ICSE

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 11 Ratio

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 11 Ratio

Ratio Exercise 11A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Express each of the following ratios in its simplest form :
(a) (i) 4 : 6
(ii) 48 : 54
(iii) 200 : 250
(b) (i) 5 kg : 800 gm
(ii) 30 cm : 2 m
(iii) 3 m : 90 cm
(iv) 2 years : 9 months
(v) 1 hour : 45 minutes
(vi) 4 min : 45 sec

Solution:

Question 2.
A field is 80 m long and 60 m wide. Find the ratio of its width to its length.
Solution:

Question 3.
State, true or false :
(i) A ratio equivalent to 7 : 9 is 27 : 21.
(ii) A ratio equivalent to 5 : 4 is 240 : 192.
(iii) A ratio of 250 gm and 3 kg is 1 : 12.
Solution:

Question 4.
Is the ratio of 15 kg and 35 kg same as the ratio of 6 years and 14 years?
Solution:

Question 5.
Is the ratio of 6 g and 15 g same as the ratio of 36 cm and 90 cm?
Solution:

Question 6.
Find the ratio between 3.5 m, 475 cm and 2.8 m.
Solution:

Question 7.
Find the ratio between 5 dozen and 2 scores. [1 score = 20]
Solution:

Ratio Exercise 11B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
The monthly salary of a person is Rs. 12,000 and his monthly expenditure is Rs 8,500. Find the ratio of his:
(i) salary to expenditure
(ii) expenditure to savings
(iii) savings to salary
Solution:

Question 2.
The strength of a class is 65, including 30 girls. Find the ratio of the number of:
(i) girls to boys
(ii) boys to the whole class
(iii) the whole class to girls.
Solution:

Question 3.
The weekly expenses of a boy have increased from ₹ 1,500 to ₹ 2,250. Find the ratio of:
(i) increase in expenses to original expenses.
(ii) original expenses to increased expenses.
(iii) increased expenses to increase in expenses.
Solution:

Question 4.
Reduce each of the following ratios to their lowest terms :
(i) 1 hour 20 min : 2 hours
(ii) 4 weeks : 49 days
(iii) 3 years 4 months : 5 years 5 months.
(iv) 2 m 40 cm : 1 m 44 cm
(v) 5 kg 500 gm : 2 kg 750 gm
Solution:

Question 5.
Two numbers are in the ratio 9 : 2. If the smaller number is 320, find the larger number.
Solution:

Question 6.
A bus travels 180 km in 3 hours and a train travels 450 km in 5 hours. Find the ratio of speed of train to speed of bus.
Solution:

Question 7.
In winters, a school opens at 10 a.m. and closes at 3.30 p.m. If the lunch interval is of 30 minutes, find the ratio of lunch interval to total lime of the class periods.
Solution:

Question 8.
Rohit goes to school by car at 60 km per hour and Manoj goes to school by scooty at 40 km per hour. If they both live in the same locality, find the ratio between the time taken by Rohit and Manoj to reach school.
Solution:

Question 9.
In a club having 360 members, 40 play carrom, 96 play table tennis, 144 play badminton and remaining members play volley-ball. If no member plays two or more games, find the ratio of members who play :
(i) carrom to the number of those who play badminton.
(ii) badminton to the number of those who play table-tennis.
(iii) table-tennis to the number of those who play volley-ball.
(iv) volleyball to the n umber of those who play other games.
Solution:

Question 10.
The length of a pencil is 18 cm and its radius is 4 cm. Find the ratio of its length to its diameter.
Solution:

Question 11.
Ratio of distance of the school from A’s home to the distance of the school from B’s home is 2 : 1.
(i) Who lives nearer to the school?
(ii) Complete the following table :
Solution:

Question 12.
The student-teacher ratio in a school is 45 : 2. If there are 4050 students in the school, how many teachers must be there?
Solution:

Ratio Exercise 11C – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
₹ 120 is to be divided between Hari and Gopi in the ratio 5 : 3. How much does each get?
Solution:

Question 2.
Divide 72 in the ratio \(2\frac { 1 }{ 2 } :1\frac { 1 }{ 2 }\)
Solution:

Question 3.
Divide 81 into three parts in the ratio 2 : 3 : 4.
Solution:

Question 4.
Divide Rs 10,400 among A, B and C in the ratio \(\frac { 1 }{ 2 } :\frac { 1 }{ 3 } :\frac { 1 }{ 4 } \)
Solution:

Question 5.
A profit of Rs 2,500 is to be shared among three persons in the ratio 6 : 9 : 10. How much does each person get?
Solution:

Question 6.
The angles of a triangle are in the ratio 3 : 7 : 8. Find the greatest and the smallest angles.
Solution:

Question 7.
The sides of a triangle are in the ratio 3 : 2 : 4. If the perimeter of the triangle is 27 cm, find the length of each side.
Solution:

Question 8.
An alloy of zinc and copper weighs 12\(\frac { 1 }{ 2 }\) kg. if in the alloy, the ratio of zinc and copper is 1 : 4, find the weight of copper in it.
Solution:

Question 9.
How will Rs 31500 be shared between A, B and C ; if A gets the double of what B gets, and B gets the double of what C gets?
Solution:

Question 10.
Mr. Gupta divides Rs 81000 among his three children Ashok, Mohit and Geeta in such a way that Ashok gets four times what Mohit gets and Mohit gets 2.5 times what Geeta gets. Find the share of each of them.
Solution:

Ratio Exercise 11D – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Which ratio is greater:

Solution:

Question 2.
Which ratio is smaller :

Solution:

Question 3.
Increase 95 in the ratio 5 : 8.
Solution:

Question 4.
Decrease 275 in the ratio 11 : 7.
Solution:

Question 5.
Decrease 850 in the ratio 17 : 6 and then increase the result in the ratio 5 : 9.
Solution:

Question 6.
Decrease 850 in the ratio 17 : 6 and then decrease the resulting number again in 4 : 3.
Solution:

Question 7.
Increase 1200 in the ratio 2 : 3 and then decrease the resulting number in the ratio 10 : 3.
Solution:

Question 8.
Increase 1200 in the ratio 3 : 7 and then increase the resulting number again in the ratio 4 : 7.
Solution:

Question 9.
The number 650 is decreased to 500 in the ratio a : b, find the ratio a : b.
Solution:

Question 10.
The number 800 is increased to 960 in the ratio a : b, find the ratio a : b.
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Concise Mathematics Class 7 ICSE Solutions Chapter 1 Integers

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 1 Integers

Integers Exercise 1A – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Evaluate:

1. 427 x 8 + 2 x 427
2. 394 x 12 + 394 x (-2)
3. 558 x 27 + 3 x 558

Solution:

Question 2.
Evaluate:

1. 673 x 9 + 673
2. 1925 x 101 – 1925

Solution:

Question 3.
Verify:

1. 37 x {8 +(-3)} = 37 x 8 + 37 x – (3)
2. (-82) x {(-4) + 19} = (-82) x (-4) + (-82) x 19
3. {7 – (-7)} x 7 = 7 x 7 – (-7) x 7
4. {(-15) – 8} x -6 = (-15) x (-6) – 8 x (-6)

Solution:

Question 4.
Evaluate:

1. 15 x 8
2. 15 x (-8)
3. (-15) x 8
4. (-15) x -8

Solution:

Question 5.
Evaluate:

1. 4 x 6 x 8
2. 4 x 6 x (-8)
3. 4 x (-6) x 8
4. (-4) x 6 x 8
5. 4 x (-6) x (-8)
6. (-4) x (-6) x 8
7. (-4) x 6 x (- 8)
8. (-4) x (-6) x (-8)

Solution:

Question 6.
Evaluate:

1. 2 x 4 x 6 x 8
2. 2 x (-4) x 6 x 8
3. (-2) x 4 x (-6) x 8
4. (-2) x (-4) X 6 x (-8)
5. (-2) x (-4) x (-6) x (-8)

Solution:

Question 7.
Determine the integer whose product with ‘-1’ is:

1. -47
2. 63
3. -1
4. 0

Solution:

Question 8.
Eighteen integers are multiplied together. What will be the sign of their product, if:

1. 15 of them are negative and 3 are positive?
2. 12 of them are negative and 6 are positive?
3. 9 of them are positive and the remaining are negative?
4. all are negative?

Solution:

Question 9.
Find which is greater?

1. (8 + 10) x 15 or 8 + 10 x 15
2. 12 x (6 – 8) or 12 x 6 – 8
3. {(-3) – 4} x (-5) or (-3) – 4 x (-5)

Solution:

Question 10.
State, true or false :

1. product of two integers can be zero.
2. product of 120 negative integers and 121 positive integers is negative.
3. a x (b + c) = a x b + c
4. (b – c) x a=b – c x a

Solution:

Integers Exercise 1B – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Divide:
(i) 117 by 9
(ii) (-117) by 9
(iii) 117 by (-9)
(iv) (-117) by (-9)
(v) 225 by (-15)
(vi) (-552) ÷ 24
(vii) (-798) by (-21)
(viii) (-910) ÷ – 26

Solution :

Question 2.
Evaluate:
(i) (-234) ÷ 13
(ii) 234 ÷ (-13)
(iii) (-234) ÷ (-13)
(iv) 374 ÷ (-17)
(v) (-374) ÷ 17
(vi) (-374) ÷ (-17)
(vii) (-728) ÷ 14
(viii) 272 ÷ (-17)

Solution:

Question 3.
Find the quotient in each of the following divisions:
(i) 299 ÷ 23
(ii) 299 ÷ (-23)
(iii) (-384) ÷ 16
(iv) (-572) ÷ (-22)
(v) 408 ÷ (-17)

Solution:

Question 4.
Divide:
(i) 204 by 17
(ii) 152 by-19
(iii) 0 by 35
(iv) 0 by (-82)
(v) 5490 by 10
(vi) 762800 by 100

Solution:

Question 5.
State, true or false :

1. 0 ÷ 32 = 0
2. 0 ÷ (-9) = 0
3. (-37) ÷ 0 = 0
4. 0 ÷ 0 = 0

Solution:

Question 6.
Evaluate:
(i) 42 ÷ 7 + 4
(ii) 12+18 ÷ 3
(iii) 19 – 20 ÷ 4
(iv) 16 – 5 x 3+4
(v) 6 – 8 – (-6) ÷ 2
(vi) 13 -12 ÷ 4 x 2
(vii) 16 + 8 ÷ 4- 2 x 3
(viii) 16 ÷ 8 + 4 – 2 x 3
(ix) 16 – 8 + 4 ÷ 2 x 3
(x) (-4) + (-12) ÷ (-6)
(xi) (-18) + 6 ÷ 3 + 5
(xii) (-20) x (-1) + 14 – 7

Solution:

Integers Exercise 1C – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Evaluate:
18-(20- 15 ÷ 3)
Solution:

Question 2.
-15+ 24÷ (15-13)
Solution:

Question 3.
35 – [15 + {14-(13 + \(\overline { 2-1+3 }\))}]
Solution:

Question 4.
27- [13 + {4-(8 + 4 – \(\overline { 1+3 }\))}]
Solution:

Question 5.
32 – [43-{51 -(20 – \(\overline { 18 -7 }\))}]
Solution:

Question 6.
46-[26-{14-(15-4÷ 2 x 2)}]
Solution:

Question 7.
45 – [38 – {60 ÷ 3 – (6 – 9 ÷ 3) ÷ 3}]
Solution:

Question 8.
17- [17 — {17 — (17 – \(\overline { 17 -17 }\))}]
Solution:

Question 9.
2550 – [510 – {270 – (90 – \(\overline { 80 + 7 }\))}]
Solution:

Question 10.
30+ [{-2 x (25-\(\overline { 13 -3 }\))}]
Solution:

Question 11.
88-{5-(-48)+ (-16)}
Solution:

Question 12.
9 x (8-\(\overline { 3 +2 }\)) – 2 (2 + \(\overline { 3 +3 }\))
Solution:

Question 13.
2 – [3 – {6 – (5 – \(\overline { 4 -3 }\))}]
Solution:

Integers Exercise 1D – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
The sum of two integers is -15. If one of them is 9, find the other.
Solution:

Question 2.
The difference between an integer and -6 is -5. Find the values of x.
Solution:

Question 3.
The sum of two integers is 28. If one integer is -45, find the other.
Solution:

Question 4.
The sum of two integers is -56. If one integer is -42, find the other.
Solution:

Question 5.
The difference between an integer x and (-9) is 6. Find all possible values ofx.
Solution:

Question 6.
Evaluate:

1. (-1) x (-1) x (-1) x  ….60 times.
2. (-1) x (-1) x (-1) x (-1) x …. 75 times.

Solution:

Question 7.
Evaluate:

1. (-2) x (-3) x (-4) x (-5) X (-6)
2. (-3) x (-6) x (-9) x (-12)
3. (-11) x (-15) + (-11) x (-25)
4. 10 x (-12) + 5 x (-12)

Solution:

Question 8.

1. If x x (-1) = -36, is x positive or negative?
2. If x x (-1) = 36, is x positive or negative?

Solution:

∴ It is a positive integer.

Question 9.
Write all the integers between -15 and 15, which are divisible by 2 and 3.
Solution:

Question 10.
Write all the integers between -5 and 5, which are divisible by 2 or 3.
Solution:

Question 11.
Evaluate:

1. (-20) + (-8) ÷ (-2) x 3
2. (-5) – (-48) ÷ (-16) + (-2) x 6
3. 16 + 8 ÷ 4- 2 x 3
4. 16 ÷ 8 x 4 – 2 x 3
5. 27 – [5 + {28 – (29 – 7)}]
6. 48 – [18 – {16 – (5 – \(\overline { 4 +1 }\))}]
7. -8 – {-6 (9 – 11) + 18 = -3}
8. (24 ÷ \(\overline { 12 -9 }\) – 12) – (3 x 8 ÷ 4 + 1)

Solution:

Question 12.
Find the result of subtracting the sum of all integers between 20 and 30 from the sum of all integers from 20 to 30.
Solution:

Question 13.
Add the product of (-13) and (-17) to the quotient of (-187) and 11.
Solution:

Question 14.
The product of two integers is-180. If one of them is 12, find the other.
Solution:

Question 15.

1. A number changes from -20 to 30. What is the increase or decrease in the number?
2. A number changes from 40 to -30. What is the increase or decrease in the number?

Solution:

Selina Concise Mathematics Class 7 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 10 Sets

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 10 Sets

Sets Exercise 10A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
State whether or not the following elements form a set; if not, give reason:
(i) All easy problems in your text book.
(ii) All three sided figures.
(iii) The first five counting numbers.
(iv) All the tall boys of your class.
(v) The last three days of the week.
(vi) All triangles that are difficult to draw.
(vii) The first three letters of the English alphabet.
(viii) All tasty fruits.
(ix) All clever boys of class 6.
(x) All good schools in Delhi.
(xi) All the girls in your class, whose heights are less than your height.
(xii) All the boys in your class, whose heights are more than your height.
(xiii) All the problems in your Mathematics book, which are difficult for Amit.
Solution:

Sets Exercise 10B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
If set A = {2, 3, 4, 5, 6}, state which of the following statements arc true and which are false :
(i) 2 ∈ A
(ii) 5, 6 ∈ A
(iii) 3, 4, 7 ∈ A
(iv) 2, 8 ∈ A
Solution:

Question 2.
If set B = {4, 6, 8, 10, 12, 14}. State, which of the following statements is correct and which is wrong :
(i) 5 ∈ B
(ii) 12 ∈ B
(iii) 14 ∈ B
(iv) 9 ∈ B
(v) B is a set of even numbers between 2 and 16.
(vi) 4,6 and 10 are die members of the set B. Also, write the wrong statements correctly.
Solution:

Question 3.
State, whether true or false :
(i) Sets {4, 9, 6,2} and {6, 2, 4, 9} are not the same.
(ii) Sets {0, 1, 3, 9, 4} and {4, 0, 1, 3, 9} are the same.
(iii) Sets {5, 4} and {5, 4, 4, 5} are not the same.
(iv) Sets {8, 3} and {3, 3, 8} are the same.
(v) Collection of vowels used in the word ‘ALLAHABAD’ forms a set.
(vi) If P is the set of letters in the word ‘ROOP’; then P = (p, o, r)
(vii) If M is the set of letters used in the word ‘MUMBAI’, then: M = {m, u, b, a, i}
Solution:

Question 4.
Write the set containing :
(i) the first five counting numbers.
(ii) the three types of angles.
(iii) the three types of triangles.
(iv) the members of your family.
(v) the first six consonants of the English Alphabet.
(vi) the first four vOWels of the English Alphabet.
(vii) the names of any three Prime-Ministers of India.
Solution:

Question 5.
(a) Write the members (elements) of each set given below :
(i) {3, 8, 5, 15, 12, 7}
(ii) {c, m, n, o, s}
(b) Write the sets whose elements are :
(i) 2, 4, 8, 16, 64 and 128
(ii) 3, 5, 15, 45, 75 and 90
Solution:

Question 6.
(i) Write the set of letters used in the word ‘BHOPAL’.
(ii) Write the set of vowels used im the word ‘BENGAL’.
(iii) Write the set of consonants used in the word ‘HONG KONG’.
Solution:

Sets Exercise 10C – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Write each of the following sets in the Roster Form :
(i) The set of five numbers each of which is divisible by 3.
(ii) The set of integers between – 4 and 4.
(iii) {x: x is a letter in the word ‘ SCHOOL’}
(iv) {x: x is an odd natural number between 10 and 20}
(v) {Vowels used in the word ‘AMERICA’}
(vi) {Consonants used in the * word ‘MADRAS’}
Solution:

Question 2.
Write each given set in the Roster Form :
(i) All prime numbers between one and twenty.
(ii) The squares of first four natural numbers.
(iii) Even numbers between 1 and 9.
(iv) First eight letters of the English alphabet.
(v) The letters of the word ‘BASKET’.
(vi) Four cities of India whose names start with the letter J.
(vii) Any four closed geometrical figures.
(viii) Vowels used in the word ‘MONDAY’.
(ix) Single digit numbers that are perfect squares as well.
Solution:

Question 3.
Write each given set in the Set- Builder Form :
(i) {2, 4, 6, 8, 10}
(ii) {2, 3, 5, 7, 11}
(iii) {January, June, July}
(iv) {a, e, i, o, u}
(v) {Tuesday, Thursday}
(vi) {1,4,9, 16, 25}
(vii) {5,10,15,20,25,30}
Solution:

Question 4.
Write each of the following sets in Roster (tabular) Form and also in Set-Builder Form.
(i) Set of all natural numbers that can divide 24 completely.
(ii) Set of odd numbers between 20 and 35.
(iii) Set of letters used in the word ‘CALCUTTA’.
(iv) Set of names of the first five months of a year.
(v) Set of all two digit numbers that are perfect square as well.
Solution:

Question 5.
Write, in Roster Form, the set of :
(i) the first four odd natural numbers each divisible by 5.
(ii) th counting numbers between 15 and 35; each of which is divisible by 6.
(iii) the names of the last three days of a week.
(iv) the names of the last four months of a year.
Solution:

Sets Exercise 10D – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
State, whether the given set is infinite or finite :
(i) {3, 5, 7, ………}
(ii) {1, 2, 3, 4}
(iii) {………., -3, -2, -1, 0, 1, 2}
(iv) {20, 30, 40, 50, …, 200}
(v) {7, 14, 21, ……….., 2401}
Solution:

Question 2.
(i) Which of the following sets is empty?
(ii) Set of counting numbers between 5 and 6.
(iii) Set of odd numbers between 7 and 19. Set of odd numbers between 7 and 9.
(iv) Set of even numbers which are not divisible by 2.
(v) {0}.
Solution:

Question 3.
State, which pair of sets, given below, are equal sets or equivalent sets:
(i) {3, 5, 7} and {5, 3, 7}
(ii) {8, 6, 10, 12} and {3, 2, 4, 6}
(iii) {7, 7, 2, 1,2} and {1, 2, 7}
(iv) {2, 4, 6, 8, 10} and {a, b, d, e, m}
(v) {5, 5, 2, 4} and {5, 4, 2, 2}
Solution:

Question 4.
State, which of the following are finite or infinite sets :
(i) Set of integers
(ii) {Multiples of 5}
(iii) {Fractions between 1 and 2}
(iv) {Number of people in India}
(v) Set of trees in the world
(vi) Set of leaves on a tree
(vii) Set of children in all the schools of Delhi
(viii) { …….., -4, -2, 0, 2, 4, 6, 8}
(ix) {- 12, – 9, – 6, – 3, 0, 3, 6, …….}
(x) {Number of points in a line segment 4 cm long}.
Solution:

Question 5.
State, whether or not the following sets are empty :
(i) {Prime numbers divisible by 2}
(ii) {Negative natural numbers}
(iii) {Women with height 5 metre}
(iv) {Integers less than 5}
(v) {Prime numbers between 17 and 23}
(vi) Set of even numbers, not divisible by 2
(vii) Set of multiples of 3, which are more than 9 and less than 15.
Solution:

Question 6.
State, if the given pairs of sets are equal sets or equivalent sets :
(i) {Natural numbers less than five} and {Letters of the word ‘BOAT’}.
(ii) {2, 4, 6, 8, 10} and {even natural numbers less than 12}
(iii) {1, 3, 5, 7, ………..} and set of odd natural numbers.
(iv) {Letters of the word MEMBER} and {Letters of the word ‘REMEMBER’}.
(v) {Negative natural numbers} and {50th day of a month}
(vi) {Even natural numbers} and {odd natural numbers}.
Solution:

Question 7.
State, whether the following are finite or infinite sets :
(i) {2, 4, 6, 8, …… 800}
(ii) {……, -5, -4, -3, -2}
(iii) {x : x is an integer between – 60 and 60}
(iv) {No. of electrical appliances working in your house}
(v) {x : x is a whole number greater than 20}
(vi) {x : x is a whole number less than 20}
Solution:

Question 8.
For each statement, given below, write True or False :
(i) {…., -8, -4, 0, 4, 8} is a finite set.
(ii) { – 32, – 28, – 24, – 20, ……….. , 0, 4, 8, 16} is an infinite set.
(iii) {x : x is a natural number less than 1} is the empty set.
(iv) {Whole numbers between 15 and 16} = {Natural numbers between 5 and 6}
(v) {Odd numbers divisible by 2} is the empty set.
(vi) {Even natural numbers divisible by 3} is the empty set.
(vii) {x : x is positive and x < 0} is the empty set.
(viii) {.., -5, -3, -1, 1, 3, 5, ..} is a finite set.
Solution:

Question 9.
State, giving reasons, which of the following pairs of sets are disjoint sets and which are or overlapping sets :
(i) A = {Girls with ages below 15 years} and B = {Girls with ages above 15 years}
(ii) C = {Boys with ages above 20 years} and D = {Boys with ages above 27 years}
(iii) A = {Natural numbers between 35 and 60} and B = {Natural numbers between 50 and 80}
(iv) P = {Students of class IX studying in I.C.S.E. Board} and Q = {Students of class IX}
(v) A = {Natural numbers multiples of 3 and less than 30} and B = {Natural numbers divisible by 4 and between 20 and 45}
(vi) P = {Letters in the word ‘ALLAHABAD’} and Q = {Letters in the word ‘MUSSOORIE’}
Solution:

Sets Exercise 10E – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Write the cardinal number of each of the following sets :
(i) A = {0, 1, 2, 4}
(ii) B = {-3, -1, 1, 3, 5, 7}
(iii) C = { }
(iv) D= {3, 2, 2, 1, 3, 1, 2}
(v) E = {Natural numbers between 15 and 20}
(vi) F = {Whole numbers from 8 to 14}.
Solution:

Question 2.
Given :
(i) A = {Natural numbers less than 10}
B = {Letters of the word ‘PUPPET’}
C = {Squares of first four whole numbers}
D = {Odd numbers divisible by 2}. Find :

Solution:

Question 3.
State true or false for each of the following. Correct the wrong statement.
(i) If A = {0}, then n(A) = 0.
(ii) n(φ) = 1.
(iii) If T ={a, l, a, h, b, d, h), then n(T) = 5.
(iv) If B ={1, 5, 51, 15, 5, l},then n(B) = 6.
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 9 Playing with Numbers

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 9 Playing with Numbers

Playing with Numbers Exercise 9A – Selina Concise Mathematics Class 6 ICSE Solutions

(Using BODMAS)
Question 1.
19 – (1 + 5) – 3
Solution:

Question 2.
30 x 6 + (5 – 2)
Solution:
>

Question 3.
28 – (3 x 8) + 6
Solution:

Question 4.
9 – [(4 – 3) + 2 x 5]
Solution:

Question 5.
[18 – (15 – 5) + 6]
Solution:

Question 6.
[(4 x 2) – (4 + 2)] + 8
Solution:

Question 7.
48 + 96 – 24 – 6 x 18
Solution:

Question 8.
22 – [3 – {8 – (4 + 6)}]
Solution:

Question 9.

Solution:

Question 10.
60 – {16 + (4 x 6 – 8)}
Solution:

Question 11.

Solution:

Question 12.
15 – [16 – {12 + 21 ÷ (9 – 2)}]
Solution:

Playing with Numbers Exercise 9B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Fill in the blanks :
(i) On dividing 9 by 7, quotient = …………. and remainder = ……….
(ii) On dividing 18 by 6, quotient = …………. and remainder = ………….
(iii) Factor of a number is ………….. of …………..
(iv) Every number is a factor of …………….
(v) Every number is a multiple of …………..
(vi) …………. is factor of every number.
(vii) For every number, its factors are ………… and its multiples are …………..
(viii) x is a factor of y, then y is a ………… of x.
Solution:

Question 2.
Write all the factors of :
(i) 16
(ii) 21
(iii) 39
(iv) 48
(v) 64
(vi) 98
Solution:

Question 3.
Write the first six multiples of :
(i) 4
(ii) 9
(iii) 11
(iv) 15
(v) 18
(vi) 16
Solution:

Question 4.
The product of two numbers is 36 and their sum is 13. Find the numbers.
Solution:

Question 5.
The product of two numbers is 48 and their sum is 16. Find the numbers.
Solution:

Question 6.
Write two numbers which differ by 3 and whose product is 54.
Solution:

Question 7.
Without making any actual division show that 7007 is divisible by 7.
Solution:

Question 8.
Without making any actual division, show that 2300023 is divisible by 23.
Solution:

Question 9.
Without making any actual division, show that each of the following numbers is divisible by 11.
(i) 11011
(ii) 110011
(iii) 11000011
Solution:

Question 10.
Without actual division, show that each of the following numbers is divisible by 8 :
(i) 1608
(ii) 56008
(iii) 240008
Solution:

Playing with Numbers Exercise 9C – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
find which of the following numbers are divisible by 2 :
(i) 352
(ii) 523
(iii) 496
(iv) 649
Solution:

Question 2.
Find which of the following number are divisible by 4 :
(i) 222
(ii) 532
(iii) 678
(iv) 9232
Solution:

Question 3.
Find the which of the following numbers are divisible by 8 :
(i) 324
(ii) 2536
(iii) 92760
(iv) 444320
Solution:

Question 4.
Find which of the following numbers are divisible by 3 :
(i) 221
(ii) 543
(iii) 28492
(iv) 92349
Solution:

Question 5.
Find which of the following numbers are divisible by 9 :
(i) 1332
(ii) 53247
(iii) 4968
(iv) 200314
Solution:

Question 6.
Find which of the following number are divisible by 6 :
(i) 324
(ii) 2010
(iii) 33278
(iv) 15505
Solution:

Question 7.
Find which of the following numbers are divisible by 5 :
(i) 5080
(ii) 66666
(iii) 755
(iv) 9207
Solution:

Question 8.
Find which of the following numbers are divisible by 10 :
(i) 9990
(ii) 0
(iii) 847
(iv) 8976
Solution:

Question 9.
Find which of the following numbers are divisible by 11 :
(i) 5918
(ii) 68,717
(iii) 3882
(iv) 10857
Solution:

Question 10.
Find which of the following numbers are divisible by 15 :
(i) 960
(ii) 8295
(iii) 10243
(iv) 5013
Solution:

Question 11.
In each of the following numbers, replace M by the smallest number to make resulting number divisible by 3 :
(i) 64 M 3
(ii) 46 M 46
(iii) 27 M 53
Solution:

Question 12.
In each of the following numbers replace M by the smallest number to make resulting number divisible by 9.
(i) 76 M 91
(ii) 77548 M
(iii) 627 M 9
Solution:

Question 13.
In each of the following numbers, replace M by the smallest number to make resulting number divisible by 11.
(i) 39 M 2
(ii) 3 M 422
(iii) 70975 M
(iv) 14 M 75
Solution:

Question 14.
State, true or false :
(i) If a number is divisible by 4. It is divisible by 8.
(ii) If a number is a factor of 16 and 24, it is a factor of 48.
(iii) If a number is divisible by 18, it is divisible by 3 and 6.
(iv) If a divide b and c completely, then a divides (i) a + b (ii) a – b also completely.
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 8 HCF and LCM

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 8 HCF and LCM

HCF and LCM Exercise 8A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Write all the factors of :
(i) 15
(ii) 55
(iii) 48
(iv) 36
(v) 84
Solution:

Question 2.
Write all prime numbers :
(i) less than 25
(ii) between 15 and 35
(iii) between 8 and 76
Solution:

Question 3.
Write the prime-numbers from :
(i) 5 to 45
(ii) 2 to 32
(iii) 8 to 48
(iv) 9 to 59
Solution:

Question 4.
Write the prime factors of:
(i) 16
(ii) 27
(iii) 35
(iv) 49
Solution:

Question 5.
If P_n means prime factors of n, find:
(i) p₆
(ii) P₂₄
(iii) p₅₀
(iv) P₄₂
Solution:

HCF and LCM Exercise 8B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Using the common factor method, find the H.C.F. of :
(i) 16 and 35
(ii) 25 and 20
(iii) 27 and 75
(iv) 8, 12 and 18
(v) 24, 36, 45 and 60
Solution:

Question 2.
Using the prime factor method, find the H.C.F. of:
(i) 5 and 8
(ii) 24 and 49
(iii) 40, 60 and 80
(iv) 48, 84 and 88
(v) 12, 16 and 28
Solution:

Question 3.
Using the division method, find the H.C.F. of the following :
(i) 16 and 24
(ii) 18 and 30
(iii) 7, 14 and 24
(iv) 70,80,120 and 150
(v) 32, 56 and 46
Solution:

Question 4.
Use a method of your own choice to find the H.C.F. of :
(i) 45, 75 and 135
(ii) 48, 36 and 96
(iii) 66, 33 and 132
(iv) 24, 36, 60 and 132
(v) 30, 60, 90 and 105
Solution:

Question 5.
Find the greatest number that divides each of 180, 225 and 315 completely.
Solution:

Question 6.
Show that 45 and 56 are co-prime numbers.
Solution:

Question 7.
Out of 15, 16, 21 and 28, find out all the pairs of co-prime numbers.
Solution:

Question 8.
Find the greatest no. that will divide 93, 111 and 129, leaving remainder 3 in each case.
Solution:

HCF and LCM Exercise 8C – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Using the common multiple method, find the L.C.M. of the following :
(i) 8, 12 and 24
(ii) 10, 15 and 20
(iii) 3, 6, 9 and 12
Solution:

Question 2.
Find the L.C.M. of each the following groups of numbers, using
(i) the prime factor method and
(ii) the common division method :
(i) 18, 24 and 96
(ii) 100, 150 and 200
(iii) 14, 21 and 98
(iv) 22, 121 and 33
(v) 34, 85 and 51
Solution:

Question 3.
The H.C.F. and the L.C.M. of two numbers are 50 and 300 respectively. If one of the numbers is 150, find the other one.
Solution:

Question 4.
The product of two numbers is 432 and their L.C.M. is 72. Find their H.C.F.
Solution:

Question 5.
The product of two numbers is 19,200 and their H.C.F. is 40. Find their L.C.M.
Solution:

Question 6.
Find the smallest number which, when divided by 12, 15, 18, 24 and 36 leaves no remainder
Solution:

Question 7.
Find the smallest number which, when increased by one is exactly divisible by 12, 18, 24, 32 and 40
Solution:

Question 8.
Find the smallest number which, on being decreased by 3, is completely divisible by 18, 36, 32 and 27.
Solution:

HCF and LCM Revision Exercise – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Find the H.C.F. of :
(i) 108, 288 and 420
(ii) 36, 54 and 138
Solution:

Question 2.
Find the L.C.M. of:
(i) 72, 80 and 252
(ii) 48, 66 and 120
Solution:

Question 3.
State true or false : Give an example.
(i) H.C.F. of two prime numbers is 1.
(ii) H.C.F. of two co-prime numbers is 1.
(iii) L.C.M. of two prime numbers is equal to their product.
(iv) L.C.M. of two co-prime numbers is equal to their product.
Solution:

Question 4.
The product of two numbers is 12096 and their H.C.F. is 36. Find their L.C.M.
Solution:

Question 5.
The product of the H.C.F. and the L.C.M. of two numbers is 1152. If one number is 48, find the other one.
Solution:

Question 6.
(i) Find the smallest number that is completely divisible by 28 and 42.
(ii) Find the largest number that can divide 28 and 42 completely.
Solution:

Question 7.
Find the L.C.M. of 140 and 168. Use the L.C.M. obtained to find the H.C.F. of the given numbers.
Solution:

Question 8.
Find the H.C.F. of 108 and 450 and use the H.C.F. obtained to find the L.C.M. of the given numbers.
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions