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These NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals Ex 2.5 Questions and Answers are prepared by our highly skilled subject experts.

NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals Exercise 2.5

Question 1.
Which is greater?
(i) 0.5 or 0.05
(ii) 0.7 or 0.5
(iii) 7 or 0.7
(iv) 1.37 or 1.49
(v) 2.03 or 2.30
(vi) 0.8 or 0.88
Answer:
(i) Comparing the digits at tenths place, we have
5 > 0
∴ 0.5 >0.05
So, 0.5 is greater.

(ii) Comparing the digits at tenths places, we have
7 > 5
∴ 0.7 > 0.5
So, 0.7 is greater.

(iii) Comparing the digits at ones place, we have
7 > 0
∴ 7 > 0.7
So, 7 is greater.

(iv) Since the digits at ones place are same, comparing the digits at tenths place, we have
3 < 4
∴ 1.37 <1.49
So, 1.49 is greater.

(v) Since the digits at ones place are same, comparing the digits at tenths place, we have
0 < 3
∴ 2. 03 < 2.30
So, 2.30 is greater.

(vi) 0.8 can be written as 0.80. Now, digits at tenths place are same, comparing the digits at hundredths place, we have
0 < 8
∴ 0.80 <0.88
So, 0.88 is greater.

Question 2.
Express as rupees using decimals:
(i) 7 paise
(ii) 7 rupees 7 paise
(iii) 77 rupees 77 paise
(iv) 50 paise
(v) 235 paise.
Answer:
(i) 7 paise = ₹ = 7 × \(\frac{1}{100}=\frac{7}{100}\) = ₹ 0.07

(ii) rupees 7 paise = ₹ = 7 + 7 × \(\frac{1}{100}\)
= ₹ 7 + ₹ 0.07 = ₹ 7.07

(iii) 77 rupees 77 paise = ₹ 77 + ₹ 77 × \(\frac{1}{100}\) = ₹ 77 + ₹ 0.77 = ₹ 77.77

(iv) 50 paise = ₹ 50 × \(\frac{1}{100}\) = ₹ 0.50

(v) 235 paise= 200 paise + 35 paise
= ₹ 2 + ₹ 35 × \(\frac{1}{100}\) = ₹ 2 + ₹ 0.35
= ₹ 2.35

Question 3.
(i) Express 5 cm in metre and kilometre
(ii) Express 35 mm in cm, m, and km
Answer:
We know that 100 cm = 1 m,
1000 m = 1 km
(i) 5cm = \(\frac{5}{100}\) m = 0.05 m
5 cm = \(\frac{5}{100 \times 100}\) km
= 0.00005 km.

(ii) We know that 1 cm =10 mm
35 mm = \(\frac{35}{10 \times 100}\) m = \(\frac{35}{1000}\)
35mm = \(\frac{35}{10 \times 100}\) m = \(\frac{35}{1000}\)
= 0.035 m
35 mm \(\frac{35}{10 \times 100 \times 1000}\) km
= \(\frac{35}{1000000}\) = 0.000035 km

Question 4.
Express in kg:
(i) 200 g
(ii) 3470 g
(iii) 4 kg 8 g
Answer:
We know that 1000 g = 1 kg
(i) 200 g = \(\frac{200}{1000}\) kg = \(\frac{2}{10}\) kg = 0.2 kg
(ii) 3470 g = \(\frac{3470}{1000}\) kg = \(\frac{347}{100}\) kg = 3.47 kg
(iii) 4 kg 8 g = 4 kg + \(\frac{8}{1000}\) kg
= 4 kg + 0.008 kg = 4.008 kg

Question 5.
Write the following decimal numbers in the expanded form:
(i) 20.03
(ii) 2.03
(iii) 200.03
(iv) 2.034
Answer:

Question 6.
Write the place value of 2 in the following decimal numbers:
(i) 2.56
(ii) 21.37
(iii) 10.25
(iv) 9.42
(v) 63.352.
Answer:
(i) In 2.56, the digit 2 is at the ones place
∴ place value of 2 is 2 × 1 = 2.

(ii) In 21.37, the digit 2 is at the tens place
∴ place value of 2 is 2 × 10 = 20.

(iii) In 10.25, the digit 2 is at the tenths place
∴ place value of 2 is 2 × \(\frac{1}{10}=\frac{2}{10}\)

(iv) In 9.42, the digit 2 is at the hundredths place
∴ The place value of 2 is 2 × \(\frac{1}{100}=\frac{2}{100}\)

(v) In 63.352, the digit 2 is at the thousandths place
∴ The place value of 2 is 2 × \(\frac{1}{1000}=\frac{2}{100}\)

Question 7.
Dinesh went from place A to place B and from there to place C. A is 7.5 km from B and B is 12.7 km from C. Ayub went from place A to place D and from there to place C. D is 9.3 km from A and C is 11.8 km from D. Who travelled more and by how much?
Answer:
Distance from A to B = 7.5 km
Distance from B to C = 12.7 km
Distance from A to C through
B = (7.5 + 12.7) km
= 20.2 km
∴ Distance travelled by Dinesh = 20.2 km

Again
Distance from A to D = 9.3 km
Distance from D to C = 11.8 km
Distance from A to C through D
= (9.3 + 11.8) km
= 21.1 km
∴ Distance travelled by Ayub = 21.1 km 21. 1 > 20.2
∴ Ayub travelled more distance.
Difference = 21.1 km – 20.2 km
= 0.90 km (or) 900 m
∴ Ayub travelled more distance by 900 m

Question 8.
Shyama bought 5 kg 300 g apples and 3 kg 250 g mangoes. Sarala bought 4 kg 800 g oranges and 4 kg 150 g bananas. Who bought more fruits?
Answer:
Since, Shyama bought 5 kg 300 g apples and 3 kg 250 g mangoes
Total fruits bought by Shyama = 5 kg
300 g + 3 kg 250 g = 8 kg 550 g
Since, Sarala bought 4 kg 800 g oranges and 4 kg 150 g bananas
Total fruits bought by Sarala
= 4 kg 800 g + 4 kg 150 g = 8 kg 950 g
8.950 > 8.550
So, Sarala bought more fruits
Difference in weight = 8 kg 950 g – 8 kg 550 g = 0 kg 400 g
= 400 g or \(\frac{400}{1000}\)kg = 0.4 kg

Question 9.
How much less is 28 km than 42.6 km?
Answer:
Difference = 42.6 km – 28 km = 14.6 km 28 km is less than 42.6 km by 14.6 km

These NCERT Solutions for Class 9 Maths Chapter 14 Statistics Ex 14.4 Questions and Answers are prepared by our highly skilled subject experts.

NCERT Solutions for Class 9 Maths Chapter 14 Statistics Exercise 14.4

Question 1.
The following number of goals were scored by a team in a series of 10 matches:
2, 3, 4, 5, 0, 3, 3, 4, 3
Find the mean median and mode of these scores.
Solution:
We know that

or, Mean = 2.8
To obtain the median we arrange the goals in ascending order to get 0, 1, 2, 3, 3, 4, 4, 5
Since the number of observations is 10.
So, there are two middle terms, i.e. the \(\left(\frac{10^{\mathrm{th}}}{2}\right)\) and \(\left(\frac{10}{2}+1\right)^{\text {th }}\) i.e. the 5th and 6th term.
i.e. The median = \(\frac{3+3}{2}\) = 3
So, the median goat was scored is 3.
In the given observation, 3 occurs most frequently i.e. four times.
So, the mode is 3.

Question 2.
In a mathematics test given to 15 students, the following marks (out of 100) are recorded.
41, 39, 48, 52, 46, 62, 54, 40, 96, 52, 98, 40, 42, 52, 60
Find the mean, median and mode of the above marks.
Solution:
We know that

To obtain the median we arrange the marks in ascending order to get.
39, 40, 40, 41, 42, 46, 48, 52, 52, 54, 54, 60, 62, 96, 98
Since the number of observation is 15.
So their are one middle term i.e. \(\left(\frac{15+1}{2}\right)^{\mathrm{th}}\) i.e. 8th term.
i.e. the median = 52.
So, the median marks get by students is 52.
In the given observation, 52 occur most frequently i.e. 3 times. So the mode is 52.

Question 3.
The following observations have been arranged in ascending order. If the median of the data is 63, find the value of x.
29, 32, 48, 50, x, x + 2, 72, 78, 84, 95
Solution:
We have given that the data arranged in ascending order i.e. 29, 32, 48, 50, x, x + 2, 72, 78, 84, 95.
Since the number of observations is 10.
So there are two middle terms, i.e. the \(\left(\frac{10^{\mathrm{th}}}{2}\right)\) and \(\left(\frac{10}{2}+1\right)^{\text {th }}\) term.
i.e. the 5th and 6th term.
i.e. the median = \(\frac{x+(x+2)}{2}\)
⇒ 63= \(\frac{2 x+2}{2}\) (∵ median =63)
⇒ 63 = x + 1
⇒ x = 62
Therefore, the value of x is 62.

Question 4.
Find the mode of
14, 25, 14, 28, 18, 17, 18, 14, 23, 22, 14, 18
Solution:
we arrange the data in the following form:
14, 14, 14, 14, 17, 18, 18, 18, 22, 23, 25, 28.
Here 14 occur most frequently i.e. four times.
So, the mode is 14.

Question 5.
Find the mean salary of 60 workers of a factory from the following table:

Solution:
First, we make the frequency distribution table of given data.

Question 6.
Give one example of a situation in which
(i) the mean an appropriate measure of central tendency.
(ii) the mean is not an appropriate measure of central tendency but the median is an appropriate measure of central tendency.
Solution:
Consider a situation when a student Vikas received their test copies.
The test had five questions, each carrying ten marks. His scores were as follows:

Vikas’s average score = \(\frac{42}{5}\) = 8.4
To arranged his scores in ascending order and found out the middle score as:

In this situation means is an appropriate measure of central tendency.
(ii) Consider another situation when a student Tanvi received their test copies. The test had again five questions, each carrying the marks. Her scores were as follows:

Tanvi’s average score = \(\frac{41}{5}\) = 8.2
To arranged her scores in ascending order and found out the middle score as:
Tanvi’s Score 4 7 10 10 10
In this situation meaning is not an appropriate measure of central tendency but the median is an appropriate measure of central tendency.

These NCERT Solutions for Class 8 Science Chapter 18 Pollution of Air and Water Questions and Answers are prepared by our highly skilled subject experts to help students while preparing for their exams.

Pollution of Air and Water NCERT Solutions for Class 8 Science Chapter 18

Class 8 Science Chapter 18 Pollution of Air and Water Textbook Exercise Questions and Answers

Page 250-251

Question 1.
What are the different ways in which water gets contaminated?
Answer:
The different ways in which water gets contaminated are as follows:

• Many industries discharge harmful chemicals into rivers and streams. Examples are oil refineries, paper factories, textile and sugar mills, etc.
• The pesticides and weedicides used for the protection of crops get dissolved in water and are washed into water bodies from the fields.
• Many times, untreated sewage is thrown directly into rivers.
• Faecal matters of mammals get added into water bodies.
• Practice of bathing and washing near a water body.
• Practice of cremating the dead bodies near river banks.

Question 2.
At an individual level, how can you help reduce air pollution?
Answer:
At an individual level, one can do the following things to reduce air pollution:

• One can use vehicles consuming fuels like CNG and unleaded petrol, rather than those using fuels like diesel, petrol, etc.
• One can avoid unnecessary usage of vehicles and try using public transport more.
• One can avoid using crackers.
• One can generate awareness about air pollution among friends and neighbours.
• One can switch over to alternative fuels instead of the fossil fuels for energy requirements. These could be solar energy, hydropower and wind energy.
• One can plant trees and nurture those trees already present in the neighbourhood.
• Dry leaves can be dumped in a compost pit rather than burning in open.

Question 3.
Clear, transparent water is always fit for drinking. Comment.
Answer:
Clear, transparent water is not always fit for drinking. This is because the water which looks clean might contain disease-carrying microorganisms and dissolved impurities in it. These microorganisms and impurities could be harmful to us. Hence, it is essential to purify water before drinking.

Question 4.
You are a member of the municipal body of your town. Make a list of measures that would help your town to ensure the supply of clean water to all its residents.
Answer:
Following is a list of measures that would help a town to ensure the supply of clean water to all its residents:

• Implementation of strict laws for industrial units so that the polluted water is not disposed off directly into rivers and takes.
• Treatment of water must be done to make it free from harmful germs, chemicals and impurities.
• The water supply pipes must be properly maintained to avoid any corrosion, breakage and leakage.
• Campaigns and awareness programmes should be organised to keep water resources clean and educate people to save water.

Question 5.
Explain the differences between pure air and polluted air.
Answer:
Following are the differences between pure air and polluted air:

Question 6.
Explain circumstances leading to acid rain. How does acid rain affect us?
Answer:
Chemicals like sulphur dioxide and nitrogen dioxide are released into the air by the smoke of vehicles. These pollutants react with the water vapour present in the air and form sulphuric and nitric acid. When it rains, these acids get dissolved in rainwater making it acidic. Such kind of rain is called acid rain.

Following is the list which shows how acid rain affects us:

• It can cause skin irritation.
• It drains out nutrients like calcium from the soil.
• It causes corrosion to bridges, buildings and other metallic objects.
• It can destroy plants and aquatic life.

Question 7.
Which of the following is not a greenhouse gas?
a. Carbon dioxide
b. Sulphur dioxide
c. Methane
d. Nitrogen
Answer:
d. Nitrogen

Question 8.
Describe the ‘Greenhouse Effect’ in your own words.
Answer:
The greenhouse effect is the trapping of sunlight in earth’s atmosphere due to increased concentration of greenhouse gases like carbon dioxide, methane and water vapour in the atmosphere. These gases trap solar radiations reflected back by the earth. This helps in keeping our planet warm and thus, helps in human survival. However, an increase in the amount of greenhouse gases can lead to an increase in the earth’s temperature leading to global warming.

Question 9.
Prepare a brief speech on global warming. You have to deliver the speech in your class.
Answer:
Global warming is a serious concern of the modern times. We are using more cars and bikes than ever. We are also consuming products at a large scale which means more and more factories are coming up to satisfy our growing needs. Alt of this has resulted in an increased level of carbon dioxide in the atmosphere. The increased level of carbon dioxide has resulted in global warming. Due to this, the summers have become hotter and winters have become much colder. We are observing increased instances of flash floods. Weather changes are drastic, and this is being attributed to global warming. Global warming might result in total disaster for us. A time will come when the temperature on the earth will finish the life. It is high time we stand up and take a pledge to fight against global warming.

Question 10.
Describe the threat to the beauty of the Taj Mahal.
Answer:
Acid rain is a major threat to the beauty of the Taj Mahal. When acid rain falls on the monument made of marble, they react with marble to form a powder-like substance that is then washed away by the rain. This phenomenon is known as marble cancer. Also, the soot particles emitted from the Mathura oil refinery located near Agra are leading to the yellowing of the marble.

Question 11.
Why does the increased level of nutrients in the water affect the survival of aquatic organisms?
Answer:
The pesticides and weedicides used for the protection of crops get dissolved in water and are washed into water bodies from the fields. These act as nutrients for algae to flourish. Once these algae die, they serve as food for decomposers like bacteria. In this process, a lot of oxygen in these ponds gets used up. This results in a decrease in the oxygen level of water which kills the aquatic organisms.

NCERT Extended Learning Activities and Projects

Question 1.
In some cities, a pollution check has been made compulsory for vehicles. Visit a petrol pump in order to learn about the process of conducting a pollution check. You may systematically record your findings in the following areas:

• Average number of vehicles checked per month.
• Time taken to check each vehicle.
• Pollutants checked for.
• The process of testing
• Permissible levels of emission of various gases.
• Measures taken if the emitted gases are above the permissible limits.
• How frequently is a pollution check required?

Hint:
Do it yourself.

Question 2.
Conduct a survey in your school to investigate various environment related activities that have been undertaken. The class can divide itself into two groups, with each group looking at a different area. For example, one group can find out whether there is an environment club in the school. What are its objectives? What is its calendar of events? How can you become a member?
If your school does not have such a club, you even think of starting one along with a few of your friends.
Hint:
Do it yourself.

Question 3.
Organise a field visit to a river in or around your town with the help of your teachers. Observations followed by discussion could focus on

• the history of the river.
• cultural traditions.
• role of the river in meeting the town’s water needs.
• pollution concerns.
• sources of pollution.
• effects of pollution on the people living by the riverside as well as those living far away.

Hint:
Do it yourself.

Question 4.
Find out with the help of your teachers and the internet (if possible), whether there are any international agreements to control global warming. Which are the gases covered under these agreements?
Hint:
Following are the international agreements aimed at controlling global warming:
The Kyoto Protocol is an international agreement on climate change, developed under the United Nations Framework Convention on Climate Change (UNFCCC). The Protocol encourages 192 parties to reduce their greenhouse gas emissions, with many developed nations having binding emissions reduction targets.

The Paris Agreement was agreed in 2015 by 175 parties. The aim of the agreement is to keep global warming to ‘well below’ 2°C, and strive to limit warming to 1.5°C.

The Montreal Protocol on ozone-damaging gases does not directly address climate change, but ozone-damaging gases contribute to global warming. The 1987 Montreal Protocol binds 196 nations to reduce the emission of ozone-damaging gases, commonly used in fridges, foam and industrial applications.

Activity 1

Objective: To study the effect of various activities on the quality of air.
Procedure: Discuss in your class the impact of each of the following options on the quality of air: walking, going by bicycle, travelling by bus or other public transport, using a car individually, travelling by car pool.
Observation:

Conclusion: We can decrease the air pollution by using less polluting fuels like CNG, and using public transport or car pool.

Water Pollution: Addition of unwanted substances in water which makes water harmful for living beings and non-living things is called water pollution.

Water Pollutants: Substances which contaminate water are called water pollutants. These include harmful substances like sewage, toxic chemicals, silt, etc.

Pollution of Ganga: Ganga is one of the most significant rivers of India. It flows through many towns, cities and villages of the northern, eastern and central India. People living in these regions are dependent upon Ganga water for their livelihood as well as for their day-to-day needs. But it has been found that Ganga is one of the 10 endangered rivers of the world according to the World Wide Fund (WWF) for Nature. This is because of its extreme pollution. The river has been called dead at several places as it has no aquatic life there.

Ganga Action Plan (1985) was launched by the Government of India in order to save Ganga river. However, increasing population and industrialisation has already ruined this river beyond repair. The Government of India has launched a new initiative known as National Mission for Clean Ganga (NMCG) in 2016.

Causes of Water Pollution:

• Increasing population and industrialisation.
• Bathing, washing clothes and defecating in rivers pollute them.
• Throwing of garbage, flowers, idols of gods and polythene bags are toxic to water bodies.
• Discharge of untreated sewage in water is very harmful. Water contaminated with sewage may contain viruses, bacteria, fungi, eggs of worms and parasites which cause diseases like cholera, typhoid and jaundice.
• Industrial discharge of harmful chemicals into rivers and streams.
• Chemicals and fertilisers from agricultural fields pollute not only the rivers and lakes, but also the underground water.

Agricultural chemicals such as fertilisers, pesticides and weedicides dissolve in water in the crop fields. From there, they are washed into water bodies such as ponds, lakes, etc. These substances act as nutrients for algae, and growth of algae enhances. After some time, algae start dying due to overgrowth. Dead mass of algae is decomposed by decomposers like bacteria.

In this process, a lot of oxygen dissolved in the water gets used up. This results in a decrease in the oxygen level that may cause the death of aquatic organisms. This phenomenon of removal of all the oxygen and nutrients from a water body resulting in extinction of all life forms in it is called eutrophication.

Potable Water: Water which is fit for drinking is called potable water. A quarter of the world’s population does not have access to safe drinking water.

Methods of Water Purification:

• Municipal bodies purify water by various physical and chemical methods before supplying drinking water to the households.
• Filtration is a common method of purification of water. Various types of water filters are used in households.
• Boiling is another common method of water purification. It kills the germs in water.
• Chlorination also helps in killing the germs in water. Chlorine tablets are available for free at government hospitals.

Activity 2

Objective: To construct a simple water filter.
Materials Required: Plastic bottle, cutter, fine cloth, cotton, sand, gravel and water sample.
Procedure:

• Take a plastic bottle and cut it into two halves at the centre.
• Use the upper half of funnel by putting it upside down in the lower half.
• Make layers in it with fine cloth followed by cotton, sand and then gravel.
• Now pour dirty water through the filter and observe the filtered water.

Observation: Clean transparent water is obtained after filtration.
Conclusion: Dirty water can be purified by filtration through layers of sand.

How to Prevent Water Pollution:

• Discharge of untreated sewage and effluents in water bodies should be strictly prohibited.
• Every city should have a sewage treatment plant.
• Public awareness about harms of idol immersion in water bodies should be decreased.
• Traditional crematoriums should be replaced with electric crematoriums.

Conservation of Water: Water is a precious resource, and hence every step should be taken to conserve water. We should follow the principle of three R’s, i.e., Reduce, Reuse and Recycle, to conserve water. We should make changes in our lifestyle to prevent wastage of water. Leaking taps should be immediately repaired. Using a bucket instead of shower for a bath helps in saving water. Water left after washing clothes and vegetables should be reused for mopping and for washing cars and scooters. Sewage water should be purified so that it can be used again.

Class 8 Science Chapter 18 Pollution of Air and Water Additional Important Questions and Answers

Very Short Answer Type Questions

Question 1.
What is air pollution?
Answer:
Contamination of air which makes it harmful for living beings is called air pollution.

Question 2.
How is carbon monoxide produced?
Answer:
Carbon monoxide is produced from the incomplete burning of fuels like petrol and diesel.

Question 3.
What is the full form of CFC?
Answer:
Chlorofluorocarbon.

Question 4.
Name some cleaner fuels.
Answer:
CNG, LPG, unleaded petrol, etc.

Question 5.
What is smog?
Answer:
A mixture of smoke and fog is called smog.

Question 6.
What is acid rain?
Answer:
When rainwater becomes acidic due to dissolution of the oxides of sulphur and nitrogen, it is called acid rain.

Question 7.
What is global warming?
Answer:
Overall increase in the temperature of the earth’s atmosphere is called global warming.

Question 8.
What is water pollution?
Answer:
Contamination of water which makes it harmful for living beings is called water pollution.

Question 9.
Name some water pollutants.
Answer:
Sewage, toxic chemicals, silts, etc.

Question 10.
Name some greenhouses gases.
Answer:
Methane, carbon dioxide, nitrous oxide and water vapour.

Question 11.
What is chlorination?
Answer:
Chlorination is the chemical method for purifying water, by adding chlorine tablets or bleaching powder to it.

Question 12.
What are the harmful effects of smog?
Answer:
The smog causes breathing difficulties like asthma, cough and wheezing in human beings and also reduces visibility.

Question 13.
Which gas is mainly responsible for global warming?
Answer:
CO₂ gas is mainly responsible for global warming.

Question 14.
When was Ganga Action Plain implemented?
Answer:
In 1985, Ganga Action Plan was implemented.

Question 15.
In which state is Ganga river most polluted?
Answer:
Ganga river is most polluted in Kanpur.

Question 16.
How are dust particles added in air?
Answer:
There are many sources of dust particles, e.g., stone quarries, mines, power plants, construction sites, etc.

Question 17.
How is carbon monoxide produced?
Answer:
Carbon monoxide is produced by incomplete burning of fuels petrol and diesel.

Question 18.
What are the natural causes of air pollution?
Answer:
Smoke and dust from forest fires and volcanic eruptions pollute the air and are the natural causes of air pollution.

Question 19.
How does boiling purify water?
Answer:
Boiling purifies water by killing the germs present in it.

Question 20.
What is the full form of three Rs?
Answer:
Reduce, Reuse and Recycle.

Short Answer Type Questions

Question 1.
Define CFCs. How do they create pollution?
Answer:
Electronic devices like refrigerators, air conditioners, etc., emit chlorofluorocarbons (CFCs). CFCs damage the ozone layer present in the atmosphere. Ozone layer is responsible for protecting us from harmful ultraviolet rays of the sun. These electronic devices cause depletion of ozone layer and form the ozone hole. Ultraviolet rays can cause sun bum and skin cancer. We can reduce the harmful effects of CFCs by using less harmful chemicals in place of CFCs.

Question 2.
What are the different methods to make water safe for drinking?
Answer:
Following methods may be used to make water safe for drinking:

• Filtration: It is a physical method of removing impurities from water. Many households use water purifiers that can filter water and make it safe for drinking.
• Boiling: It kills the germs present in the water. Many people boil water before drinking it.
• Chlorination: Chlorine is a natural cleaning agent for water which makes it fit for consumption. Often chlorine tablets are added in water to remove impurities from it.

Question 3.
How can we prevent water pollution?
Answer:
Water pollution can be prevented in the following ways:

• Industries should strictly adhere to the laws and do not dispose off untreated sewage water into the rivers or any other water body directly.
• More water treatment plants should be established near the industrial areas.
• We should save water as much as we can, for example, we can make sure that there are no leaking taps in the house.
• We should reuse water if we can, for example, the water that we use for washing clothes can also be used for cleaning the house floors.

Question 4.
How do automobiles pollute air?
Answer:
Automobiles usually have internal combustion engines which use petrol or diesel as fuel. Combustion of petrol or diesel results in emission of many polluting gases, tike carbon dioxide, carbon monoxide, sulphur dioxide, nitrogen dioxide, etc. Moreover, minute particles are also emitted from automobile engines. Thus, automobiles end up polluting the air.

Question 5.
Write a short note on ozone layer.
Answer:
Ozone layer is a protective layer in the atmosphere. This layer prevents the harmful ultraviolet radiations of the sun from entering our atmosphere. Ultraviolet radiations can cause skin cancer in humans and animals, and are also harmful for plants. Any damage to the ozone layer can be highly detrimental to the living beings.

Question 6.
What is eutrophication?
Answer:
Draining away of all the nutrients from a water body is called eutrophication. It happens because of excessive amount of chemicals in water. This results in proliferation of algae and other plants in water bodies with stagnant water. Once these plants die, they are consumed by decomposers. The process of decomposition utilises most of the oxygen from water. This results in deficiency of oxygen for aquatic animals. Gradually, the water body becomes devoid of any life form and is considered dead.

Question 7.
Why is it dangerous to burn polymers?
Answer:
When polymers such as plastics are burned, carbon containing gases are released. During the burning process, the carbon combines with oxygen present in the atmosphere and forms oxides of carbon. These gases have been linked with global warming, depletion of the ozone layer, acid rain, etc. They create harmful effects on our ecosystem and on the health of living beings. Hence, burning of polymers is dangerous.

Question 8.
How is our holy Ganga getting polluted? What is its effects? What is being done to prevent its pollution?
Answer:
Ganga is mainly getting polluted by dumping of untreated sewage every day. In addition, most of the human activities like bathing, washing of clothes and immersion of ashes or unburnt corpses also cause pollution. Most of the industries further contribute to the Ganga’s pollution load by releasing chemical effluents. Religious practices are also one of the major causes of Ganga’s pollution.

This pollution makes the water toxic which not only affects human health but also kills fishes in large sections of the river. To prevent pollution and to improve the quality of water of the Ganga river, government started Ganga Action Plan in 1985.

Question 9.
What measures are being taken to save Taj Mahal?
Answer:
Various measures are being taken to save the beauty of the Taj Mahal. The Supreme Court of India has ordered the industries to switch over to cleaner and pollution-free fuels. Automobiles have been ordered to use CNG and LPG as fuel. Unleaded petrol will be made available to be used as fuel in vehicles instead of leaded petrol and diesel.

Question 10.
What are the effects of global warming?
Answer:
Global warming is causing melting of icebergs and glaciers. It results in increased cases of flash floods and a rise in sea level. It also causes drastic changes in weather patterns. Severe draughts are also caused due to global warning.

Question 11.
Suggest two methods by which water can be made potable at home.
Answer:
At home, water can be made potable by killing the germs in the following ways:

1. Boiling: Boiling the water for 15-20 minutes kills all the germs.
2. Purifier with ultraviolet light: A special type of light called ultraviolet light kills germs. It is used in several water purifiers available in the market today.

Question 12.
Akshita saw a child sleeping in a car parked with closed doors and windows rolled up in an open area on a sunny day near the market. She immediately raised an alarm and with the help of police, she got the window glass rolled down.
a. Why was it not safe to keep the door with window glass rolled up for a child inside the car?
b. Name two gases that can lead to the above effect.
Answer:
a. It was not safe for the child in the car with locked doors and windows rolled up because the sunlight would result in the greenhouse effect in the car. This would increase the temperature in the car and also result in the increase in CO₂ level which would lead to suffocation.
b. Carbon dioxide gas and methane gas can lead to the greenhouse effect.

Long Answer Type Questions

Question 1.
How is water treated at the waterworks to make it potable?
Answer:
Tap water supplied to our homes is made potable in the waterworks. The processes used are as follows:
a. Sedimentation and decantation is first done to remove larger particles of solid impurities.
b. Alum is then added to the water to separate the smaller particles by making them heavier so that they settle down.
c. The water is then filtered by passing it through sand fitters.
d. Germs are killed by adding chlorine to the water. The process is called chlorination.

Question 2.
List the main pollutants of air, and give the ill effects of each.
Answer:
The main pollutants of air and their effects are as follows:
a. Suspended particulate matter (SPM): These are minute solid particles suspended in the air. The finer of these particles cannot be filtered by the hair in our nose and hence are a major cause of lung diseases.

b. Carbon monoxide: Carbon monoxide is one of the most dangerous pollutants. It is extremely poisonous. It mixes with the blood and prevents it from carrying oxygen. It may even lead to death in higher concentrations.

c. Excess carbon dioxide: Excess carbon dioxide in the atmosphere traps the heat rays of the sun. This is believed to cause an increase in the temperature of the earth. This can cause large scale melting of ice in the polar regions and also an increase in sea water. This ultimately can lead to flooding of coastal areas by sea water.

d. Sulphur dioxide and nitrogenn dioxide: Sulphur dioxide is poisonous. It affects our lungs. This gas reacts with water to form sulphuric acid, and this gives rise to acid rain. Nitrogen dioxide is also poisonous. It irritates the eyes and affects the lungs.

e. Chlorofluorocarbons (CFCs): These can damage the ozone layer in the atmosphere, causing an increase in the amount of ultraviolet rays from the sun reaching the earth. This causes damage to our eyes and skin.

f. Lead: Lead compounds cause various problems such as mental disorders and brain damage.

Question 3.
Give some methods of conserving water.
Answer:
Some of the methods of water conservation are as follows:

• Using water judiciously and avoiding wastage of water at home.
• Using better methods of irrigation.
• Recycling of water in factories and using it several times before it is disposed off.
• Treating sewage and factory wastes before disposing them off.
• Water harvesting of rainwater to raise the groundwater level.

Picture Based Question

Question 1.
Observe the given picture and answer the following questions.

a. What is the picture showing?
b. Name the government action plan to resolve this problem.
c. Give one cause of this problem.
Answer:
a. The picture is showing a polluted stretch of the river Ganga.
b. Ganga Action Plan.
c. Disposal of garbage and wastes in the river is one of the major causes of water pollution.

Question 2.
Identify the following figure and answer the questions.

a. How do such types of construction pollute air?
b. Name the possible air pollutants produced by these structures.
c. Name the gases produced by these structures causing acid rain.
Answer:
a. The factories pollute air by producing smoke, carbon particles and other gases in the air.
b. These factories produce various pollutant gases like CO, oxides of sulphur and nitrogen, etc.
c. Sulphur dioxide and nitrogen dioxide.

Question 3.
Observe the following building carefully and answer the questions:

a. Where is the building located?
b. Name the material used to construct this building.
c. Name some industries located around it.
d. Write the effect of acid rain on it.
e. What is other name of corrosion of white marble?
Answer:
a. This building is of the Taj Mahal. It is located in Agra.
b. It is made up of white marble.
c. Rubber processing factory, automobile industry, chemical industry and Mathura Oil Refinery are some industries located around the Taj Mahal.
d. The acid rain causes the corrosion of marble due to which it loses its beauty.
e. The other name of corrosion of marble is marble cancer.

These NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals Ex 2.4 Questions and Answers are prepared by our highly skilled subject experts.

NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals Exercise 2.4

Question 1.
Find:
(i) 12 ÷ \(\frac { 3 }{ 4 }\)
(ii) 14 ÷ \(\frac { 5 }{ 6 }\)
(iii) 8 ÷ \(\frac { 7 }{ 3 }\)
(iv) 4 ÷ \(\frac { 8 }{ 3 }\)
(v) 3 ÷ 2\(\frac { 1 }{ 3 }\)
(vi) 5 ÷ 3\(\frac { 4 }{ 7 }\)
Answer:

Question 2.
Find the reciprocal of each of the following fractions. Classify the reciprocals as proper fractions, improper fractions and whole numbers.
(i) \(\frac { 3 }{ 7 }\)
(ii) \(\frac { 5 }{ 8 }\)
(iii) \(\frac { 9 }{ 7 }\)
(iv) \(\frac { 6 }{ 5 }\)
(v) \(\frac { 12 }{ 7 }\)
(vi) \(\frac { 1 }{ 8 }\)
(vii) \(\frac { 1 }{ 11 }\)
Answer:
(i) The reciprocal of \(\frac { 3 }{ 7 }\) is \(\frac { 7 }{ 3 }\) .
It is an improper fraction.

(ii) The reciprocal of \(\frac { 5 }{ 8 }\) is \(\frac { 8 }{ 5 }\)
It is an improper fraction.

(iii) The reciprocal of \(\frac { 9 }{ 7 }\) is \(\frac { 7 }{ 9 }\) .
It is a proper fraction.

(iv) The reciprocal of \(\frac { 6 }{ 5 }\) is \(\frac { 5 }{ 6 }\) .
It is a proper fraction.

(v) The reciprocal of \(\frac { 12 }{ 7 }\) is \(\frac { 7 }{ 12 }\) .
It is a proper fraction.

(vi) The reciprocal of \(\frac { 1 }{ 8 }\) of is 8.
It is a whole number.

(vii) The reciprocal of \(\frac { 1 }{ 11 }\) is 11.
It is a whole number.

Question 3.
Find:
(i) \(\frac{7}{3}\) ÷ 2
(ii) \(\frac{4}{9}\) ÷ 5
(iii) \(\frac{6}{13}\) ÷ 7
(iv) 4\(\frac{1}{3}\) ÷ 3
(v) 3\(\frac{1}{2}\) ÷ 4
(vi) 4\(\frac{3}{7}\) ÷ 7
Answer:

Question 4.
Find:

Answer:

These NCERT Solutions for Class 7 Maths Chapter 7 Fractions InText Questions Questions and Answers are prepared by our highly skilled subject experts.

NCERT Solutions for Class 7 Maths Chapter 7 Fractions InText Questions

NCERT In-text Question Page No. 137

Question 1.
Show \(\frac { 3 }{ 5 }\) on a number line.
Answer:
First we write 1 as \(\frac { 3 }{ 5 }\) and divide the number line into 5 equal parts.

Question 2.
Show \(\frac{1}{10}, \frac{0}{10}, \frac{5}{10}\) and \(\frac{10}{10}\) on a number line.
Answer:
We draw a number line. Divide the length between 0 and 1 into 10 equal parts.

The point B represents \(\frac{1}{10}\)
The point A represents \(\frac{0}{10}\)
The point C represents \(\frac{5}{10}\)
The point D represents \(\frac{10}{10}\)

Question 3.
Can you show any other fraction between 0 and 1? Write five more fractions that you can show and depict them on the number line.
Answer:
Step-by-step explanation:
To find the fraction between 0 and 1.
We should always remember one thing that “Denominator should be large than the numerator always”.
Thus, the fraction between 0 and 1 is:
\(\frac { 2 }{ 5 }\) = 0.4 5
\(\frac { 34 }{ 35 }\) = 0.97
\(\frac { 1 }{ 10 }\) = 0.4
\(\frac { 51 }{ 65 }\) = 0.78
\(\frac { 24 }{ 28 }\) = 0.85

Question 4.
How many fractions lie between 0 and 1?
Think, discuss and write your answer?
Answer:
An infinite number of fractions lie between 0 and 1.

NCERT In-text Question Page No. 138

Question 1.
Give a proper fraction :
(a) whose numerator is 5 and denominator is 7.
(b) whose denominator is 9 and numerator is 5.
(c) whose numerator and denominator add up to 10. How many fractions of this kind can you make?
(d) whose denominator is 4 more than the numerator.
Answer:
A proper fraction whose:
(a) numerator is 5 and denominator is 7 = \(\frac { 5 }{ 7 }\)
(b) denominator is 9 and numerator is 5 = \(\frac { 5 }{ 9 }\)
(c) numerator and denominator add up to 10.
Pairs of numbers having sum 10 ‘ =(1,9), (2, 8), (3, 7), (4, 6) (5, 5)
Therefore, the proper fractions are \(\frac{1}{9}, \frac{2}{8}, \frac{3}{7}, \frac{4}{6}\)
(d) denominator is 4 more than the numerator.
\(=\frac{1}{5}, \frac{2}{6}, \frac{15}{19}, \frac{105}{109}, \frac{199}{203}\)

Question 2.
A fraction is given. How will you decide, by just looking at it, whether, the fraction is
(a) less than 1? (b) equal to 1?
Answer:
(a) If the numerator is smaller than the denominator, then the fraction will be less than 1.
(b) If the numerator is equal to the denominator, then the fraction will be equal to 1

Question 3.
Fill up using one of these : “>’, ‘<’ or ‘=’


Answer:

NCERT In-text Question Page No. 142

Question 1.
Are \(\frac { 1 }{ 3 }\) and \(\frac{2}{7} ; \frac{2}{5}\) and \(\frac{2}{7} ; \frac{2}{9}\) and \(\frac{6}{27}\) equivalent ? Give reason.
Answer:
(i) \(\frac { 1 }{ 3 }\) and\(\frac { 2 }{ 7 }\) ∵ 1 x 7 = 7, 3 x 2 = 6 and 7 ≠ 6 , i.e. 1 x 7 ≠ 3 x 2
∴ \(\frac { 1 }{ 3 }\) and\(\frac { 2 }{ 7 }\) are not equivalent and are not equivalent fractions.

(ii) \(\frac { 2 }{ 5 }\) and\(\frac { 2 }{ 7 }\) ∴ 2 x 7 = 14, 5 x 2 = 10 and 14 ≠ 10, i.e. 2 x 7 ≠ 5 x 2

(iii) \(\frac { 2 }{ 9 }\) and\(\frac { 6 }{ 27 }\) ∵ 2 x 27 = 54, 9 x 6 = 54
and 54 = 54, i.e. 2 x 27 = 9 x 6
\(\frac { 2 }{ 9 }\) and\(\frac { 6 }{ 27 }\)

Question 2.
Give example of four equivalent fractions.
Answer:
Following pairs of fractions are equivalent.
(a) \(\frac { 2 }{ 8 }\) and \(\frac { 1 }{ 4 }\)
(b) \(\frac { 5 }{ 12 }\) and \(\frac { 15 }{ 36 }\)
(c) \(\frac { 8 }{ 11 }\) and \(\frac { 16 }{ 22 }\)
(d) \(\frac { 4 }{ 26 }\) and \(\frac { 2 }{ 13 }\)

Question 3.
Identify the fractions in each. Are there fractions equivalent?

Answer:
(i) The given figure represents the fraction \(\frac { 6 }{ 8 }\)
We have: \(\frac{6}{8}=\frac{6 \div 2}{8 \div 2}=\frac{3}{4}\)

(ii) The given figure represents the fraction \(\frac { 9 }{ 12 }\)
We have \(\frac{9}{12}=\frac{9 \div 3}{12 \div 3}=\frac{3}{4}\)

(iii) The given figure represents the
fraction \(\frac { 12 }{ 16 }\)
We have: \(\frac{12}{16}=\frac{12 \div 4}{16 \div 4}=\frac{3}{4}\)

(iv) The given figure represents the fraction \(\frac { 4 }{ 26 }\)
We have: \(\frac{12}{16}=\frac{12 \div 4}{16 \div 4}=\frac{3}{4}\)
Since, all the fractions represent \(\frac { 3 }{ 4 }\),
i.e. \(\frac{6}{8}=\frac{9}{12}=\frac{13}{16}=\frac{15}{20}\) = (each \(\frac { 3 }{ 4 }\))
Thus, the given figures represent equivalent fractions.

NCERT In-text Question Page No. 143

Question 1.
Find five equivalent fractions of each of the following:
(i) \(\frac { 2 }{ 3 }\)
(ii) \(\frac { 1 }{ 5 }\)
(iii) \(\frac { 3 }{ 5 }\)
(iv) \(\frac { 5 }{ 9 }\)
Answer:

NCERT In-text Question Page No. 146

Question 1.
Write the simplest form of:
(i) \(\frac{15}{75}\)
(ii) \(\frac{16}{72}\)
(iii) \(\frac{17}{51}\)
(iv) \(\frac{48}{28}\)
(v) \(\frac{80}{24}\)
Answer:
(i) Factors of 15 are: 1, 3, 5 and 15
Factors of 75 are: 1, 3, 5, 15 25 and 75
Common factors are: 1, 3, 5 and 15
∴ HCF of 15 and 75 = 15
Now, \(\frac{15}{75}=\frac{15 \div 15}{75 \div 15}=\frac{1}{5}\)
Thus, simplest form of \(\frac{15}{75} \text { is } \frac{1}{5}\)

(ii) Factors of 16 are: 1, 2, 4, 6, 8 and 16 Factors of 72 are: 1, 2, 3, 4, 6, 8, 9, 12, 18 24, 36 and 72
∴ Common factors are: 1, 2, 4, 6 and 8
Now, \(\frac{16}{72}=\frac{16 \div 8}{72 \div 8}=\frac{2}{9}\)
Thus, the simplest form of \(\frac{16}{72}\) is \(\frac{2}{9}\)

(iii) Factors of 17 are: 1 and 17
Factors of 151 are: 1, 3 and 17
Common factors is 17
∴ HCF of 17 and 51 – 17
Now \(\frac{17}{51}=\frac{17 \div 17}{51 \div 17}=\frac{1}{3}\)
Thus, the simplest form ot \(\frac { 17 }{ 51 }\) is \(\frac { 1 }{ 3 }\).

(iv) Factors of 42 are: 1, 2, 3, 6, 7, 14, 21 and 42
Factors of 28 are: 1, 2, 4, 7, 14 and 28 Common factors are: 1, 2, 7 and 14
∴ HCF of 42 and 28 = 14
Now \(\frac{42}{28}=\frac{42 \div 14}{28 \div 14}=\frac{3}{2}\)
Thus, the simplest form of \(\frac{42}{28} \text { is } \frac{3}{2}\)

(v) Factors of 80 are: 1, 2, 4, 5, 8, 10, 16, 20, 40 and 80
Factors of 24 are: 1, 2, 3, 4, 6, 8, 12 and 24
Common factors are: 1, 2, 4 and 8
∴ HCF of 80 and 24 = 8
Now, \(\frac{80}{24}=\frac{80 \div 8}{24 \div 8}=\frac{10}{3}\)
Thus, the simplest torm \(\frac{80}{24} \text { is } \frac{10}{3}\)

Question 2.
Is \(\frac{49}{64}\) in its simplest form?
Answer:
Steps to simplifying fractions. Find the HCF of numerator and denominator GCD of 42 and 64 is 2. Divide both the numerator and denominator by the GCD 21
Reduced fraction: \(\frac { 21 }{ 32 }\) .Therefore, 42/64
21 32 simplified is \(\frac { 21 }{ 32 }\).

NCERT In-text Question Page No. 148

Question 1.
You get one-fifth of a bottle of juice and your sister gets one third of the same size of a bottle of juice. Who gets more?
Answer:
My sister gets more because \(\frac{1}{3}>\frac{1}{5}\)

NCERT In-text Question Page No. 149

Question 2.
Which is the larger fraction?
(i) \(\frac{7}{10} \text { or } \frac{8}{10}\)
(ii) \(\frac{11}{24} \text { or } \frac{13}{24}\)
(iii) \(\frac{17}{102} \text { or } \frac{12}{102}\)
Why are these comparisons easy to make?
Answer:
(i) \(\frac{7}{10}<\frac{8}{10}\)
Denominators are same and 7 < 8
∴ \(\frac{7}{10}<\frac{8}{10}\)

(ii) \(\frac{11}{24}<\frac{13}{24}\)
Denominators are same and 11 < 13
∴ \(\frac{11}{24}<\frac{13}{24}\)

(iii) \(\frac{17}{102} \text { and } \frac{12}{102}\)
Denominators are same and 17< 12
∴ \(\frac{17}{102}>\frac{12}{102}\)
(b) These comparisons are easy because these are like fractions.

Question 3.
Write these in ascending and also in descending order:
(a) \(\frac{1}{8}, \frac{5}{8}, \frac{3}{8}\)
(a) \(\frac{1}{5}, \frac{11}{5}, \frac{4}{5}, \frac{3}{5}, \frac{7}{5}\)
(a) \(\frac{1}{7}, \frac{3}{7}, \frac{13}{7}, \frac{11}{7}, \frac{7}{7}\)
Answer: We can write the like fractions in ascending or in descending order according to the order of their numerators.
(a) \(\frac{1}{8}, \frac{5}{8}, \frac{3}{8}\)
∵ 1,3 and 5 are in ascending order.
∴ \(\frac{1}{8}, \frac{3}{8}\) and \(\frac{5}{8}\) are in ascending order
and \(\frac{5}{3}, \frac{3}{8}\) and \(\frac{1}{8}\) are in descending order.

(b) \(\frac{1}{5}, \frac{11}{5}, \frac{4}{5}, \frac{3}{5}, \frac{7}{5}\)
∵ 1, 3, 4, 7 11 are in ascending order and 11, 7, 4, 3 and 1 are in descending order.
∴ Fractions in ascending order:
\(∴\)
∴ Fractions in descending order:
\(\frac{11}{5}, \frac{7}{5}, \frac{4}{5}, \frac{3}{5}, \frac{1}{5}\)

(c) \(\frac{1}{7}, \frac{3}{77}, \frac{13}{7}, \frac{11}{7}, \frac{7}{7}\)
∵ 1, 3, 7, 11 and 13 are in ascending order and 13, 11, 7, 3 and 1 are in descending order.
\(\frac{1}{7}, \frac{3}{7}, \frac{7}{7}, \frac{11}{7}, \frac{13}{7}\)
∴ Fractions in descending order:
\(\frac{13}{7}, \frac{11}{7}, \frac{7}{7}, \frac{3}{7}, \frac{1}{7}\)

NCERT In-text Question Page No. 151

Question 1.
Arrange the following in ascending and descending order:
(a) \(\frac{1}{12}, \frac{1}{23}, \frac{1}{5}, \frac{1}{7}, \frac{1}{50}, \frac{1}{9}, \frac{1}{17}\)
(b) \(\frac{3}{7}, \frac{3}{11}, \frac{3}{5}, \frac{3}{2}, \frac{3}{13}, \frac{3}{4}, \frac{3}{17}\)
(c) Write 3 more similar examples and arrange them in ascending and descending order.
Answer:
We know that in ‘unlike’ fractions having same numerator, the greater the value of the denominator, the smaller the value of the fractional number.
(a) ∵ 50, 23, 17, 12, 9, 7 and 5 are in descending order.
∴ Fractions in ascending order are:
\(\frac{1}{50}, \frac{1}{23}, \frac{1}{17}, \frac{1}{12}, \frac{1}{9}, \frac{1}{7}, \frac{1}{5}\) and fractions in descending order are:
\(\frac{1}{50}, \frac{1}{23}, \frac{1}{17}, \frac{1}{12}, \frac{1}{9}, \frac{1}{7}, \frac{1}{5}\)

(b) ∵ 17, 13, 11, 7, 5, 4 and 2 are in descending order
∴ Ascending order of the given fractions is \(\frac{3}{17}, \frac{3}{13}, \frac{3}{11}, \frac{3}{7}, \frac{3}{5}, \frac{3}{4}, \frac{3}{2}\) and descending order of the given fraction is
\(\frac{3}{2}, \frac{3}{4}, \frac{3}{5}, \frac{3}{7}, \frac{3}{11}, \frac{3}{13}, \frac{3}{17}\)

(c) Three more examples of unlike fractions with same numerator are:

Arrange the above in ascending and descending order by yourself
Answer:

NCERT In-text Question Page No. 155

Question 1.
My mother divided an apple into 4 equal parts. She gave me two parts and my brother one part. How much apple did she give to both of us together?
Answer:
mother gave to me \(\frac { 1 }{ 2 }\) part
mother gave to my brother \(\frac { 1 }{ 4 }\) part
She gave both off us
\(\frac{1}{2}+\frac{1}{4}=\frac{3}{4}\) part

Question 2.
Mother asked Neelu and her brother to pick stones from the wheat. Neelu picked one fourth of the total stones in it and her brother also picked up one fourth of the stones. What fraction of the stones did both pick up together?
Answer:
neelu picked stones = \(\frac { 1 }{ 4 }\)
brother picked up the stones = \(\frac { 1 }{ 4 }\)
The total fraction of the stones they both 1 1 1
pick up together = \(\frac{1}{4}+\frac{1}{4}=\frac{1}{2}\) of total stones.

Question 3.
Sohan was putting covers on his note books. He put one fourth of the covers on Monday. He put another one fourth on Tuesday and the remaining on Wednesday. What fraction of the covers did he put on Wednesday?
Answer:
Sohan put one-fourth of the covers on Monday, i.e., 1/4 covers.
He put one-fourth on Tuesday, i.e., 1/4 covers and the remaining on Wednesday.
Now, covers put on Monday and Tuesday
= \(\frac{1}{4}+\frac{1}{4}=\frac{1+1}{4}=\frac{2}{4}\)
So, covers put on Wednesday

NCERT In-text Question Page No. 156

Question 4.
Add with the help of a diagram.
(i) \(\frac{1}{8}+\frac{1}{8}\)
(ii) \(\frac{2}{5}+\frac{3}{5}\)
(iii) \(\frac{1}{6}+\frac{1}{6}+\frac{1}{6}\)
Answer:
Method I: Look at the figure. It is divided into 8 equal parts.

Its shaded part = \(\frac { 2 }{ 8 }\)
i.e. = \(\frac{1}{8}+\frac{1}{8}=\frac{1+1}{8}=\frac{2}{8} \text { or } \frac{1}{4}\)
Method II: We can also represent the above sum in the following manner:

Question 5.
Add \(\frac{1}{12}+\frac{1}{12}\) How will we show this pictorially and by using paper folding?
Answer:
We have \(\frac{1}{12}+\frac{1}{12}=\frac{1+1}{12}=\frac{2}{12}=\frac{1}{6}\)
To show \(\frac{1}{12}+\frac{1}{12}\) pictorially, we have:

Using paper folding (the activity): Do it yourself.

Question 6.
Make 5 more examples of problems given in 1 and 2 above. Solve them with your friends.
Answer:
Do it yourself.

NCERT In-text Question Page No. 157

Question 1.
Find the difference between \(\frac { 7 }{ 8 }\) and \(\frac { 3 }{ 8 }\) .
Answer:
\(\frac{7}{8}-\frac{3}{8}=\frac{7-3}{8}=\frac{4}{8}=\frac{1}{2}\)
The difference between \(\frac { 7 }{ 8 }\) and \(\frac { 3 }{ 8 }\) is \(\frac { 1 }{ 2 }\).

Question 2.
Mother made a gud patti in a round shape. She divided it into 5 parts. Seema ate one piece from it. If I eat another piece then how much would be left?
Answer:
Seema ate = \(\frac { 1 }{ 5 }\)
1 eat = \(\frac { 1 }{ 5 }\)
Total part eaten is
\(\frac{1}{5}+\frac{1}{5}=\frac{2}{5}\)
The left part would be
= \(1-\frac{2}{5}=\frac{5-2}{5}=\frac{3}{5}\)

Question 3.
My elder sister divided the watermelon into 16 parts. I ate 7 out them. My friend ate 4. How much did we eat between us? How much more of the watermelon did I eat than my friend? What portion of the watermelon remained?
Answer:
1 ate = \(\frac { 7 }{ 16 }\)
My friend ate = \(\frac { 4 }{ 16 }\)
We both eat \(\frac{7}{16}+\frac{4}{16}=\frac{7+4}{16}=\frac{11}{16}\)
the watermelon more I eat than my friend is \(\frac{7}{16}+\frac{4}{16}=\frac{7-4}{16}=\frac{3}{16}\)
The portion of the watermelon remained \(1-\frac{11}{16}=\frac{16-11}{16}=\frac{5}{16}\)

Question 4.
Make five problems of this type and solve them with your friends.
Answer:
Do it yourself.

NCERT In-text Question Page No. 159

Question 1.
Subtract \(\frac { 2 }{ 5 }\) from \(\frac { 5 }{ 7 }\) .
Answer:

Question 2.
Subtract \(\frac { 2 }{ 5 }\) from \(\frac { 5 }{ 7 }\) .
Answer:
\(\frac{5}{7}-\frac{2}{5}\)
∵ LCM of 7 and 5 is 35.
∴ \(\frac{2}{5}=\frac{2 \times 7}{5 \times 7}=\frac{14}{35}\)
Now, we have:
\(\frac{5}{7}-\frac{2}{5}=\frac{25}{35}-\frac{14}{35}=\frac{35-14}{35}=\frac{11}{35}\)

These NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals Ex 2.3 Questions and Answers are prepared by our highly skilled subject experts.

NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals Exercise 2.3

Question 1.
Find:
(i) \(\frac{1}{4}\) of (a) \(\frac{1}{4}\), (b) \(\frac{3}{5}\), (c) \(\frac{4}{3}\)
(ii) \(\frac{1}{7}\) of (a) \(\frac{2}{9}\), (b) \(\frac{6}{5}\), (c) \(\frac{3}{10}\)
Answer:

Question 2.
Multiply and reduce to lowest form (if possible)
(i) \(\frac { 2 }{ 3 }\) × 2 \(\frac { 2 }{ 3 }\)
(ii) \(\frac{2}{7} \times \frac{7}{9}\)
(iii) \(\frac{3}{8} \times \frac{6}{4}\)
(iv) \(\frac{9}{5} \times \frac{3}{5}\)
(v) \(\frac{1}{3} \times \frac{15}{8}\)
(vi) \(\frac{11}{2} \times \frac{3}{10}\)
(vii) \(\frac{4}{5} \times \frac{12}{7}\)
Answer:

Question 3.
Multiply the following fractions:

Answer:

= \(\frac{5 \times 3}{7 \times 1}=\frac{15}{7}\) = 2\(\frac{1}{7}\)

Question 4.
Which is greater?
(i) \(\frac{2}{7}\) of \(\frac{3}{4}\)or \(\frac{3}{5}\) of \(\frac{5}{8}\)
(ii) \(\frac{1}{2}\) of \(\frac{6}{7}\) or \(\frac{2}{3}\) of \(\frac{3}{7}\)
Answer:

Question 5.
Saili plants 4 saplings in a row in his garden. The distance between two \(\frac{3}{4}\) adjacent saplings is m. Find the distance between the first and the last sapling.
Answer:

Let A, B, C and D be the four saplings planted in a row.
Distance between two adjacent saplings \(\frac{3}{4}\)m
∴ Distance between the first and the last saplmg = AD = 3 × AB
3 \(\frac{3}{4}=\frac{3 \times 3}{4}=\frac{9}{4}\)m = 2\(\frac{3}{4}\)m
Distance = 2 \(\frac{1}{4}\) m

Question 6.
Lipika reads a book for 1\(\frac{3}{4}\) hours every day. She reads the entire book in 6 days.
How many hours in all were required by her to read the book?
Answer:
Total Number of days = 6
Reading time for one day = 1\(\frac{3}{4}\) hours
Total number of reading hours
= 6 × 1\(\frac{3}{4}\) hours
6 × 7 \(\frac{7}{4}=\frac{6 \times 7}{4}=\frac{3 \times 7}{2}=\frac{21}{2}\)
= 10 \(\frac { 1 }{ 2 }\) hours
Total time taken to read the book
= 10 \(\frac { 1 }{ 2 }\) hours

Question 7.
A car runs 16 km using one litre of petrol. How much distance will it cover using 2\(\frac { 3 }{ 4 }\) litres of petrol.
Answer:
Distance covered in 1 litre of petrol = 16 km
Distance covered in 2 \(\frac { 3 }{ 4 }\) litres of petrol = 16 × 2\(\frac { 3 }{ 4 }\)
16 × \(\frac { 11 }{ 4 }\) km
4 × 11 = 44 km
∴ Distance covered = 44 km.

Question 8.

Answer: