find x, such that:

Solution:

Question 13.
Express each of the following rational numbers to the lowest terms :

Solution:

Question 14.
Express each of the following rational numbers in the standard form.

Solution:

Rational Numbers Exercise 2B – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Mark the following pairs of rational numbers on the separate number lines :

Solution:

Question 2.
Compare:

Solution:

Question 3.
Compare:

Solution:

Question 4.
Arrange the given rational numbers in ascending order :

Solution:

Question 5.
Arrange the given rational numbers in descending order:

Solution:

Question 6.
Fill in the blanks :

Solution:

Rational Numbers Exercise 2C – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Add:

Solution:

Question 2.
Add:

Solution:

Question 3.
Evaluate:

Solution:

Question 4.
Evaluate:

Solution:

Question 5.
Subtract :

Solution:

Question 6.
Subtract :

Solution:

Question 7.
The sum of two rational numbers is \(\frac { 11 }{ 24 }\). If one of them is \(\frac { 3 }{ 8 }\), find the other.
Solution:

Question 8.
The sum of two rational numbers is \(\frac { -7 }{ 11 }\). If one of them is \(\frac { 13 }{ 24 }\), find the other.
Solution:

Question 9.
The sum of two rational numbers is -4. If one of them is \(-\frac { 13 }{ 12 }\) , find the other.
Solution:

Question 10.
What should be added to \(-\frac { 3 }{ 6 }\) to get \(-\frac { 11 }{ 24 }\) ?
Solution:

Question 11.
What should be added to \(\frac { -3 }{ 5 }\) to get 2?
Solution:

Question 12.
What should be subtracted from \(\frac { -4 }{ 5 }\) to get 1?
Solution:

Question 13.
The sum of two numbers is \(-\frac { 6 }{ 5 }\). If one of them is -2, find the other.
Solution:

Question 14.
What should be added to \(\frac { -7 }{ 12 }\) to get \(\frac { 3 }{ 8 }\)?

Solution:

Question 15.
What should be subtracted from \(\frac { 5 }{ 9 }\)to get \(\frac { 9 }{ 5 }\) ?
Solution:

Rational Numbers Exercise 2D – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Evaluate:

Solution:

Question 2.
Multiply:

Solution:

Question 3.
Evaluate:


Solution:

Question 4.
Find the cost of 3 \(\frac { 1 }{ 2 }\) m cloth, if one metre cloth costs ₹325 \(\frac { 1 }{ 2 }\).
Solution:

Question 5.
A bus is moving with a speed of 65 \(\frac { 1 }{ 2 }\) km per hour. How much distance will it cover in 1 \(\frac { 1 }{ 3 }\) hours.
Solution:

Question 6.
Divide:

Solution:

Question 7.
Evaluate:

Solution:

Question 8.
The product of two numbers is 14. If one of the numbers is \(\frac { -8 }{ 7 }\), find the other.
Solution:

Question 9.
The cost of 11 pens is ₹3 \(\frac { 2 }{ 3 }\). Find the cost of one pen.
Solution:

Question 10.
If 6 identical articles can be bought for ₹2 \(\frac { 6 }{ 17 }\). Find the cost of each article.
Solution:

Question 11.
By what number should \(\frac { -3 }{ 8 }\) be multiplied so that the product is \(\frac { -9 }{ 16 }\) ?
Solution:

Question 12.
By what number should \(\frac { -5 }{ 7 }\) be divided so -15 that the result is\(\frac { -15 }{ 28 }\) ?
Solution:

Question 13.
Evaluate :

Solution:

Question 14.
Seven equal piece are made out of a rope 5 of 21 \(\frac { 5 }{ 7 }\) m. Find the length of each piece.
Solution:

Rational Numbers Exercise 2E – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Evaluate:

Solution:

Question 2.
The sum of two rational numbers is \(\frac { -3 }{ 8 }\). If one of them is \(\frac { 3 }{ 16 }\), find the other,
Solution:

Question 3.
The sum of two rational numbers is -5. If one of them is \(\frac { -52 }{ 25 }\) , find the other.
Solution:

Question 4.
What rational number should be added to \(-\frac { 3 }{ 16 }\) to get \(\frac { 11 }{ 24 }\)
Solution:

Question 5.
What rational number should be added to \(-\frac { 3 }{ 5 }\) to get 2?
Solution:

Question 6.
What rational number should be subtracted from \(-\frac { 5 }{ 12 }\)to get \(\frac { 5 }{ 24 }\)
Solution:

Question 7.
What rational number should be subtracted from \(\frac { 5 }{ 8 }\) to get \(\frac { 8 }{ 5 }\) ?
Solution:

Question 8.
Evaluate:

Solution:




Question 9.
The product of two rational numbers is 24. If one of them is \(-\frac { 36}{ 11 }\), find the other.
Solution:

Question 10.
By what rational number should we multiply \(\frac { 20 }{ -9 }\) ,so that the product may be \(\frac { -5 }{ 9 }\) ?
Solution:

Selina Concise Mathematics Class 7 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 30 Revision Exercise Symmetry (Including Constructions on Symmetry)

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 30 Revision Exercise Symmetry (Including Constructions on Symmetry)

Revision Exercise Symmetry Exercise 30 – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
State, whether true or false :

Solution:


Question 2.
Construct a triangle ABC, in which AB = AC = 5 cm and BC 6 cm. Draw all its lines of Symmetry.
Solution:

Question 3.
Examine each of the following figures carefully, draw line(s) of symmetry in which ever figure possible :

Solution:

Question 4.
Construct a triangle XYZ, in which XY = YZ = ZX = 4.5 cm. Draw all its lines of symmetry.
Solution:

Question 5.
Construct a triangle ABC, in which AB = BC = 4 cm and ∠ABC = 60°. Draw all its lines of symmetry.
Solution:

Question 6.
Draw the line(s) of symmetry for each figure drawn below :

Solution:

Question 7.
In each of the following case, construct a point that is symmetric to the given point P with respect to the given line AB.

Solution:

Question 8.
Mark two points A and B 5.5 cm apart. Draw a line PQ so that A and B are symmetric with respect to the line PQ. Give a special name to line PQ.
Solution:

Question 9.
For each letter of the English alphabet, draw the maximum possible number of lines of symmetry.
Solution:

Question 10.
Draw all the possible lines of symmetry for each figure given below :
>
Solution:

Question 11.
For each shaded portion given below, draw all the possible lines of symmetry :
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 29 The Circle

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 29 The Circle

The Circle Exercise 29A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Use the figure given below to fill in the blanks :
(i) R is the …… of the circle.
(ii) Diameter of a circle is …… .
(iii) Tangent to a circle is … .
(iv) EF is a …… of the circle.
(v) …… is a chord of the circle.
(vi) Diameter = 2 x …..
(vii) ……. is a radius of the circle.
(viii) If the length of RS is 5 cm, the length of PQ = ……
(ix) If PQ is 8 cm long, the length of RS =…..
(x) AB is a ….. of the circle

Solution:

Question 2.
Draw a circle of radius 4.2 cm. Mark its centre as O. Take a point A on the circumference of the circle. Join AO and extend it till it meets point B on the circumference of the circle,
(i) Measure the length of AB.
(ii) Assign a special name to AB.
Solution:

Question 3.
Draw circle with diameter :
(i) 6 cm
(ii) 8.4 cm.
In each case, measure the length of the radius of the circle drawn.
Solution:

Question 4.
Draw a circle of radius 6 cm. In the circle, draw a chord AB = 6 cm.
(i) If O is the centre of the circle, join OA and OB.
(ii) Assign a special name to ∆AOB
(iii) Write the measure of angle AOB.
Solution:

Question 5.
Draw a circle of radius 4.8 cm and mark its centre as P.
(i) Draw radii PA and PB such that ∠APB = 45°.
(ii) Shade the major sector of the circle
Solution:

Question 6.
Draw a circle of radius 3.6 cm. In the circle, draw a chord AB = 5 cm. Now shade the minor segment of the circle.
Solution:

Question 7.
Mark two points A and B ,4cm a part, Draw a circle passing through B and with A as a center

Solution:

Question 8.
Draw a line AB = 8.4 cm. Now draw a circle with AB as diameter. Mark a point C on the circumference of the circle. Measure angle ACB.
Solution:

The Circle Exercise 29B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Construct a triangle ABC with AB = 4.2 cm, BC = 6 cm and AC = 5cm. Construct the circumcircle of the triangle drawn.
Solution:

Question 2.
Construct a triangle PQR with QR = 5.5 cm, ∠Q = 60° and angle R = 45°.
Construct the circumcircle cif the triangle PQR.
Solution:

Question 3.
Construct a triangle ABC with AB = 5 cm, ∠B = 60° and BC = 6. 4 cm.
Draw the incircle of the triangle ABC.
Solution:

Question 4.
Construct a triangle XYZ in which XY = YZ= 4.5 cm and ZX = 5.4 cm. Draw the circumcircle of the triangle and measure its circumradius.
Solution:

Question 5.
Construct a triangle PQR in which, PQ = QR = RP = 5.7 cm. Draw the incircle of the triangle and measure its radius.
Solution:

The Circle Revision Exercise – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
The centre of a circle is at point O and its radius is 8 cm. State the position of a point P (point P may lie inside the circle, on the circumference of the circle, or outside the circle), when :
(a) OP = 10.6 cm
(b) OP = 6.8 cm
(c) OP = 8 cm
Solution:

Question 2.
The diameter of a circle is 12.6 cm. State, the length of its radius.
Solution:

Question 3.
Can the length of a chord of a circle be greater than its diameter ? Explain.
Solution:

Question 4.
Draw a circle of diameter 7 cm. Draw two radii of this circle such that the angle between these radii is 90°. Shade the minor sector obtained. Write a special name for this sector.
Solution:

Question 5.
State, which of following statements are true and which are false :
(i) If the end points A and B of the line segment lie on the circumference of a circle, AB is a diameter.
(ii) The longest chord of a circle is its diameter.
(iii) Every diameter bisects a circle and each part of the circle so obtained is a semi-circle.
(iv) The diameters of a circle always pass through the same point in the circle.
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 28 Polygons

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 28 Polygons

Polygons Exercise 28A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
State, which of the following are polygons :

Solution:

Question 2.
Find the sum of interior angles of a polygon with :
(i) 9 sides
(ii) 13 sides
(iii) 16 sides
Solution:

Question 3.
Find the number of sides of a polygon, if the sum of its interior angles is :
(i) 1440°
(ii) 1620°
Solution:

Question 4.
Is it possible to have a polygon, whose sum of interior angles is 1030°.
Solution:

Question 5.
(i) If all the angles of a hexagon arc equal, find the measure of each angle.
(ii) If all the angles of an octagon are equal, find the measure of each angle,
Solution:

Question 6.
One angle of a quadrilateral is 90° and all other angles are equal ; find each equal angle.
Solution:

Question 7.
If angles of quadrilateral are in the ratio 4 : 5 : 3 : 6 ; find each angle of the quadrilateral.
Solution:

Question 8.
If one angle of a pentagon is 120° and each of the remaining four angles is x°, find the magnitude of x.
Solution:

Question 9.
The angles of a pentagon are in the ratio 5 : 4 : 5 : 7 : 6 ; find each angle of the pentagon.
Solution:
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Question 10.
Two angles of a hexagon are 90° and 110°. If the remaining four angles arc equal, find each equal angle.
Solution:

Polygons Exercise 28B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Fill in the blanks :
In case of regular polygon, with

Solution:

Question 2.
Find the number of sides in a regular polygon, if its each interior angle is :
(i) 160°
(ii) 150°
Solution:

Question 3.
Find number of sides in a regular polygon, if its each exterior angle is :
(i) 30°
(ii) 36°
Solution:

Question 4.
Is it possible to have a regular polygon whose each interior angle is :
(i) 135°
(ii) 155°
Solution:

Question 5.
Is it possible to have a regular polygon whose each exterior angle is :
(i) 100°
(ii) 36°
Solution:

Question 6.
The ratio between the interior angle and the exterior angle of a regular polygon is 2 : 1. Find :
(i) each exterior angle of this polygon.
(ii) number of sides in the polygon.
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions