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ML Aggarwal Class 7 Solutions Chapter 7 Percentage and Its Applications Ex 7.2 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 7 Percentage and Its Applications Ex 7.2

Question 1.
Find:
(i) 15% of 250
(ii) 25% of 120 litres
(iii) 1% of 1 hour
(iv) 75% of 1 kg
(v) 120% of ₹ 250
(vi) 0.6% of 2 km
Solution:

Question 2.
8% of children of a class of 25 like getting wet in the rain. How many children like getting wet in the rain?
Solution:

Question 3.
Vasundhara ate 3 ice cream cups out of 20 kept in the fridge. What per cent did she eat?
Solution:

Question 4.
Express:
(i) 20 as a percentage of 50
(ii) 60 litres as a percentage of 40 litres
(iii) 90 cm as a percentage of 4.5 m
(iv) 350 g as a percentage of 5.6 kg
Solution:

Question 5.
What per cent is:
(i) 12 of 80
(ii) 25 paise of 4 rupees
(iii) 300 g of 2 kg
Solution:

Question 6.
A school team won 6 games this year against 4 games won last year. What is the per cent increase?
Solution:

Question 7.
The price of a shirt decreased from ₹ 80 to ₹ 60, find the percentage of decrease in the price of the shirt.
Solution:

Question 8.
My mother says, in her childhood petrol was ₹ 1 per litre. It is ₹ 65 per litre today. By what percentage has the prices of petrol gone up?
Solution:

Question 9.
Rate of basmati rice last year was ₹ 40 a kg. This year they are costly by 20%. What is the price this year?
Solution:

Question 10.
300 students took an exam. 28% failed. Calculate the number of students who passed the exam.
Solution:

Question 11.
Out of 15000 voters in a constituency, 60% voted. Find the number of voters who did not vote.
Solution:

Question 12.
20% of the length of a flagpole is painted green, 45% is painted yellow and the remaining red. If the length of the pole is 18 m, what length of it is painted red?
Solution:

Question 13.
Chalk contains 10% calcium, 3% carbon, 12% oxygen and the remaining sand. Find the amount of carbon and calcium (in grams) in 2\(\frac { 1 }{ 2 }\) kg of chalk. Also, find the amount of sand (in kg).
Solution:

Question 14.
Find the whole quantity if:
(i) 25% of it is 9
(ii) 75% of it is 15
(iii) 12% of it is ₹ 1080
(iv) 8% of it is 40 litres
Solution:

Question 15.
Mohini saves ₹ 400 from her salary. If this is 10% of her salary, then what is her salary?
Solution:

Question 16.
16% of the apples in a basket go bad. If there are 42 good apples in the basket, find the total number of apples in the basket.
Solution:

Question 17.
In an examination, a student has to secure 45% marks to pass the exam. If Varun got 251 marks and failed by 19 marks, what are the maximum marks?
Solution:

Question 18.
On a rainy day, 94% of the students were students absent on that day was 174, find the total strength of the school.
Solution:

Question 19.
40% of the population of a town are men and 39% are women. If the number of children is 12600, find the number of men.
Solutions:

Question 20.
If the price of a watch is increased by 15%, the increase in the price is ₹ 90. What was the price of watching earlier?
Solution:

Question 21.
(i) Find the number which when increased by 30% becomes 39.
(ii) Find the number which when decreased by 8% becomes 506.
Solution:

Question 22.
The price of a shirt is reduced by 7% to ₹ 465. What is its original price?
Solution:

ML Aggarwal Class 7 Solutions Chapter 7 Percentage and Its Applications Ex 7.1 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 7 Percentage and Its Applications Ex 7.1

Question 1.
Convert the following percents into fractions in simplest form:
(i) 25%
(ii) 150%
(iii) 7\(\frac { 1 }{ 2 }\) %
(iv) 33\(\frac { 1 }{ 3 }\) %
Solution:

Question 2.
Convert the following fractions into percents:
(i) \(\frac { 1 }{ 8 }\)
(ii) \(\frac { 5 }{ 4 }\)
(iii) \(\frac { 9 }{ 16 }\)
(iv) \(\frac { 3 }{ 7 }\)
(v) \(\frac { 11 }{ 15 }\)
(vi) 1\(\frac { 3 }{ 8 }\)
Solution:

Question 3.
(i) 6 students out of 40 students in a class are absent. What percentage of students are absent ?
(ii) Antony secured 384 marks out of 500 marks. Find the percentage of marks secured by Antony.
(iii) A shop has 500 shirts, out of which 15 are defective. What percentage of shirts are defective?
(iv) Vani has a collection of bangles. She has 20 gold bangles and 10 silver bangles. What is the percentage of each type of bangles?
(v) There are 120 voters and 90 of them voted. What percent did not vote?
Solution:

Question 4.
Estimate the part of the figure which is shaded and hence find the percentage of the part which is shaded.

Solution:

Question 5.
Convert the following percentage into ratios in sirup rest form:
(i) 14 %
(ii) 1\(\frac { 3 }{ 4 }\) %
(iii) 33\(\frac { 1 }{ 3 }\) %
(iv) 37.5 %
Solution:

Question 6.
Express the following ratios as percentages:
(i) 5 : 4
(ii) 1 : 1
(iii) 2 : 3
(iv) 9 : 16
Solution:

Question 7.
An alloy consists of 7 parts of zinc and 33 parts of copper. Find the percentage of copper in the alloy ?
Solution:

Question 8.
Chalk contains calcium, carbon and sand in the ratio 12 : 3 : 10. Find the percentage of carbon in the chalk 12%.
Solution:

Question 9.
If ₹ 2500 is to be divided among Ravi, Raju and Roy, so that Ravi gets two parts, Raju three parts and Roy five parts. How much money will each get? What will it be in percentages?
Solution:

Question 10.
Convert the following percentages to decimals:
(i) 28%
(ii) 3%
(iii) 0. 44%
(iv) 37\(\frac { 1 }{ 2 }\) %
Solution:

Question 11.
Convert the following decimals to percents:
(i) 0.65
(ii) 0.9
(iii) 2.1
(iv) 0.02
Solution:

Question 12.
(i) If 42% of the students in a class are girls, then what percent of the students in the class are boys?
(ii) We have a basket full of apples, oranges, and mangoes if 50% are apples, 30% are oranges, then what percent are mangoes?
Solution:

ML Aggarwal Class 7 Solutions Chapter 6 Ratio and Proportion Objective Type Questions for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 6 Ratio and Proportion Objective Type Questions

Mental Maths
Question 1.
Fill in the blanks:
(i) The simplest form of the ratio \(\frac { 1 }{ 6 }\) : \(\frac { 1 }{ 4 }\) is ………
(ii) 75 cm : 1.25 m = ……..
(iii) If two ratios are equivalent, then the four quantities are said to be in ………
(iv) If 8, x, 48 and 18 are in proportion then the value of x is ………
(v) If the cost of 10 pencils is ₹ 15, then the cost of 6 pencils is ……..
(vi) If a cyclist is travelling at a speed of 15 km/h, then the distance covered by him in 20 minutes is ……..
Solution:

Question 2.
State whether the following statements are true (T) or false (F):
(i) A ratio is always greater than 1.
(ii) Ratio of half an hour to 20 seconds is 30 : 20.
(iii) The ratio 5 : 7 is greater than the ratio 5 : 6.
(iv) If the numbers 3, 5, 12 and x are in proportion then the value of x is 20.
(v) The ratio 3 : 2 and 4 : 5 are equivalent.
Solution:

Multiple Choice Questions

Choose the correct answer from the given four options (3 to 14):
Question 3.
A ratio equivalent to 6 : 10 is
(a) 3 : 4
(b) 18 : 30
(c) 12 : 40
(d) 5 : 3
Solution:

Question 4.
A ratio equivalent to the ratio \(\frac { 2 }{ 3 }\) : \(\frac { 3 }{ 4 }\) is
(a) 4 : 6
(b) 8 : 9
(c) 6 : 8
(d) 9 : 8
Solution:

Question 5.
The ratio of 75 mL to 3 litres is
(a) 25 : 1
(b) 40 : 1
(c) 1 : 40
(d) 3 : 200
Solution:

Question 6.
The ratio of the number of sides of a rectangle to the number of edges of a cuboid is
(a) 1 : 2
(b) 1 : 3
(c) 2 : 3
(d) none of these
Solution:

Question 7.
In a class of 35 students, the number of girls is 20. The ratio of number of boys to the number of girls in the class is
(a) 3 : 4
(b) 4 : 3
(c) 7 : 4
(d) 7 : 3
Solution:

Question 8.
The ratio of number of girls to the number of boys in a class is 6 : 7. If there are 21 boys in the class, then the number of girls in the class is
(a) 39
(b) 24
(c) 18
(d) 13
Solution:

Question 9.
Two numbers are in the ratio 3 : 5. If the sum of the numbers is 144, then the largest number is
(a) 48
(b) 54
(c) 72
(d) 90
Solution:

Question 10.
If x, 12, 8 and 32 are in proportion, then x is
(a) 6
(b) 4
(c) 3
(d) 2
Solution:

Question 11.
If 3, 12 and x are in continued proportion, then x is
(a) 4
(b) 6
(c) 16
(d) 48
Solution:

Question 12.
If the weight of 5 bags of sugar is 27 kg, then the weight of one bag of sugar is
(a) 5.4 kg
(b) 5.2 kg
(c) 5.4 kg
(d) 5.6 kg
Solution:

Question 13.
Sonali bought one dozen notebooks for ₹ 66. What did she pay for one notebook?
(a) ₹ 6.50
(b) ₹ 6.60
(c) ₹ 5.60
(d) ₹ 5.50
Solution:

Question 14.
The speed of 90 km/h is equal to
(a) 10 m/sec
(b) 18 m/sec
(c) 25 m/sec
(d) none of these
Solution:

Value Based Questions

Question 1.
Sudhanshu divided his property into two parts in the ratio 8 : 5. If the first part is ₹ 1,60,000 and second part is donated to an orphanage, find the amount donated to the orphanage. What values are being promoted?
Solution:

Higher Order Thinking Skills (HOTS)

Question 1.
Present ages of Rohit and Mayank are in the ratio 11 : 8. 8 years hence the ratio of their ages will be 5 : 4. Find their present ages.
Solution:

Question 2.
Ratio of length and breadth of a rectangle is 3 : 2. If the length of the rectangle is 5 m more than the breadth, find the perimeter of the rectangle.
Solution:

ML Aggarwal Class 7 Solutions Chapter 6 Ratio and Proportion Ex 6.4 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 6 Ratio and Proportion Ex 6.4

Question 1.
Convert the following speeds into m/sec:
(i) 72 km/h
(ii) 9 km/h
(iii) 1.2 km/minutes
(iv) 600 m/hour
Solution:

Question 2.
Convert the following speeds into km/h:
(i) 15 m/sec
(ii) 1.5 m/sec
Solution:

Question 3.
Which is greater- the speed of 30 m/sec or 30 km/h?
Solution:

Question 4.
An aeroplane is flying at a speed of 720 km/h.
(i) If the aerial distance between two cities is 1800 km, how much time will the aeroplane take in crossing these cities?
(ii) How much distance does the aeroplane cover in 40 minutes?
(iii) How far will it fly in 15 seconds?
Solution:

Question 5.
A dog is walking at a speed of 6 km/h.
(i) How much distance does it cover in 5 minutes?
(ii) How much time would it take to cover 200 metres?
Solution:

Question 6.
A swimming pool is 50 metres long. A boy can swim across the length and then return to his starting position in 5 minutes. What is his swimming speed in km/h?
Solution:

Question 7.
A bus takes 48 minutes to cover a certain distance when travelling at a speed of 50 km/h. How much time will it take to cover the same distance when travelling at a speed of 30 km/h?
Solution:

ML Aggarwal Class 7 Solutions Chapter 4 Exponents and Powers Ex 4.1 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 4 Exponents and Powers Ex 4.1

Question 1.
Fill in the blanks:
(i) In the expression 3⁷, base = …….. and exponent = ……..
(ii) In the expression (-7)⁵, base = ………. and exponent = …….
(iii) In the expression \(\left( \frac { 2 }{ 5 } \right) ^{ 11 }\), base = …… and exponent = …….
(iv) If base is 6 and exponent is 8, then exponential form = ……..
Solution:

Question 2.
Find the value of the following:
(i) 2⁶
(ii) 5⁵
(v) (-6)⁴
(vi) \(\left( \frac { 2 }{ 3 } \right) ^{ 4 }\)
(v) \(\left( \frac { -2 }{ 3 } \right) ^{ 5 }\)
(vi) (-2)⁹
Solution:

Question 3.
Express the following in the exponential form:
(i) 6 × 6 × 6 × 6 × 6
(ii) t × t × t
(iii) 2 × 2 × a × a × a × a
(iv) a × a × a × c × c × c × c × d
Solution:

Question 4.
Simplify the following:
(i) 7 × 10³
(ii) ²⁵ × 9
(iii) 3³ × 10⁴
Solution:

Question 5.
Simplify the following:
(i) (-3) × (-2)³
(ii) (-3)² × (-5)²
(iii) (-2)³ × (-10)⁴
(iv) (-1)⁹
(v) 25² × (-1)³¹
(vi) 4² × 3³ × (-1)¹²²
Solution:

Question 6.
Identify the greater number in each of the following:
(i) 4³ or 3⁴
(ii) 7³ or 3⁷
(iii) 4⁵ or 5⁴
(iv) 2¹⁰ or 10²
Solution:

Question 7.
Write the following numbers as powers of 2:
(i) 8
(ii) 128
(iii) 1024
Solution:

Question 8.
To what power (-2) should be raised to get 16?
Solution:

Question 9.
Write the following numbers as powers of (-3):
(i) 9
(ii) -27
(iii) 81
Solution:

Question 10.
Find the value of x in each of the following:
(i) 7^x = 343
(ii) 3^x = 729
(in) (-8)^x = -512
(iv) (-4)^x = -1024
(v) \(\left( \frac { 2 }{ 5 } \right) ^{ x }\) = \(\frac { 32 }{ 3125 }\)
(vi) \(\left( \frac { -3 }{ 4 } \right) ^{ x }\) = \(\frac { -243 }{ 1024 }\)
Solution:

Question 11.
Write the prime factorization of the following numbers in the exponential form:
(i) 72
(ii) 360
(iii) 405
(iv) 540
(v) 2280
(vi) 3600
(vii) 4725
(viii) 8400
Solution:

ML Aggarwal Class 7 Solutions Chapter 3 Rational Numbers Check Your Progress for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 3 Rational Numbers Check Your Progress

Question 1.
Write five rational numbers equivalent to \(\frac { 5 }{ -11 }\)
Solution:

Question 2.
Express \(\frac { 9 }{ -15 }\) as a rational number with:
(i) denominator 5
(ii) numerator -12
(iii) denominator 30
Solution:

Question 3.
Write each of the following numbers in standard form:

Solution:

Question 4.
Which of the following are pairs of equivalent rational numbers?

Solution:

Question 5.
Arrange the following rational numbers in ascending order:

Solution:

Question 6.

Solution:

Question 7.
Insert five rational numbers between \(\frac { -3 }{ 5 }\) and \(\frac { -1 }{ 2 }\).
Solution:

Question 8.
Find the sum:

Solution:

Question 9.
Subtract:

Solution:

ML Aggarwal Class 7 Solutions Chapter 3 Rational Numbers Objective Type Questions for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 3 Rational Numbers Objective Type Questions

Mental Maths

Question 1.
Fill in the blanks:
(i) Two rational numbers are called equivalent if they have …… value.
(ii) The number \(\frac { -4 }{ 7 }\) lies to the …….. of zero on the number line.
(iii) The rational number \(\frac { -5 }{ -11 }\) lies to the ……. of zero on the number line.
(iv) The rational number \(\frac { -84 }{ 156 }\) reduced to simplest form is ………
(v) The standard form of the rational number \(\frac { 14 }{ -12 }\) is ………
(vi) There are ….. rational numbers between two different rational numbers.
(vii) Two rational numbers \(\frac { p }{ q }\)and \(\frac { r }{ s }\) are equal if an only if q × r = ……..
(viii)The multiplicative inverse of -3\(\frac { 1 }{ 5 }\) is ……..
(ix) \(\frac { -3 }{ 7 }\) ÷ \(\frac { -7 }{ 3 }\) = ………
(x) If p and q are positive integers, then \(\frac { p }{ q }\) is a …… rational number and \(\frac { p }{ -q }\) is a ……
Solution:

Question 2.
State whether the following statements are true (T) or false (F).
(i) Zero is the smallest rational number.
(ii) Every integer is a rational number.
(iii) Every rational number is an integer.
(iv) Every fraction is a rational number.
(v) Every rational number is a fraction.
(vi) The reciprocal of -1 is -1.
(vii) The quotient of two integers is always a rational number.
(viii) The value of a rational number remains the same if both its numerator and denominator are multiplied (or divided) by the same (nonzero) integer.
(ix) Between two distinct integers, we can always insert an integer.
(x) Between two distinct rational numbers, we can al ways insert a rational number.
(xi) There exists atleast one integer between two different rational numbers.
(xii) The reciprocal of 2\(\frac { 6 }{ 7 }\) is \(\frac { -7}{ 20 }\).
(xiii) All terminating decimal numbers are rational numbers.
Solution:

Multiple Choice Questions

Choose the correct answer from the given four options (3 to 14):
Question 3.
The rational number \(\frac { 110 }{ -132 }\) when reduced to standard form is
(a) \(\frac { 10 }{ -12 }\)
(b) \(\frac { 5 }{ -6 }\)
(c) \(\frac { -5 }{ 6 }\)
(d) \(\frac { 110 }{ -132 }\)
Solution:

Question 4.
The Additive inverse of \(\frac { -7 }{ 12 }\) is
(a) \(\frac { 12 }{ -7 }\)
(b) \(\frac { -7 }{ 12 }\)
(c) \(\frac { -5 }{ 12 }\)
(d) \(\frac { 7 }{ 12 }\)
Solution:

Question 5.
The Multiplicative inverse of \(\frac { -4 }{ 9 }\) is
(a) \(\frac { 4 }{ 9 }\)
(b) \(\frac { -9 }{ 4 }\)
(c) \(\frac { 9 }{ 4 }\)
(d) none of these
Solution:

Question 6.
The reciprocal of the rational number -2\(\frac { 3 }{ 7 }\) is
(a) \(\frac { -17 }{ 7 }\)
(b) \(\frac { 7 }{ 17 }\)
(c) \(\frac { -7 }{ 17 }\)
(d) none of these
Solution:

Question 7.
The product of rational number \(\frac { -2 }{ 5 }\) and its multiplicative inverse is
(a) 1
(b) 0
(c) \(\frac { 4 }{ 25 }\)
(d) \(\frac { 2 }{ 5 }\)
Solution:

Question 8.
The product of rational number \(\frac { -2 }{ 3 }\) and its additive inverse is
(a) 1
(b) \(\frac { 2 }{ 3 }\)
(c) \(\frac { 4 }{ 9 }\)
(d) \(\frac { -4 }{ 9 }\)
Solution:

Question 9.
The sum of rational number \(\frac { -1 }{ 3 }\) and its reciprocal is
(a) 0
(b) 1
(c) \(\frac { -10 }{ 3 }\)
(d) \(\frac { -3 }{ 10 }\)
Solution:

Question 10.

Solution:

Question 11.

Solution:

Question 12.

Solution:

Question 13.
In the standard form of a rational number, the denominator is always
(a) 0
(b) a negative integer
(c) 1
(d) a positive integer
Solution:

Question 14.
The sum of two rational numbers is -1. If one of them is \(\frac { -5 }{ 7 }\), then the other is
(a) \(\frac { 5 }{ 7 }\)
(b) \(\frac { -2 }{ 7 }\)
(c) \(\frac { 12 }{ 7 }\)
(d) \(\frac { -12 }{ 7 }\)
Solution:

Value Based Questions

Question 1.
Rohit donated \(\frac { 1 }{ 5 }\) of his monthly income to an NGO working for the education of old women, \(\frac { 1 }{ 4 }\) of his salary spent on food, \(\frac { 1 }{ 3 }\) on rent and \(\frac { 1 }{ 15 }\) on other expenses. If he is left with ₹ 9000, find his monthly income. What values are being promoted?
Solution:

Higher Order Thinking Skills (HOTS)

Question 1.
From a rope 15 m long, 4\(\frac { 1 }{ 3 }\) m is cut off and \(\frac { 3 }{ 5 }\) of the remaining is cut off again. Find the length of the remaining part of the rope.
Solution:

Question 2.
Perimeter of a rectangle is 2 m less than \(\frac { 2 }{ 5 }\) of the perimeter of a square, if the perimeter of the square is 40 m, find the length and breadth of the rectangle given that the breadth is \(\frac { 1 }{ 3 }\) of the length.
Solution:

ML Aggarwal Class 7 Solutions Chapter 3 Rational Numbers Ex 3.3 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 3 Rational Numbers Ex 3.3

Question 1.
Add the following pairs of rational numbers:

Solution:

Question 2.
Find the sum:

Solution:

Question 3.
Subtract:

Solution:

Question 4.
Find:

Solution:

Question 5.
The sum of two rational numbers is \(\frac { 2 }{ 5 }\) if one of them is \(\frac { -4 }{ 7 }\), find the other.
Solution:

Question 6.
What rational number should be added to \(\frac { -5 }{ 12 }\) to get \(\frac { -7 }{ 8 }\)?
Solution:

Question 7.
What rational number should be subtracted from \(\frac { -2 }{ 3 }\) to get \(\frac { -5 }{ 6 }\)?
Solution:

Question 8.
Find the product:

Solution:

Question 9.
Find the value of:

Solution:

Question 10.
The product of two rational numbers is \(\frac { 18 }{ 35 }\) If one of them is \(\frac { -2 }{ 5 }\), find the other.
Solution:

Question 11.
Find the value of:

Solution:

Question 12.
Find the reciprocal of the following:

Solution:

ML Aggarwal Class 7 Solutions Chapter 5 Sets Ex 5.2 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 5 Sets Ex 5.2

Question 1.
Classify the following sets into empty set, finite set and infinite set. In case of (non-empty) finite sets, mention the cardinal number.
(i) {all colours of a rainbow}
(ii) {x | x is a prime number between 7 and 11}
(iii) {multiples of 5}
(iv) {all straight lines drawn in a plane}
(v) {x | x is a digit in the numeral 550131527}
(vi) {x | x is a letter in word SUFFICIENT}
(vii) {x | x = 4n, n ∈ I and x < 10}
(viii) {x | x ∈ N, x is a prime factor of 180}
(ix) {x : x is a vowel in the word WHY}
(x) {x : x = 5n, n ∈ W and x < 60}
Solution:

Question 2.
Which of the following describe the same sets:
(i) {vowels of English alphabet} and {e, a, u, i, o}
(ii) {a, b, d} and {d, a, b, b}
(iii) {letters of PUPPET} and {E, T, P, U}
(iv) {1, 2, 3} and {2, 3, 4}
(v) {1, 2, 3, 4, 5} and {x | x ∈ N, x ≤ 5}
Solution:

Question 3.
Find pairs/groups of equal sets from the following sets:
A = {0, 1, 2, 3}
B = {x : x² < 10, x ∈ W}
C = {letters of word FOLLOW}
D = {days of a week}
E = {x | x ∈ W, x < 4}
F = {letters of word FLOW}
G = {Monday, Tuesday, ……… , Sunday}
H = {letters of word WOLF}
Solution:

Question 4.
Find pairs/groups of equivalent sets from the following sets.
A = {colours of a rainbow}
B = {letters of word GOOD}
C = {x : x is a digit in the numeral 371011489}
D = {letters of word TOM}
E = {x : x ∈ I, x² < 10}
F = {months of a year}
G = {days of a week}
H = {x | x = 3n, n ∈ W and n < 12}
I = {all even numbers between 1 and 53}
J = {all letters of English alphabets}
Solution:

Question 5.
In the following, find whether A ⊂ B or B ⊂ A or none of these:
(i) A = { 1, 2, 3}, B = {2, 3, 3, 3, 1, 3}
(ii) A = {2, 4, 6,….}, B = {all natural numbers}
(iii) A = {x | x ∈ I, x² < 20}, B = {0, 1, 2, 3, 4}
(iv) A = {letters of KING},
B = {letters of QUEEN}
Solution:

Question 6.
State whether each of the following statement is true or false for the sets A and B where
A = {letters of CLOUD} and B = {letters of KOLKATA}
(i) A ⊂ B
(ii) B ⊂ A
(iii) A ↔ B
Solution:

Question 7.
Write all the subsets of the following sets:
(i) Φ
(ii) {3, 5}
(iii) {2, 4, 6}
Solution:

Question 8.
If A = {x : x = 2n, n < 5}, then find A when
(i) ξ = N
(ii) ξ = W
(iii) ξ = I
Solution:

ML Aggarwal Class 7 Solutions Chapter 3 Rational Numbers Ex 3.2 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 3 Rational Numbers Ex 3.2

Question 1.
Draw a number line and represent the following rational numbers on it:
(i) \(\frac { 3 }{ 8 }\)
(ii) \(\frac { -3 }{ 4 }\)
(iii) \(\frac { -7 }{ 8 }\)
(iv) \(\frac { -17 }{ 8 }\)
Solution:

Question 2.
The points P, Q, R, S, T, U, A and B on the number line are such that TR = RS = SU and AP = PQ = QB. Name the rational numbers represented by P, Q, R and S respectively.

Solution:

Question 3.
State whether the following statements are true or false:
(i) The rational number \(\frac { -13 }{ -5 }\) lies to the right of zeroxin the number line.
(ii) The rational numbers \(\frac { -5 }{ -7 }\) and \(\frac { 7 }{ -9 }\) lie on opposite sides of zero on the number line.
(iii) The rational numbers \(\frac { -17 }{ 6 }\) and \(\frac { 8 }{ -15 }\) lie on opposite sides of zero on the number line.
Solution:

Question 4.
Which of the two rational numbers is greater in each of tl following pairs?

Solution:

Question 5.
Fill in the boxes with the correct symbol out of >, < and =:

Solution:

Question 6.
Arrange the following rational numbers in ascending order:

Solution:

Question 7.
Arrange the following rational numbers in descending order:

Solution:

Question 8.
Insert five rational numbers between:
(i) -3 and -2
(ii) \(\frac { -2 }{ 3 }\) and \(\frac { -1 }{ 3 }\)
Solution:

Question 9.
Insert five rational numbers between:
(i) \(\frac { -4 }{ 5 }\) and [lat3.1
ex]\frac { -2 }{ 3 }[/latex]
(ii) \(\frac { -1 }{ 2 }\) and \(\frac { 2 }{ 3 }\)
Solution: