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The Abolition of Slavery in French Colonies

Introduction

Numerous social reforms were brought about by the French Revolution of 1789 in the eighteenth century. Slavery was abolished in French colonies during that time, which was a remarkable development. Feudalism in France’s “Ancient Regime” was characterised by a high prevalence of slavery. Due to Europeans’ reluctance to work as plantation labourers, France built overseas colonies in the Caribbean as part of imperialism and began the slave trade for these colonies. Slavery, however, became a topic of discussion after the era of absolute monarchy ended and the National Assembly was established, and it still holds sway today. But once the Jacobins gained power, this subject once more gained attention, and in the end, slavery was outlawed in 1794.

Slavery

Humans were objectified and treated as property held by a master in the phenomenon known as slavery. Basic human rights were denied to these slaves, who lived under their masters’ orders. From the sixteenth century, slavery was widespread in France. More than a thousand slaves were exported from Africa at the beginning of the seventeenth century, which marked the beginning of the slave trade. In the Caribbean colonies of Saint Domingue, Martinique, and Guadeloupe, French plantation owners had access to favourable climatic conditions for the cultivation of cash crops like tobacco, sugar, coffee, and indigo. While all of these plantations needed more labour, Europeans themselves were unwilling to relocate to these foreign countries and work in these plantations.

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Due to the labour deficit, the triangular slave trade between Europe, Africa, and America was made possible (including north and south America). French traders used to set sail for Africa under this commercial system from French port cities like Bordeaux and Nantes. Slave merchants or dealers would purchase slaves from local chiefs in coastal areas of Africa, transport them inhumanely (with shackles and stamps) for three months across the Atlantic Ocean to the Caribbean, and then sell them to plantation owners there.

These slaves were overused or exploited to satisfy the rising needs for indigo, sugar, and coffee. In reality, Bordeaux and Nantes, two French port cities, experienced increased economic prosperity as a result of their participation in the expanding slave trade. And this is how slavery became so entrenched in France and its colonies abroad.

Movements Against Slavery

  • Slavery was still a problem throughout the “Ancient Regime,” but it was criticised during the seventeenth century. Saint-Domingue, a French colony, was experiencing its slave insurrection at the same time that Haitian independence from France was being forged. As a result, Haiti became the first nation to be founded by slaves.
  • After the autocratic monarchy was overthrown and a new constitution with the Rights of Man and Citizen was adopted, slavery became a contentious topic in the National Assembly during a time of political unrest. 
  • Now, it was debatable as to whether or not all French subjects, including those living in French colonies, should be granted human rights. However, none of the legislation was enacted because the National Assembly was afraid of the opposition from the middle class’s wealthier members, who were actively engaged in the international slave trade.
  • The National Convention outlawed slavery in 1794 after the Jacobins gained control, and a statute was passed to free all slaves in French colonies. This ordinance was maintained for 10 years until the time of the Directory, but due to improper enforcement, Napoleon Bonaparte repealed it in 1804 and reinstated slavery.
  • In the late eighteenth and early nineteenth centuries, England, a nation that had long resisted slavery, exerted consistent pressure on other European nations to stop trading in slaves or people treated inhumanely. 
  • However, other European nations, particularly France, continued to trade in slaves in secret. Additionally, a statute outlawing slavery was established in 1831, warning all European nations to outlaw the slave trade and insisting that coercive measures would be used against anyone found to be engaged in it. 
  • The Second Republic of France‘s provincial administration formed a commission to outlaw slavery as a result of the monarchy’s decline, and on April 27, 1848, they officially proclaimed the institution’s abolition.

Summary

The French Revolution of 1789 was one of the great revolutionary events, bringing about several changes in France’s social and political landscape as well as those of neighbouring nations. The elimination of slavery in France and the slave trade in French colonies was one of the Revolution’s notable outcomes. With the expansion of colonization, colonial powers like France engaged in the slave trade due to the lack of manpower in the colonies for plantation work. As a result, people were exploitatively transported from Africa to America as slaves. However, with the start of the Second Republic of France in 1848, slavery was once again abolished as a result of England’s pressure on other European nations to outlaw it.

FAQs

1.What was the ‘Ancient Regime’ in France?
Ans. Before the French Revolution, France had a sociopolitical system known as the “Ancient Regime.” In this system, society was split into three estates, and the dictatorial ruler of the nation held absolute control.

2.What do you understand by Imperialism?
Ans. Imperialism is a strategy for spreading power and dominance through the military conquest of the lands and political systems of other nations.

3.Why was the National Assembly Apprehensive about the Middle Class Passing any Law against Slavery in the 1790s?
Ans. Members of the Third Estate, which included the wealthy middle class and others who relied on the slave trade for their economic development, made up the National Assembly itself. Therefore, despite some of its members’ criticism, the National Assembly was unable to pass any legislation to stop the slave trade.

4. What does the French Second Republic Mean?
Ans. The term “Second French Republic” refers to the republican government that was established in France for a second time in 1848 as a result of the collapse of the Orleans monarchy. In 1852, this Second Republic came to an end.

5.Why did Napoleon Reintroduce Slavery in 1804?
Ans. Napoleon wanted to increase French colonial influence in the Caribbean. He needed a lot of labourers to colonise the Louisiana region of North America. In fact, in 1804, he indulged in trade and reinstated slavery. In a sense, it served as his plan for enlarging the French empire.

Ashoka: A Unique Ruler

Introduction

The third Mauryan emperor Ashoka, sometimes referred to as Ashoka the Great, reigned in ancient India from 268 to 232 BC. He was the second son of the Mauryan emperor Bindusar. Although he was not the heir of the Mauryan throne, he was more adored than his elder brother Sushima.  Ashoka was an ambitious ruler and a gallant warrior. Some folklores suggest that Ashoka conspired against all his siblings to reach the throne. However, he is not only known for his war abilities but for the realizations he had after the war of Kalinga that led him to accept the doctrines of Buddhism and spread peace around the world.

Maurya empire

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Ashoka: The Great

Ashoka was born in the year 304 BC to Subhadrangi, daughter of a Brahmin. It is said that Ashoka spent his childhood away from the royal pleasures and in a village. However, he was trained with good morale and this made him popular among the crowd. He was loved by his people and received titles of honor from them. For several reasons, Ashoka was referred to as Ashoka the Great. Some of them are as follows:

  • The largest empire in the Indian subcontinent was founded by Ashoka. 
  • One of the largest armies was that of Ashoka, which included infantry, cavalry, and war elephants. 
  • The greatest conquistador was Ashoka. He resolved never to use violence again after the Kalinga conflict and gave his life to Buddhism.
  • He dispatched his son, daughter, and many missionaries to spread Buddhism over the continent. 
  • He constructed countless viharas and stupas, the most notable of which is the enormous Sanchi Stupa, which UNESCO has listed as a World Heritage Site.

Ashoka: The Ruler

  • Following his accession to the throne, Ashoka decided to expand his empire and carried out all the royal responsibilities outlined in Kautilya’s Arthashastra.
  • This ongoing conflict lasted for eight years. Aside from these battles, he maintained good relations with other countries and maintained stability in all the regions that Chandragupta and Bindusar had previously controlled. 
  • He gave himself the name “Devanampriya,” which means gods’ favourite.
  • Kashmir and Kalinga, the only left-wing state in south India, were two targets Ashoka had long aimed to capture. His efforts were concentrated on Kalinga after he was successful in annexing Kashmir. The conflict significantly altered Ashoka’s life.

Ashoka’s War

The War of Kalinga was the largest and most well-known conflict during Ashoka’s rule. The Kalinga kingdom was a commercial state with easy access to the sea that was located in what is now the state of Odisha. In the year 260 BCE, Ashoka attacked Kalinga city. 

In India’s history, it was the bloodiest conflict ever. When Ashoka visited the battlefield to celebrate his victory after winning the war, he was horrified and deeply saddened by the scale of the carnage. At that very moment, he experienced a great conversion of heart and condemned war and all forms of violence after witnessing the devastation and feeling regret for the Kalinga. He swore he would never take up a weapon or use force of any kind. He subsequently adopted Buddhism as his religion, followed its path, and swore to disseminate the Buddha’s teachings.

Ashoka as a Devotee

Ashoka was dramatically altered by the Kalinga conflict. He converted to Buddhism and embraced the Dhamma, or Conquest by Dharma, philosophy. Ashoka erected several engraved rock and pillar edicts and thousands of stupas around India to publicise Buddha’s work and propagate his teachings. 

For people to adhere to the teachings and uphold the dharma, Ashoka’s rules and the Buddha’s teachings were etched on those pillars. One of the best-known dicta of dharma is the lion capital of the pillar at Sarnath, which eventually became the flag of India. Ashoka gave the order to erect 84,000 stupas throughout his territory, each housing the Buddha’s remains. Sanchi Stupa is among the most well-known stupas.

Sanchi stupa

Ashoka’s Administration:

  • The kingdom of Ashoka was split into provinces, which were further subdivided into villages by Visayas and Janpadas. 
  • The provinces of his dominion were separated into five. 
  • Magadh was the central Province, and each Province was independent, given a certain amount of autonomy.
  • He adhered to the ideal of non-violence and had as his goal the welfare and security of his citizens. 
  • Amatya and appointed officials, who all directly answered to the king, were trusted and knowledgeable authorities in charge of overseeing all administrative and judicial functions. 
  • He had a competent and organised government.

Summary

One of the most amazing and legendary monarchs of ancient India was Ashoka. He gained much of his notoriety following the Battle of Kalinga when he decided to stop fighting. As the monarch who abstained from battle, he is well-known throughout history. Ashoka ruled over the whole Indian subcontinent and created the largest empire in historical India. After the Battle of Kalinga, he converted to Buddhism and became its most ardent supporter. To promote the teachings of Buddhism, he dispatched many missionaries and carved numerous stone edicts.

Frequently Asked Questions (FAQs)

1.What was Ashoka’s Dhamma?
Ans. Dhamma is best understood as instructions, and Ashoka’s Dhamma were guidelines for a more ethical social order. It was an order that needed to be obeyed for the good of society.

2.What were the messages given by Ashoka for the Betterment of Society?
Ans. The messages given by Ashoka for the betterment of society were:

  • Respecting everyone’s cast. 
  • Being gentle with the poor. 
  • Doing welfare of citizens. 
  • Respecting each religion.

3. Where is Kalinga located in Present Day?
Ans: Kalinga included a large part of present-day Odisha, north-easter regions of Andhra Pradesh, and large portions of Chhatisgarh.

An Empire, Dynasty, and Kingdoms

Introduction

In the past, there have been numerous empires that included several kingdoms and were ruled by various dynasties. These three are connected on the one hand, while also having certain differences on the other. A dynasty can play a crucial role in both an empire and a kingdom. The terms “dynasty” and “empire” are more frequently used interchangeably, as in “Mughal empire or Mughal dynasty.” Similar to a kingdom, an empire is a state or nation governed by an emperor, respectively. Additionally, there are numerous ways in which these terminologies differ from one another.

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Empire

What is an Empire?

Empire, Dynasty and Kingdom

An empire is a type of political system in which one state uses territorial conquests to expand and consolidate its dominance over a sizable territory while subjugating other states and nations, or a group of states and countries. An empire is often ruled by an emperor, however, there are instances in history where an empire has existed without a specific ruler. One such instance is the “British Empire” in India. In this approach, an empire is a group with a single sovereign authority and a centralised structure where the emperor had ultimate control. The idea of an empire’s emergence prepared the path for imperialism. In imperialism, nations dispatch a military expedition to other nations to build colonies.

What is a Dynasty?

A dynasty is a series of successive heads of the same family who rule over an empire or a kingdom. Primogeniture, or the idea that the eldest son of the king would inherit the throne, is typically the foundation of the succession process in dynasties. When a dynasty was deposed by members of another family or lineage, it came to an end. The dynasties are “hereditary,” meaning that rather than aptitude or skill, the powers are passed down through the generations depending on birth. The fact that a male is typically anticipated to ascend as the next monarch rather than a female shows how more “patriarchal” the idea of the dynasty was.

 What is a Kingdom?

A kingdom is a country or area that is governed by an absolute monarch (a king or queen), who makes decisions that affect the entire country. A kingdom may be a portion of an empire, where the emperor may delegate control of a particular territory to any of his kin. Multiple dynasties may succeed a single kingdom, although a kingdom cannot be exclusively connected with one dynasty. For administrative purposes, the kingdoms are further divided into provinces, where several officials are appointed and used to report to the monarch.

The idea of a kingdom originated in India during the later Vedic period, when janapadas, a tribal society, evolved into mahajanapadas and were eventually referred to as a kingdom. As numerous kingdoms began to compete for power, continual conflicts began.

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What is the difference between an Empire, Dynasty and Kingdom?

EmpireDynastyKingdoms
A political entity ruled by an emperor is an empire.A succession of kings from the same family or bloodline is referred to as a “dynasty.”A kingdom is a territory under a king or queen.
A wide area of land was made up of an empire. Even a few kingdoms could belong to an empire.A dynasty has nothing to do with the geographic area. Rather a dynasty rules over a empire or kingdom.The size of a kingdom might vary depending on its territorial scope.
Someone who may or may not be related to the ruler rules an empire.Regardless of the circumstances, a dynasty is always made up of members of the same family.A monarch may be chosen by the members of a certain key official and group or may inherit the throne from his or her family.

Examples-Ancient India

  • The first indigenous empire of India, the Empire-Mauryan Empire, ruled over the whole Indian subcontinent from 321 BCE until 185 BCE. 
  • The Gupta Empire, often known to rule during the Golden Age of Indian history, ruled over what is known as ancient India from the fourth to the sixth centuries BCE.
  • Several dynasties, including the Nanda, Haryanka, Pandya, Pallava, Maurya, and Sunga dynasties, existed in ancient India. 
  • Kingdom- Magadha was one of the illustrious kingdoms of prehistoric India.
  • There were several other kingdoms present during the period, including Avanti, Vatsa, Kosala, Kuru, etc.

Summary

A political entity ruled by an emperor is an empire. A succession of kings from the same family or bloodline is referred to as a “dynasty.” A kingdom is a territory under a king or queen. The first indigenous empire of India, the Empire-Mauryan Empire, ruled over the entire Indian subcontinent from 321 BCE until 185 BCE. There were several other kingdoms present during the period, including Avanti, Vatsa, Kosala, Kuru, etc.

Frequently Asked Questions (FAQs)

1. Why was the Gupta Period called the Golden Age of India?

Ans. Economic prosperity and outstanding accomplishments in the fields of science, technology, art, architecture, literature, mathematics, religion, and philosophy were witnessed throughout this time. The Gupta era is therefore known as the “Golden Age” of Indian history.

2. Is there any Country in the World which is still Ruled by Kings and Queens?

Ans. Yes, there are 44 countries in the world which have a monarchial system of governance. Where a monarch is considered as the head of state. United Kingdom, UAE, are popular examples.

3. Do we have an Empire or Kingdom Existing in India Today?

Ans. No, there is no longer an empire or kingdom in India. Now that we have a democratic system of governance, those who labour for the general benefit of the populace directly or indirectly elect the nation’s leaders.

The Watan Jagirs

Introduction

During the Mughal era, the Mughals established the idea of Watan jagirs, where Watan denotes the realms of the local kings in that region and jagir denotes the land gift. After repeated conflicts with the Mughals, these regional kingdoms, in a sense, recognized their suzerainty over them. Akbar, who understood the value of Rajput support in enabling him to consolidate and expand his kingdom, initiated this watan jagir policy throughout his rule. He, therefore, made an effort to win the Rajputs’ allegiance by putting the Watan Jagir philosophy into practice by providing them with important posts with lots of autonomy.

What is Watan Jagir?

The Rajputs remained the Mughals’ greatest obstacle to extending and establishing their empire during this time. Mughals devised the concept of Watan jagirs to address this. Even though the Mughal kings prevailed in the fight, they did not acquire the kingdom of the victorious ones under this system. Instead, the king of that particular region or province was permitted to continue ruling his kingdom as long as he was willing to submit to the Mughal emperor. According to this idea, a king continued to rule his kingdom while the Mughal emperor was in charge. These monarchs eventually received a significant amount of authority in their watan jagirs.

One of the intriguing things about this watan jagir was that it wasn’t hereditary, so if the king of a watan jagir dies, his successor won’t get the entire watan; instead, the portion of it will be given to him by his mansab. The Mughals used to exert authority over Rajput monarchs in this manner.

How did Watan Jagirs rise under Rajputs

Gaining the respect and confidence of the Rajputs was crucial for the Mughals to grow their empire. As a result, the Mughals made an effort to win the support of the Rajputs by deepening their relations with them, giving them important positions in the government and army, adopting non-interference policies in their internal matters, and giving them watan jagirs. Rajput-Mughal ties were well-managed before Shajahn’s rule, but things started to deteriorate after Aurangzeb assumed the throne of the Mughals. And this started to worry both the Mughal elite and the Rajput kings.

Although Watan Jagir was first implemented by Akbar, it was effectively entrenched under Jahangir’s rule. Rajput’s rajas of Amber and Jodhpur, for example, received great autonomy to rule their watan. Some of these Rajput rajas provided the Mughals with steadfast service. They received outside jagirs (the nearby ones) or subas as payment for their service, in addition to their watan jagirs. The Subedari of Gujarat and Malwa were greeted by Raja Ajit Singh of Jodhpur, and the Subedari of Malwa was held with Sawai Raja Jai Singh of Amber.

As Mughal power waned, these Rajput monarchs began expanding their domains by conquering the regions surrounding their watans, which were portions of imperial or Mughal lands. The Rajputs of Jodhpur’s conquest of Nagpur and Amber‘s takeover of Bundi are two instances of this type of expansion.

Roles and Duties

  • Chiefs from the Rajput tribe held important positions in the Mughal era. Raja Todarmal, Birbal, Man Singh, and other significant Rajputs from the Mughal government and army are a few noteworthy instances. 
  • During Akbar’s rule, Raja Todarmal was in charge of the revenue administration. In the area of revenue administration, he made changes. As a result, the entire revenue structure he created was known as “Todar Mal’s Bandobast.” 
  • Birbal, the emperor’s principal advisor and the head of the Mughal army, was another significant Rajput in Akbar’s court. Another significant general in the Mughal army was Raja Man Singh.

Rise and Decline

  • The Mughal-Rajput relations were badly harmed by Aurangzeb’s accession to the throne since his predecessors had done a great job of maintaining them because they understood how significant the Rajputs’ assistance was to the expansion of their empire. 
  • The policies of Aurangzeb underwent numerous revisions. The ‘watan jagirs’ territories granted to Rajput kings were taken away, they were denied crucial positions, and the government began meddling in their internal and religious issues. 
  • These were all offences by the Rajputs. They then began planning an attack on the Mughals. Rajputs began to lose prominence in this way.
  • At the same time, Rajputs and Mughals were being overthrown by Marathas, who had begun to take control of the position. Thus, the Rajput influence as well as the subsequent Mughals came to an end, and the Maratha confederacy emerged in India.

Summary

Due to a pressing political need for two of the major governing elites of northern India to strengthen their positions, Mughal-Rajput relations emerged during the sixteenth century. The allocation of watan jagirs to Rajput rulers with some authority was a significant step toward this arrangement. These Rajput kings gradually began expanding their watan jagirs by annexing the surrounding lands. But as the empire continued to grow, this partnership began to experience problems by the seventeenth century. Both the collapse of the Rajputs and the declaration of the independent regional kingdom were facilitated by internal strife among the Rajputs. In the end, the dominance of the Mughal-Rajput ties faced a significant threat from the advent of the Maratha.

Frequently Asked Questions (FAQs)

 1.Who were the Rajputs?
Ans. The Kshatriya clan of the Varna system gave rise to the Rajputs. These Rajputs were primarily warriors who participated in conflicts and battles. They are responsible for the area’s defence.

2. How did Aurangzeb’s religious policy offend the Rajputs?
Ans. Since the Rajput kings were all Hindu, Aurangzeb sought to convert all of India to Islam. He conducted numerous actions against Hindus to achieve this purpose, including the imposition of Jaziyah, the destruction of temples and idols, and discriminatory tolls for Hindu traders. The Rajput kings were upset by all of these actions, and they began to lose faith in the Mughals.

3. What were the revenue reforms known as Todarmal Bandobast?
Ans. A tool called a jarib was used to measure the land. According to its quality, the land was split into good, intermediate, and terrible areas. One of the goods had a fixed revenue over ten years. The collection of taxes had to be done kindly. The payment was cancelled in the event of a natural calamity.

Algal Blooms

Introduction

Algae are photosynthetic eukaryotes with one or more cells that live in watery environments. They serve as the foundation of aquatic food chains that supply nutrients to a variety of aquatic herbivores. An algal bloom occurs when the population of algae suddenly increases, usually as a result of changed environmental conditions. A bloom of algae resembles foam or scum floating over the water. Some algal blooms emit a foul stench as a result of the overgrowth of bacteria. A distinguishing characteristic of an algal bloom is the physical colouring of the water.

What is an Algal Bloom?

Algal blooms occur either in freshwater or marine water systems, resulting in the rapid growth of algae. As a result of the pigments, water appears red, brown, reddish-brown, or green. The size of algae may vary from unicellular organisms to macroscopic multicellular organisms. In contrast to multicellular entities, algal blooms are characterised by microscopic organisms. In stagnant water, an algal mat forms when the population size is elevated. As a result, aquatic organisms have less oxygen available to them.

Algal blooms seen in freshwater result in the rapid growth of algae. As a result of the pigments, the water appears green.

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What are the causes of Algal Bloom?

Climate: 

  • During the time of summer, ponds and lakes experience a marked increase in temperature and light intensity, both of which may lead to algal blooms.
  • The stillness of stagnant water, such as ponds and lakes, causes the top layers of water to heat up while the deeper layers of water remain relatively cool. 
  • As a result of low wind speeds, surface water tends to be still, allowing thermal stratification to occur. 
  • Extended drought due to poor rainfall and reduced water flow into freshwater systems make them stagnant. This is an added advantage for algae to multiply their numbers.

Nutrient load:

  • Dissolved minerals provide nutrients to aquatic species. When water is overloaded with nutrients (excess nitrogen and phosphorus), algae are fertilized and grow rapidly. The process of loading nutrients into the water body is known as eutrophication.
  • Nitrogen and phosphorus-rich fertilizers are sprayed on farmlands and crops. Water streams drain fertilizer into lakes and reservoirs after heavy rains. Water bodies are polluted by urban wastes carried by stormwater runoff.
  • Algal blooms on shorelines are caused by nutrients carried by rivers and deposited into oceans.

United effect:

  • Algal bloom cannot be solely caused by nutrient enrichment. Several factors must come together to produce an unusual environmental condition for algae to bloom. 
  • It is possible for algae not to bloom in muddy ponds, even though the water is nutrient-rich, warm, and stagnant.
  • Due to the turbidity of muddy waters, and lack of sunlight needed for photosynthesis they cannot grow.

Importance of Algal Bloom   

  • Algal blooms render water unsafe for consumption by both animals and humans. 
  • Some algal blooms have a slimy appearance and a bad odour. 
  • They cause serious economic losses by making the water unfit for leisure activities like swimming, boating, and fishing. 
  • In the water, some algal blooms release poisons or compounds that can seriously ill human beings. They are referred to as harmful algal blooms (HAB).

Effects of Algal Bloom

Effect on the ecosystem:

  • Algal bloom can be thought of as a disturbance to the natural environment because of its impact on it. Any species’ population fluctuations can have a direct or indirect impact on other creatures living in the particular ecosystem. A single algae species’ overpopulation stunts the development of other organisms, which has clear implications for the food chain
  • Dead zone: The lifespan of algae is brief. After the life cycle is complete, a fast rise in population causes dead biomass to accumulate. It creates a need for extensive breakdown. Dissolved oxygen is depleted by decomposers, which reduces its availability to other life forms. Aquatic organisms have a difficult time surviving and exhibit significant mortality in a habitat with little dissolved oxygen. A dead zone results from this. Dead zones result in significant economic losses for the fishing and shellfish industries.
  • The dead, rotting algae float as floating particles that block fish gills and kill them. 
  • When algae create poisons that are detrimental to people and other living things, then they are known as harmful algal bloom (HAB). Direct contact with HAB can result in a deadly disease and severe sickness, fever, diarrhea, and skin rashes.
  • Water that has algal blooms is unsafe for drinking and other recreational uses.

How does Algal Bloom affect the Quality of Water?

  • Depending on the species, algal blooms can look like scum, froth, or paint. 
  • They could tint the water and emit a foul, pungent stench. 
  • Algal pigments give water its reddish, pinkish, yellowish, brownish, or golden appearance. 
  • Water becomes unsafe for drinking when algae develop. Drinking water that contains dangerous algal blooms poses serious health hazards. 
  • The neurological system, liver, and gastroenterological system are all negatively impacted by toxins. 
  • Toxins in HAB water cannot be eliminated by boiling or cooking.

Summary

Algal blooms occur either in freshwater or marine water systems, resulting in the rapid growth of algae.  During the summer, ponds and lakes experience a marked increase in temperature and light intensity, both of which may lead to algal blooms. Algae are fertilized and grow rapidly when water is overloaded with nutrients (excess nitrogen and phosphorus). Algal blooms render water unsafe for consumption by both animals and humans.  The dead, rotting algae float as floating particles that block fish gills and kill them.

Frequently Asked Questions 

1.How Long does an Algal Bloom Last?
Ans. Algal blooms are a transient phenomenon that continues for a maximum of five months. While apparent algal blooms fade away as a result of cleaning and restoration efforts, toxins cannot disappear unless the water goes through an effective treatment procedure.

2. How can Algal blooms be Stopped in Lakes and Reservoirs?
Ans. Aerators are installed in lakes to prevent immobility. Aerators continuously circulate water to avoid stagnation since motionless water causes thermal stratification.

3. Describe Red Tide.
Ans. Algal bloom in oceans is frequently referred to as “red tide.” When ocean waters are physically discoloured, it is more acceptable. Red tides are not always dangerous algal blooms.

Alcohol Drug Abuse Prevention Control

Introduction

Drugs, often known as medicines, are composed of chemical or natural compounds used to identify, treat, and prevent diseases or their symptoms. These medicines, when taken in limited amounts, are beneficial, but can be dangerous if not taken as prescribed. Drugs are known to alter a person’s mental state and physical well-being. As a result, long-term drug usage of more than the prescribed amounts may result in physiological alterations and can prove fatal.

Long-term drug usage of more than the prescribed amounts may result in physiological alterations and can prove fatal.

Drug Abuse

Drug misuse is characterized as the unintentional use of medications that are not being used therapeutically in the required amounts. It unduly alters a person’s mental state and causes several issues, such as behavioural modifications, criminal activity, and a lack of efficacy in society. Nicotine, alcohol, heroin, club drugs, marijuana, and others are some of the drugs that are abused.

Sources of Drugs

Drugs initially were found in plant extracts, but recently are also synthesized in laboratories. Common sources of drugs-

  • Plant source

Plants are a rich resource of various medicinally important compounds. Hence these can be used in treating various ailments. Following are a few plants and the drugs that they provide.Nux vomica– Strychnine,Papaver somniferum- Morphine, Atropa belladonna – Atropine, Digitalis purpurea- Digitoxin and digoxin.

  • Animal source

Glands and internal organs of some animals are a rich source of various medicines such as Sheep thyroid giving thyroxine, the Liver of cod fish giving col liver oil, Pancreas of pigs providing insulin. Etc.

  • Microbial sources

Various microorganisms release various chemical components for their self-defence which can be used as antimicrobial medicines by humans. Some of the drugs given by microbes are-Penicillin, Streptomycin, Dextran, Xanthan etc.

  • Biosynthetic sources

Biosyhtetic drugs are drugs engineered in labs but organisms (plant or animal or microbe) are used for the development of the drugs. Some methods through which biosynthetic drugs are made are-the rDNA technology, immunology, biotechnology, molecular biology etc. For eg- the Hepatitis B vaccine.  

Prevention and Control

The social experiences of children and adolescents affect how their minds develop. This may lead to the development of the habit of smoking, drinking alcohol, or using drugs. Hence parents and instructors should direct them in the appropriate direction and prevent such kinds of abuse.

The following actions can be taken to prevent and manage alcohol and drug abuse:

  • Children typically imitate the behaviours of their family members, neighbours, and role models. Therefore, how parents and other family members feel about using alcohol, drugs, and smoking may have an impact on how children think.
  • Hence, if any member of the family drinks or uses drugs then that should be stopped immediately.
  • Continue monitoring the child’s attitude and behaviour patterns.
  • When children are struggling with pressures, stress, disappointments, and failures, they require counselling, and parents and teachers should take the appropriate steps to do so.
  • If it is discovered that the youngsters are abusing alcohol and/or drugs, their family members should notify the parents and take immediate action on that matter.
  • Such issues of drug abuse are highly-sensitive matters, hence should be dealt with with care and precaution.

Summary

A substance that interacts with the body’s macromolecules to produce a physiological or psychological response is considered a drug.  It can be given by several means, including ingestion, inhalation, intravenous, and smouldering. Regular usage of alcohol and drugs can result in drug addiction, which then leads to drug dependency, which adversely affects both the individual and society. Drugs target the human central nervous system and hence can negatively impact the body. Hence, their use should be minimized, and patients should only take medicines when necessary and for therapeutic reasons only.

Frequently Asked Questions 

1. What are synthetic drugs?
Ans: Synthetic medications are those that have had the chemical derivatives of natural drugs rearranged to change their original qualities and chemical structures. Examples include phenytoin, antihistamines, paracetamol, acetylsalicylic acid, and chloroquine.

2. What are semi-synthetic sources?
Ans: Semi-synthetic drugs are from natural sources, and are hybrids that merely undergo chemical alterations, to increase their effectiveness. Examples include heroin (from morphine), ampicillin (from penicillin), and homatropine (from atropine).

3. Give the most common causes of drug abuse.
Ans: Disappointments, Depression, Failures, exposure to drugs from parents or family members, Curiosity, etc are some of the few reasons for drug and alcohol abuse.

Air Pollution Control

Introduction

The thin layer of air or gases that surrounds the earth is known as the atmosphere.

The earth’s life depends on air, which is a fundamental component of nature. One of the most important worldwide issues is the contamination of the air. The air we breathe is contaminated with dangerous chemicals, biological agents, or physical things which not only harm the environment and materials but also endanger the health of people and other living things. Both natural and artificial causes are contributors to air pollution, but human activity is the main contributor.

Types of Pollutants

There are basically two types of pollutants- 

  • Primary pollutants– These pollutants are directly emitted from various resources and lead to air pollution. Some of the primary pollutants are- Carbon monoxide, Sulphur dioxide, Nitrogen oxides, Suspended particles, Volatile organic compounds, Chlorofluorocarbons, etc.
  • Secondary pollutant-When there is a chemical or physical interaction between primary pollutants and an atmospheric component, secondary pollutants are formed. These secondary pollutants are not any specific chemicals or particles. Some secondary pollutants are- Smog, Ground level ozone, sulfuric acid, nitric acid with water vapour, etc.

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Causes of Air Pollution

Causes of air pollution are as follows-

  • Burning fossil fuels like coal, oil, and gasoline results in the majority of air pollution since they are used to provide energy for transportation or electricity.
  • Several particulate matter emissions, including, CO2, SO2, and CO, can result in pollution from industrial activity.
  • Smoking tobacco, cooking smoke, hazardous chemicals from home painting supplies, etc. all contribute to air pollution.
  • Ammonia is one of the most hazardous gases in the environment and is produced as a byproduct of numerous agricultural usage.

This image shows the various reasons for air pollution.

Harmful Effects

Air pollution has adverse effects on humans as well as the environment. Following are the ill effects of air pollution-

Air pollution effect on humans-

  • Aerosol sprays and paint removers include methylene chloride, which can be carcinogenic.
  • Gasoline and benzene can lead to leukemia.
  • Lung cancer is brought on by gases generated when fossil fuels are burned.
  • Asthma and other respiratory illnesses like COPD are caused by suspended particles such as dust, pollen, ashes, etc.
  • The likelihood of pneumonia, lung inflammation, chest pain, cough, exhaustion, shortness of breath, and fever is increased by nitric oxide and sulphur dioxide exposure.

Air pollution effect on the environment-

  • Acid Rain is the term for the precipitation of dangerous nitric and sulfuric acids along with rainwater. These gases are generated by the burning of fossil fuels and combine with rainwater to produce various acids, such as nitric acid and sulfuric acid.
  • Aquatic life and various tree species are negatively impacted by acidic buildup in the water body by a major decline in biodiversity.
  • Buildings, monuments, and sculptures built of sandstone, limestone, marble, and granite are damaged and discoloured by acid rain.
  • Ozone depletion occurs due to air pollutant such as CFCs. Due to this depletion UV light then penetrates the earth’s surface and has serious consequences like DNA mutation, skin cancers etc.
  • Also, air pollution causes other harmful effects such as Global warming, and climate change which affect the biodiversity of the Earth adversely.

Prevention

To prevent air pollution following should be done-

  • Reduction of forest fires.
  • Stop burning crackers.
  • All chimneys should contain filters.
  • Use green energy 
  • Using carpooling and public transportation.
  • The Air Act of 1981, which forbids burning fuel that contributes to air pollution, must be followed.
  • Implement planting trees.
  • Paper, plastic, metals, and organic materials should all be recycled and used.

Control

Following ways are there to control air pollution-

  • Reduce vehicular pollution. Numerous vehicles on the road each day produce dangerous air pollution. Use fewer cars and more environmentally friendly forms of transportation.
  • Using alternative and eco-friendly forms of  fuels.
  • Utilizing unleaded gasoline
  • Plant more trees. 

Summary 

When dangerous chemicals like chemical, biological, and physical pollutants from both man-made and natural sources contaminate the atmosphere, it causes air pollution, which is an unwelcome change. Rising morbidity and mortality, has an impact on not just the climate but also on public and individual health. Carbon monoxide, carbon dioxide, lead, nitrogen oxides, ground ozone, particulate matter, sulphur oxides, CFC’s, Hydrocarbons etc. are examples of common air pollutants which cause air pollution. Plants are referred to as the “lungs” of an ecosystem as they take in carbon dioxide and give fresh oxygen to the environment. Hence, they should be planted more to prevent air pollution.

Frequently Asked Questions 

1. Describe a Scrubber.
Ans: A scrubber is a device that traps any particle matter or other similar contaminants in the air and cleans the air to prevent pollution. It contains an ionized liquid that traps the small particles of a contaminant.

2. Explain Alternative Fuels.
Ans: There are several compounds known as alternative fuels that can be used in place of traditional fuels like gasoline, diesel, etc. CNG, hydrogen, and other such fuels are examples of alternative fuels. These are unconventional and don’t pollute the air.

3. What is Smog?
Ans: Smog is an air contaminant and is made when fog, smoke, and sunlight are combined. Sulphurous smog and photochemical smog are the two types of smog. When sulphur oxides are present in significant concentrations in the air, sulphurous smog, also known as London smog, forms. When sunlight and at least one volatile organic compound (VOC) react in the sky, photochemical smog, often known as Los Angeles smog, is created.

Terms of an Expression

Introduction

An expression made up of variables, constants, coefficients, and mathematical operations like addition, subtraction, etc. is known as an algebraic expression. A variable is a symbol without a predetermined value. In an algebraic expression, a symbol with a fixed numerical value is referred to as the constant. A term is either a variable, a constant, or both combined through mathematical operations. A coefficient is a quantity that has been multiplied by a variable and is constant throughout the entire problem. Algebraic expressions have many uses, including representing real-world issues as well as solving various and complex mathematical equations to determine revenue, cost, etc.

Algebraic Expressions

An expression made up of variables, constants, coefficients, and mathematical operations like addition, subtraction, etc. is known as an algebraic expression. Algebraic expressions have many uses, including representing real-world issues and solving various and complex mathematical equations, finding revenue, cost, etc.

Based on a variety of number of terms, there are three main categories of algebraic expressions, i.e., monomial, binomial, and polynomial.

What is a Term in Algebra

A term is a group of numbers or variables that have been added, subtracted, divided, or multiplied together; a factor is a group of numbers or variables that have been multiplied; and a coefficient is a number that has been multiplied by a variable. Three terms, 9x², x, and 12, make up the expression 9x² + x + 12.

By drawing this conclusion, it is clear that an expression is made up of a number of terms, variables, factors, coefficients, and constants.

Terms of an Expression

A term can be a number, a variable, the sum of two or more variables, a number and a variable, or a product of both. A single term or a collection of terms can be used to create an algebraic expression. For instance, 2x and 5y are the two terms in the expression 2x + 5y.

A mathematical expression has one or more terms. A term in an expression can be a constant, a variable, the product of two variables (xy) or more (xyz), or the product of a variable and a constant (2x), among other things.

Different types of terms in an Algebraic Expression

There are different types of terms in algebraic expressions, 

Algebraic Expressions

Variables

These types of terms are usually represented by a symbol (most commonly its English alphabets), like x, y, z, a, b, etc. these symbols are there to represent unknown arbitrary values, hence the name ‘variables’ (since their values can vary).

Coefficient

These are not a type of a term but rather a part of a term that contains variables, coefficients are the numbers that are in multiplication with variables.

Constants

These terms are the numbers separate from the variables, and as the name suggest, they are a constant number, i.e., they are fix and never change unless they are under an operation with another constant term.

Also Read: Like and Unlike Terms

Algebraic Expressions Based on Number of Terms

A single term or a number of terms can be used to create an algebraic expression. Based on the number of terms, there are various types of expressions. These are listed below:

  • Monomial Expressions: – An algebraic expression in which an expression has only one term is known as a monomial. For example, 3x, xyz, x²
  • Binomial Expression: – An algebraic expression in which an expression has two terms is known as a monomial. For example, 5x + 8, xyz + x³
  • Polynomial Expression: – An expression in which an expression has more than two-term within a variable is known as a polynomial. For example, 2x + 4y + 7z,  + 5x + 3

Factors of terms: Identifying Factors

Factorization of terms refer to an algebraic expression that is written as a multiple of variables and constants.

We will now determine the factors of the terms in the given expression. To do this, we must first separate the terms and then look for their multiples. The results of this process are the factors of the given expression.

Let the expression be,

3xy + 5z²

Then the terms are,

3xy, 5z²

And the factorization of the terms are,

3 × 𝑥 × y and 5 × z × z

Solved Examples

Example 1: Identify the different terms, variables and coefficients in the following expressions

a.  + 3xy

b. 2ab + 5c²

Solution: 

a. Expression:  + 3xy

Terms: x², 3xy

Variables: x, y

Coefficients: 1 for x², 3 for xy

b. Expression: 2ab + 5c²

Terms: 2ab, 5c²

Variables: a, b, c

Coefficients: 2 for ab, 5 for c²

Summary

An expression made up of variables, constants, coefficients, and mathematical operations like addition, subtraction, etc. is known as an algebraic expression. Coefficients, constants, and variables are a few of the key words in the context of algebraic expressions. Similar terms are those in algebraic expressions that are constants or involve similar variables raised to similar exponents. In algebraic expressions, unlike terms are those terms that do not share the same variables or that share the same variables but have different exponents. Algebraic expressions are all polynomials, but not all algebraic expressions are polynomials. Polynomials are algebraic expressions without fractional or non-negative exponents. Algebraic expressions include fundamental identities that are used in the subject.

FAQs

1.What are Polynomials?

Ans. Polynomials are algebraic expressions with more than 2 terms and the variables have non-negative integer exponents.

2.What is a Quadratic Equation?

Ans. A quadratic equation is a polynomial equation, with maximum exponent on a variable being 2.

3. What is a term in an Algebraic Expression?

Ans. A term can be a number, a variable, the sum of two or more variables, a number and a variable, or a product of both. A single term or a collection of terms can be used to create an algebraic expression.

Rational Numbers – Types of Rational Numbers – Solved Examples

Introduction

There are numerous quantities and measures that cannot be stated just in terms of integers. Rational numbers were crucial in expressing how such quantities were measured. These quantities included time, money, length, and weight. Some of the quantities for which the rational numbers are most frequently employed include those ones. Rational numbers are also required in trigonometry in addition to counting and measuring. The trigonometric ratios are expressed as rational numbers. Calculations based on the Pythagorean Theorem employ a specific kind of rational integer. 

Rational Number 

Rational Numbers

The rational number can be described as the ratios expressed in numbers. The term “rational” contains the word “ratio” as well. Therefore, any ratio is represented by rational numbers. These ratios may be lower than one to one or higher than one. Let’s comprehend how rational numbers should be explained. Rational numbers are defined as any number which can be expressed in the form of where a and b are coprime integers and b ≠ 0. The denominator is not equal to zero and both the numerator “a” and denominator “b” have integer values. The outcome of the division method used to simplify the rational number is in decimal form. The decimal representation of a rational number can either be non-terminating repeating decimals or terminating decimals.

How to find Rational Numbers

Verify that each given number meets the following requirements.

  • The amount must be expressed as a fraction with a denominator greater than or equal to 0.
  • To get the decimals, the fraction can be further decomposed.
  • Positive, negative, and 0 are all included in the set of rational numbers, which is represented as a fraction. Because they may be written as a fraction, each whole number and integer is a rational number.

Types of Rational Numbers

Positive Rational Numbers

The positive rational numbers are signified as the rational numbers having positive numerators and denominators. The rational numbers  and are positive rational numbers.

Negative Rational Numbers

The negative rational numbers are signified as the rational numbers having any one of the numerators and denominators less than 0. The rational numbers  and are negative rational numbers.

Integers

The integers can be expressed as fractions having a denominator of one. Therefore, all integers are a class of rational numbers. Integers can have the forms of 0, -8, 56 etc.

You can also read our detailed article on Positive and Negative Rational Numbers.

Terminating Decimals

The decimals are the outcome of simplifying rational numbers. Some values following the decimal point may be where these decimals end. Terminating decimals are the name given to these rational numbers. For example: 0.235, 0.056, etc.

Non-Terminating Repeating Decimals are one Type of Rational Number.

Any rational integer is a non-terminating repeating decimal if, after simplification, the outcome is a decimal with repeating digits after the decimal point. A single digit or a group of digits can be one of the recurring values. For example: 0.5533, 0,222, 0.659659, etc.

Summary

Rational numbers are the numbers that can be written in the form of a fraction, where numerator and denominator are integers. The rational numbers are represented in the form of p/q where,q the denominator is not equal to 0.  Five separate categories of rational numbers exist. Both the numerator and the denominator are bigger than zero with positive rational numbers. Any numerator or denominator of a negative rational number is less than zero. Rational numbers that have a denominator of 1 are known as integers. The rational numbers also include recurring decimals that do not terminate.

Practice Solved Example

Example: The decimal expansions of some real numbers are given below. In each case, decide whether they are rational or not. If they are rational, write in the form of p/q. 

a. 0.140140014000140000…    

We have, 0.140140014000140000… It is a non-terminating and non-repeating. So, it is irrational. It cannot be written in the form of P/q.

b.

We have,    a non-terminating but repeating decimal expansion. So, it is Rational.

Let x =

Then, x = 0.1616 ——–1

100x = 16.1616 —-2

On subtracting 1 from 2 we get,

100x – x = 16.1616-0.1616

99x = 16

x =

Frequently Asked Questions

1.The number of Rational numbers between 25 and 26 is Finite. State the give statement is True or False.

Ans: False, any two rational numbers can be integrated by an infinite number of other rational numbers. Therefore, there are infinite rational numbers between 21 and 26.

2. Why does the Rational Number not have a 0 as its Denominator?

Ans: The outcome is not a defined value if the denominator of the rational number is 0. As a result, the rational number’s denominator never equals 0.

3. Can a Rational Number have a Numerator and Denominator of Zero?

Ans: No, the numerator may equal 0. However, for every rational number, the denominator can never be 0.

4. Which Technique is used to Transform a Rational number’s Standard form to Decimals?

Ans: The standard form of a rational number is converted to decimals using the division method.

Properties of Addition and Subtraction of Integers

Introduction

Natural numbers, their additive inverses, and zero are all collectively known as a set of Integers. We get a whole number when we subtract a small number from a larger number. However, there are no whole numbers that can represent the difference between a large number and a smaller number, such as 12 – 37. We created integers to describe such differences. Integer Addition follows all the rules of algebra, whereas Integer Subtraction doesn’t.

Properties of Addition and Subtraction

Addition and Subtraction of Integers

In addition, and subtraction of integers, we will learn how to add and subtract integers with the same and different signs. Certain rules must be followed when performing operations on integers.

When you add two positive integers, you get a positive integer, but when you add two negative integers, you get a negative integer sum. Adding two different signed integers, on the other hand, results in subtraction only, with the result having the same sign as the larger number. For example,

Addition with the same sign

3 + 5 = 8 or (- 7) + (- 5) =- 12

Addition with a different sign

6 + (- 4) = 2 or (- 6) + 4 =- 2

As for subtraction, when you subtract the integers, you add the additive inverse of the second integer, i.e., you can simply just change the sign of the second integer and add the two numbers using the rules of addition. For example,

7 – 5 = 7 + (- 5) = 2

9 – (- 2) = 9 + 2 = 11

(- 3) – (- 5) = (- 3) + 5 = 2

(- 6) – 7 = (- 6) + (- 7) =- 13

Properties of Integer Addition and Subtraction

Integers have a few properties that govern how they operate. These principles or properties can be used to solve a wide range of equations. Integers are any positive or negative numbers, including zero, to refresh your memory. These integers’ properties will aid in quickly simplifying and answering a series of integer operations.

All addition, subtraction, multiplication, and division properties and identities apply to all integers. The set of positive, zero, and negative numbers represented by the letter Z is known as the set of integers. Integers have the following five operational properties:

  • Closure Property
  • Commutative Property
  • Associative Property
  • Distributive Property
  • Identity Property

Closure Property

According to the closure property, the set of all integers is closed under addition and multiplication, i.e., the addition or multiplication of any two integers will always result in an integer. Subtraction of integers also follows the closure property; division however does not follow the same rule for integers. For example, 2 divided by 5 is not an integer.

If a and b are two integers, then if,

c = a + b and d = a × b

Then both c and d are also integers

Changing b with – b,

e = a – b is also an integer.

Commutative Property

According to the commutative property of addition and multiplication, the order of terms does not affect the result. Let a and b be two integers, then by the commutative law:

a + b = b + a

Also,

a × b = b × a

But subtraction and division do not follow the same rules.

Associative Property

According to the associative property of addition and multiplication, it doesn’t matter how numbers are grouped; the result is the same. Regardless of the order of the terms, parenthesis can be used.

a + (b + c) = (a + b) + c

Also,

a × (b × c) = (a × b) × c

However, again, subtraction and division are not associative for Integers.

Distributive Property

The distributive property explains how one mathematical operation can distribute over another within a bracket. To make the calculations easier, the distributive property of addition or the distributive property of subtraction could be used. In this case, integers are multiplied or divided by each number in the bracket before being added or subtracted again.

a × (b ± c) = (a × b) ± (a × c)

Identity Property

When zero is added to any integer no matter the order, the result is the same number, according to the additive identity property of integers. Zero is known as additive identity.

Let a be an integer

Then, since 0 is known as the additive identity

a + 0 = a = 0 + a

Similar to this, we have a multiplicative identity. When a number is multiplied by 1 in any order, the product is the integer itself, according to the multiplicative identity property for integers.

Again, let a be an integer,

Then, since 1 is known as the multiplicative identity

a × 1 = a = 1 × a

Again, like most other properties, subtraction and division do not follow the identity property.

Solved Examples

Example 1: Simplify the following expressions

a. (- 2) + (- 4) – 5 + 13

b. 4 × 27 + 4 × 31 – 4 × 53

Solution:

a. (- 2) + (- 4) – 5 + 13

First, we will use parentheses to separate different operations

⇒ ((- 2) + (- 4) – 5) + 13

Here we have separated the only positive term, but we still have 3 terms in the parentheses,

⇒ (((- 2) + (- 4)) – 5) +13

Now solving the operations in the parentheses one by one,

⇒ ((- 6) – 5) + 13

⇒ (- 11) + 13

⇒ 2

b. 4 × 27 + 4 × 31 – 4 × 53

First, we can see that 4 is a common factor in all the products. So we will factor it out,

⇒4 × (27 + 31 – 53)

Now we will separate the terms inside the parentheses using centric parentheses

⇒ 4 × ((27 + 31) – 53)

No solving the parentheses one after the other

⇒ 4 × (58 – 53)

⇒ 4 × 5

⇒ 20

Summary

This article gives an insight into the properties of addition and subtraction of integers. According to the addition closure property, the sum of any two integers will always be an integer. According to the subtraction closure property, the sum of, or the difference between, any two integers will always be an integer. The commutative property of integer addition states that the order of addition of integers does not matter, the result remains the same regardless. Subtraction, on the other hand, is not commutative for integers. According to the associative property of addition, the order in which numbers are grouped does not affect the outcome. The nature of integer subtraction is not associative.

Frequently Asked Questions (FAQs)

1.What are Integers? How are they different from other types of Numbers, such as Natural Numbers and whole numbers?

Ans. Integers are numbers that have no decimal value, whole values represent them. The integers contain both positive and negative numbers, along with the number 0. The positive integers are known as natural numbers, whereas the positive integers with 0, aka the non-negative integers, are known as whole numbers.

2.What are the rules for Adding Integers?

Ans. The addition of integers follows two simple rules,

  1. Adding two integers of the same sign results in the addition of the value of those numbers, and the result has the same sign as the additives.
  2. Adding two integers of different signs results in a difference in the value of integers, and the result has the same sign as the number with the higher value.

3.Which Properties of Integer Addition can be applied to Integer Subtraction?

Ans. The following properties of integer addition can be applied to integer subtraction,

  • Closure: The closure property states that the result of the operations is in the same set as the input, i.e., subtracting two integers will always result in an integer.
  • Distributive: Distributive property states that the operation of multiplication can distribute over operations such as addition or subtraction, i.e., the product of a number and a difference of two numbers is the same as the difference of the product of the two numbers with the first.

4.What is an Inverse?

Ans. The inverse of a number is another number, which, when operated under a certain operation with the original number, results in the identity of that operation. That is, for addition, the inverse is defined as the number which when added together with the original number results in 0, and for multiplication, multiplies to give 1.