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What Are Infinitives? Examples, Types, and Uses of Infinitives (PDF)

An infinitive is an action word that capacities as a thing, descriptor, or modifier to offer a viewpoint, the motivation behind an article or activity, or answer the inquiries who, what, or why.

An infinitive as a rule starts with “to” and is trailed by the base type of an action word (the basic type of the action word that you would find in the word reference).

For English action words, the infinitive (base structure) is motioned with ‘to’, which stands preceding it in the vast majority of the cases (for exemptions for this training, examine split infinitive). A few instances of infinitives are:

to go, to do, to drink, to hear, to acknowledge, to fly, to work out, to compose, to watch, to break, and so forth.

An infinitive action word is “to” trailed by an action word. Assuming you will study, or to drive, or to cook, you are utilizing infinitive action words. Continue to peruse for infinitive models in various sentences, just as their various structures and capacities.

Examples of Infinitive Verbs

You can frame an infinitive action word by adding “to” before any base action word. Infinitive action words are not formed like different action words; they stay in their infinitive structures in a sentence. Instances of normal infinitive action words include:

  • to be (I need to be a space explorer.)
  • to dream (James hopes against hope about landing the position.)
  • to have (We will have a child.)
  • to hold (Do you need to hold the little dog?)
  • to look (I’m reluctant to take a gander at the untidy room.)
  • to peruse (The main graders are figuring out how to peruse this year.)
  • to compose (I’m intending to compose a letter to the organization.)
  • to rest (It’s an ideal opportunity to rest.)
  • to toss (If Gina doesn’t get everything she might want, she will pitch a fit.)
  • to need (It’s normal to need your group to win.)

Despite the fact that infinitives incorporate action words, they are not action words. Infinitive action words are verbals, and that implies they can be utilized as things, modifiers, or qualifiers. Contingent upon the words they follow, infinitives can work as various pieces of a sentence, yet not action words.

Instances of Infinitive Verbs as Adverbs

At the point when infinitives follow a descriptor, they’re working as modifiers. They can likewise change the action word in the sentence to respond to the inquiry “Why?” For instance:

  • Billie is at last all set.
  • I ascended the mountain to see the view.
  • Peruse the manual to see more about fixing the sound system.
  • Cameron goes to see the world.
  • I purchased a fix to quit smoking.
  • My father will be so glad to meet you!
  • You are so natural to converse with.
  • Kelly went to the store to purchase apples.
  • How about we purchase snow stuff to go skiing.
  • I attended a university to turn into a designer.

Notice that any of these infinitives can show up in any sentence. Everything relies upon how they’re working and what they’re adjusting. Regardless, infinitives are an incredible method for adding more detail to a sentence.

Instances of Infinitive Verbs as Adjectives

Infinitives can likewise alter things in a sentence. At the point when infinitive action words go about as descriptors, they portray the thing that they follow.

  • Do you have any clothing to wash?
  • My cherished dinner to make is macaroni and cheddar.
  • The best technique to utilize is the involved strategy.
  • The Superbowl is the game to watch.
  • Peter is a troublesome person to comprehend.
  • He unquestionably gave me something to contemplate.
  • That watch is an important treasure to pass down.
  • This what is unquestionably significant to know.
  • You’ll forever have a sister to trust in.
  • History is my most un-most loved subject to study.

In contrast to infinitives that go about as things in the sentence, adjectival infinitives answer the inquiry “What kind?” For instance, in the sentence “Do you have any clothing to wash?” the infinitive “to wash” explains why sort of clothing you’re searching for.

Instances of Infinitive Verbs as Nouns

Infinitives can work as things when they follow specific action words. In these cases, the infinitive action word is functioning as an immediate item or backhanded article. At the point when there are extra words after the infinitive action words, they become infinitive expressions. For instance, in the accompanying sentences, the action words are stressed and the infinitives are bolded.

  • We chose to go out.
  • I need to swim in the pool.
  • Mother loves to give gifts.
  • Do you commit to come clean?
  • I’d like to see an activity film.
  • He reminded her to go midtown.
  • To move is my daughter’s fantasy.
  • I might want to thank you for coming out this evening.
  • He prefers not to drink soft drink from a can.
  • I neglected to take my nutrients today.

These infinitive action words and expressions answer the “What?” questions presented by the action words in the sentences. For instance, in the primary sentence, “We chose to go out,” the infinitive expression “to go out” addresses the inquiry “What did we choose?”

Kinds of Infinitives

An infinitive can be a to-infinitive or uncovered infinitive (without to). There is no contrast between them. So we can order them as follow.

  • 1. Uncovered infinitive
  • 2. Full infinitive
  • 3. Split infinitive

1. Instances of uncovered Infinitives

You’ve seen a few instances of infinitive action words that incorporate “to” – yet only one out of every odd infinitive does. These are known as uncovered infinitives, which work the very same way as infinitive action words do. They follow modular assistant action words (can, ought to, will, would, will, could, may, might, etc) in a sentence. For instance:

  1. I can sit tight for the outcomes. (NOT “I can to hang tight for the outcomes”)
  2. Would it be a good idea for us to call our folks? (NOT “Would it be advisable for us to call our folks?”)
  3. Henry may loan us his truck. (NOT “Henry may to loan us his truck.”)
  4. Our family will be OK. (NOT “Our family will to be alright.)

These infinitives work as objects to the modular action words (I right? I can stand by) in the sentences. They work the same way in sentences with action words of insight (hear, see, feel, sense) and action words of consent (bid, let, need, know, help, would be advised to, sooner than, would prefer, etc). For instance:

  • Oliver made me share my lunch with him.
  • You would do well to come clean with me.
  • Tracker would prefer to go to class.
  • I saw her swim ten laps.
  • Lola likes you.
  • Would you be able to assist me with conveying this higher up?

It might appear to be hard to remember these principles and action words. Notwithstanding, you are the best adjudicator of when to utilize exposed infinitives. In the event that a sentence sounds off-kilter with “to,” feel free to attempt the exposed infinitive.

2. Full Infinitives:

The point when an infinitive is utilized with the word ‘to’ or to + infinitive is called the full infinitives.

To + infinitive = full infinitive.

Employments of Full Infinitives:

Full infinitives can work as a thing, a modifier, or an intensifier in a sentence.

As Subject: To call, after everything hardships don’t appear to be beneficial. (‘To call’ is the activity that drives the sentence)

Direct Object: They all need to go. (‘To go’ is the immediate article that can be a substitute for a thing that gets the activity of the action word in the sentence)

Subject Complement: The object is to win. (‘To win’ is the subject supplement. A Subject supplement resembles an immediate item, click on the connection to understand more: Basic Sentence structure)

Adjective: He wasn’t permitted to take an interest. (‘To take an interest’ adjusts permitted, it depicts what kind of stipend is being talked about, so the expression fills in as a modifier)

Adverb: He assigned his name to the group to make a decent attempt. (‘To make a decent attempt’ clarifies why the assigning of his name occurred, so it’s an intensifier adjusting the action word selected)

At the point when we utilize full infinitive, we are generally alluding to the current infinitive, there are, be that as it may, four other types of the full infinitive:

  •  The ideal Infinitive (“to have + third of the action word” generally found in restrictive kind 3)
  • They pardoned to have played the match.
  •  The ideal Continuous Infinitive (“to have been + verb+ ing” is utilized to communicate a proceeding however presently finished activity).
  • They more likely than not been working for a really long time.
  •  The ceaseless Infinitive (“to be + action word + ing” is utilized to communicate a proceeding with activity after an action word or assistant which should be trailed by the infinitive).
  • You should kid.
  • The detached Infinitive (“to be + third of the action word” is utilized in certain developments utilizing the latent voice. It is especially normal after assistant action words (may, ought to, could, and so on)

3. Split Infinitives

At the point when you place a qualifier or word intensifying expression between the ‘to’ and the action word and split the infinitive form ‘to’ is called the parted infinitive.

To painstakingly stroll, to strongly go, to truly play, and so on

  • The mentor encouraged the players to truly play and dominate the game.
  • The educator advised us to rapidly finish the task.
  • We are here to influentially show infinitives and its sorts

Utilizing split is denounced as a rule; notwithstanding, they are normally recorded as a hard copy, everything being equal. However, recall when you are in question; try not to involve split infinitives in your sentences.

The infinitive can be utilized as a thing. As a thing, it tends to be the subject or object of the action word.

  • To observe issue is simple. (Here the infinitive ‘to find’ is the subject of the action word is.)
  • To blunder is human. (Here the infinitive ‘to blunder’ is the subject of the action word is.)
  • He jumps at the chance to play a game of cards. (Here the infinitive ‘to play’ fills in as the object of the action word likes.)
  • I would rather not go. (Here the infinitive ‘to go’ fills in as the object of the action word need.)
  • The infinitive can likewise be the supplement of an action word.
  • Her most noteworthy delight is to sing. (Here the infinitive ‘to sing’ is the supplement of the action word is.)
  • The infinitive can likewise be the object of a relational word.
  • The speaker is going to start. (Here the infinitive ‘to start’ is the object of the relational word about.)

The infinitive can likewise be utilized to qualify an action word.

  • He called to see my sibling.
  • We eat to live.
  • I came to cover Caesar.

The infinitive can be utilized to qualify a descriptor.

  • Figs are great to eat.
  • The young men are restless to learn.
  • He is too sick to even consider accomplishing any work.

The infinitive can be utilized to qualify a thing.

  • This isn’t an ideal opportunity to play.
  • Here is a house to let.

The infinitive can be utilized to qualify a sentence.

  • To come clean, I don’t have any interest in legislative issues.

What are Adverbs? Definition, Rules, Examples, and Worksheets (PDF)

An Adverb is a word that modifies the meaning of a verb, an adjective, or another adverb. It tells us how, where, when, how much, and with what frequency, a job is performed. The words such as quickly, very, and quite are, therefore, adverbs.

Let’s take a simple example: Sham runs quickly. This sentence quickly shows how Sham runs; that is, quickly modifies the verb runs.

What are the Kinds of Adverbs

When we are learning about Adverbs you should also know that adverbs are divided into seven different kinds which are as follow:

1. Adverbs of Time: It shows when something is happening. Like once, never, tomorrow, daily, etc. are adverbs of time.

Examples of Adverbs of Time:

  • Ram hurt his knee yesterday.
  • Wasted time never returns.
  • She will visit the hospital tomorrow.
  • He comes to school daily.

2. Adverbs of Frequency: It shows how often something is happening. Like twice, always, every day, frequently, seldom, etc.

Examples of Adverbs of Frequency:

  • He seldom comes here.
  • The Science class happens twice a week.
  • The teacher called again.
  • He frequently comes first in class.

3. Adverbs of Place: It shows where the thing is happening. Like somewhere, Anywhere, Near, Far, etc.

Examples of Adverbs of Place:

  • In spring, flowers bloom everywhere.
  • They need you there.
  • You live far away.
  • The teacher told him to come in.

4. Adverbs of Manner: It shows how or in what manner something is done or happening. Like honestly, joyfully, clearly, bravely, etc.

Examples of Adverbs of Manner:

  • She reads clearly
  • The child slept soundly.
  • The boy works hard.
  • The story was well written.

5. Adverbs of Quantity: It shows how much, or to what extent something is done or happening. Like fully, partially, altogether, almost, etc.

Examples of Adverbs of Quantity:

  • He is good enough for doing work.
  • She sings pretty well.
  • Sham was partly right.
  • She almost finished the work.

6. Adverbs of Affirmation and Negation: It shows affirmations like certainly, never, surely, definitely, absolutely, etc. And if we tail about Adverbs of Negation that are No, Don’t, Can’t, etc.

Examples of Adverbs of Affirmation and Negation:

  • I do not know him.
  • Surely you are mistaken.
  • She never leaves her house.
  • I can’t work with him.

7. Adverbs of Conjunction: It shows the effect and relation between the two clauses like moreover, however, accordingly, etc.

Examples of Adverbs of Conjunction:

  • He was busy yet helped me with my work.
  • He was going for an important meeting accordingly; he made sure he reached on time.
  • He didn’t prepare for his exams; as a result, he failed his exams

What do adverbs do ?

As we have studied previously in the definition of Adverb that it modifies verb to tell us when, how, where, how often, how much the action is performed. To make it simple let’s go through the following table.

WhenRam worked yesterday.
WhereRam work here.
How Ram works slowly.
How muchRam works partially.
How oftenRam works twice a week.

From the above table try to imagine a boy name RAM and the action he performs, which are represented through adverbs.

Forms of Adverbs

Some Adverbs are in the same form as the corresponding Adjectives; like they can be used as both.

Let’s go through some examples of Adverb forms to understand this concept:

If the adjective ends in –able, -le, replace the -e with -y.

  • Probable – probably
  • Gentle – gently

If the adjective ends in –ic, add -ally. Exception: public -> publicly

  • Basic – basically
  • Tragic – tragically
AdjectivesAdverbs
Ram is our fast bowler.                                  Ram can bowl fast.
He is the best boy in this class.He behaves best.
He went to the back entrance.Go back.

Some Nouns express adverbial relations of distance, time, place, degree, and are often used as Adverbs.

Examples-

  • She walked two miles.
  • The book is only a hundred rupees.
  • These are called Adverbial Accusative.

Position of Adverbs

Where do you put your adverb either before or after a verb or in-between the sentence? It is somewhat tricky when it comes to the position of adverbs; let’s understand it with some examples.

Front Position (Placed at the beginning of a sentence)

Adverbs of frequency: such as frequency, sometimes, usually, normally, etc.

Exception: Always, ever, rarely, seldom, and never.

Examples-

  • Normally she wears red clothes.
  • Usually, the summer is hot and humid.

Adverbs of Manner: Such as suddenly, badly, quietly, etc.

Examples-

  • Suddenly, it began to rain.
  • Unfortunately, everything is going bad.

Adverbs of Time: Last night, yesterday, tonight, etc.

Examples- Yesterday, I went out to an amazing party.

End Position (Placed at the end of a sentence)

Adverbs of frequency: usually, normally, often, sometimes, and occasionally.

Not: always, ever, rarely, and seldom.

Example:

  • I go to bed at 10 pm, usually.
  • I don’t read the newspaper often.

Adverbs of Manner: Slowly, suddenly, badly, quietly, etc.

Example:

  • She played basketball brilliantly.
  • She did her work carefully.

Adverbs of Time: today, already, soon, finally, etc.

Example:

  • There is no rain today.
  • I am going on vacation tomorrow.

Mid Position (It is present in the middle of a sentence)

These are present before other verbs.

Adverbs of Degree: even, also, just, mainly, etc.

Examples- You don’t even listen to what I say.

Adverbs of frequency: such as never, rarely, sometimes, usually, always, etc.

Examples- He is often late for school.

Adverbs of Time: such as finally, eventually, already, still, soon, etc.

Examples-

  • We’ve already eaten our lunch.
  • We are still working on the project.

Adverb of Manner: Depends on sentence which tells us how something is done, such as slowly, suddenly, badly, quickly, etc.

Example- He slowly backed his car into the garbage.

How To Find Adverbs Easily?

An adverb is the most emphasized word in a sentence that provides you answer about the way a task is done. A simple method is to start asking questions related to the sentence you are provided, here are some examples:

  1. He is doing his work slowly. [how he is doing his work?]
  2. Radha is working quietly. [how is radha working?]
  3. Sham ate the chocolate cake greedily. [how sham ate the cake?]
  4. Our magazines come daily. [when our magazines come?]
  5. Olivia live far away. [where olivia lives?]

Worksheets of Adverbs

As we have learned about Adverbs, now it’s time to practice the following questions.

Q1. Identify and circle the adverb in following sentences:-

  1. I already finished my homework.
  2. The balloon rose quickly in the sky.
  3. Sham is playing basketball outside.
  4. My mom cares deeply about me.
  5. Are you always tired in the morning?
  6. I hardly ever watch this show.
  7. Sham always comes first in class.
  8. I can’t wait to go to zoo tomorrow and see the elephant.
  9. Even baby giraffes move gracefully and carefully.
  10. Katrina practices her piano regularly.

Q2. Insert the given adverbs in their normal position:

  1. We know the answer ( already )
  2. I shall meet you (this evening, in the park )
  3. She invited me to visit her ( often )
  4. The train has left us ( just )
  5. He is in time for meals ( never )

Q3. Use adverbs from the box to complete the sentence.

Here              easily              later                 quickly                     very
  1. She aced her test_________________.
  2. Sachin won the race, because he ran so_______________.
  3. _____________, he finished his homework.
  4. The dog sat ______________ still waiting for his food.
  5. Smith walked ______________ from his neighbour’s house.

What are Participles in English Grammar? Its Types, Examples, and Worksheets (PDF)

Participles are verb forms that are used to work for any of the following three purposes. Participles are used in a sentence (1) as an adjective to modify nouns, or (2) to work with auxiliary verbs for creating the continuous and perfect verb tenses, or (3) to create a passive voice. So participles are words derived from verbs. Participles are usually formed by adding “_ing, _d, _ed, or _t” with the main verb form.

Examples of Participles as Adjectives

The rising sun, The boiled water, The breaking news: In all these examples the participles rising, boiled, breaking, etc are modifying the nouns sun, water, and news respectively. All the mentioned participles are formed from the base verbs rise, boil, and break.

Examples of Participles to form Verb Tenses

  • I am reading a storybook. (Present participle reading)
  • He is watching the program. (Present participle watching)
  • Those clothes are washed. (Past participle washed)

In the above three sentences, participles are used to form verb tenses.

Examples of Participles to form Passive Voice

  • Riya was attacked by a snake while she was walking on the road.
  • That city was destroyed by a massive earthquake.

In the above two sentences, the participles attacked and destroyed are used as passive voices.

Types of Participles

In English grammar, Verbs usually have two types of participles: a present participle and a past participle.

Present Participles:

Present participles end in “-ing” and function in a sentence as (i) part of a continuous tense,
relying on an auxiliary verb to be complete; (ii) as an adjunct to a finite verb,
indicating a secondary action; or (iii) as an attributive or predicative adjective, modifying a noun.
Examples of Present Participles: closing, looking, eating, singing, being, etc.

Past Participles:

Past participles usually end in “-ed,” “-d,” or “-t”. They (i) create perfect verb
tenses ( past perfect, present perfect, and future perfect), or (ii) function as adjectives modifying nouns (again, either attributively or predicatively). Past participles are (iii) also used to form passive voice forms.
Examples of Past Participles: closed, looked, eaten, sung, been, etc.

Use of Participles as adjectives and participle phrases

Both present and past participles can be used as part of participle phrases or as adjectives. Note that using participles a longer sentence can be condensed into a shorter one.
For example, The sentence “The hunter pointed the gun to the bird, that was flying” can be modified as “The hunter pointed the gun to the flying bird” using participle.

A participle phrase is formed by combining the participle with other words and the complete group acts as adjectives in the sentence. For example, Wearing his red cap, Advik went to play crocket. I this sentence, wearing his red cap is the participle phrase.

Participles Worksheet

By now you must have a basic understanding of what a participle is. It’s time to solve the following participle worksheets.

Participles Worksheet 1: Read the following sentences and underline the participles. Also state if they are used as adjectives, participle phrases, or tenses.

  1. The complaining man was walking towards the bus.
  2. My brother, exhausted after cycling for two hours, has fallen asleep on the sofa.
  3. The bent pipe began to leak.
  4. My injured foot kept me up all night.
  5. The swimming frog is very small.
  6. Aharsi, hiding behind the door, was completely silent.
  7. Having stayed up all night watching TV, Advik was exhausted.
  8. Having seen the movie before, I wouldn’t want to see it again.
  9. The glistening icicles looked magical.
  10. Gazing at the girl, the cat purred.

Participles Worksheet 2: Fill in the blanks using proper Participles of the verb given in bracket.

  1. Can you translate the sentences of the people ________ (speak) Russian?
  2. ___________ (Tell) the news, Ram disappeared in the crowd.
  3. While ____________ (play) in the field, Shyam didn’t hear the phone call.
  4. At Indore, We visited Lal Bagh Palace _______(build) around 150 years ago.
  5. Uttam doesn’t believe the facts ________(present) to him.
  6. __________ (buy) the ticket, Swarnali entered the theatre.
  7. Mohor showed the photographs __________(take) ten years ago.
  8. The kid’s ________(shout) in the park, lives in that hostel.
  9. ___________(be) an average student, Ameya could not answer all the questions.
  10. During winter the warmth of _________ (shine) sun makes us happy.

Divisibility Rules in Mathematics | Divisibility Rule for 2 to 20 (PDF)

The divisibility rule in mathematics is defined as the certain shorthand steps for finding if a given number is divisible by a fixed divisor (integer). Divisibility rules are a set of very useful specific rules which help users to determine the divisibility of a given number. The divisibility rules are developed to find if a number is divisible for numbers 2 to 20. In mathematics, divisibility rules are very useful and it makes the process faster by avoiding the actual division process.

How do divisibility rules work?

Divisibility rules examine the digits of the given number without performing the actual division. In the following section, we will explore more about the divisibility rules.

Divisibility Rule for 2

A given number will be divisible by 2 if the number is an even number. Even numbers are identified as numbers whose last digit is 0, 2, 4, 6, or 8. So, if the one’s position number is any of the above-mentioned numbers it will be divisible by 2. This rule is called the divisibility rule for 2.

Example: Let’s apply the divisibility rule for 2 for the numbers 456238 and 4789213. The last digit of 456238 is 8. So, it is divisible by 2. Whereas the last digit of 4789213 is 3. Hence, it is not divisible by 2.

Divisibility Rule for 3

A given number will be divisible by 3 only if the sum of all the digits is divisible by 3. This is called the divisibility rule for 3.

Example: We will check if the number 123456 is divisible by 3. The sum of all the digits is 1+2+3+4+5+6=21. This sum 21 is divisible by 3. Hence, the number 123456 is divisible by 3. Again, the number 1234561 is not divisible by 3 as the total sum of the digits 1+2+3+4+5+6+1=22 is not divisible by 3.

Divisibility Rule for 4

A number will be divisible by 4 if the last two digits of the number are divisible by 4 or the last two-digit are 00.

Example: Let’s apply the divisibility rule of 4 to find if the numbers 1234900 and 9763446 are divisible by 4. The last two digits of 1234900 are 00. So, it is divisible by 4. On the other hand, the last two digits of 9763446 are 46 which is not divisible by 4. Hence, the number 9763446 is not divisible by 4.

Divisibility Rule for 5

A given number will be divisible by 5 if it has either 0 or 5 as its last digit (one’s place).

Example: As per the divisibility rule of 5, the number 9876453215 is divisible by 5 as it has 5 in its one’s position; whereas, the number 5678909862 is not divisible as the last digit is 2.

Divisibility Rule for 6

A number will be divisible by 6 when the number is even and it is divisible by 3. Means to be divisible by 6, the number must have to be individually divisible by 2 as well as 3.

Example: By applying the divisibility rule on 11136, we can find that the number 11136 is even means divisible by 2 and the sum of numbers (12) is divisible by 3 which means the number 11136 will be divisible by 6.

Divisibility rule for 7

The divisibility rule of 7 is not straight forward similar to the above rules. The divisibility rule for 7 is a bit tricky and we will explain the same in the following steps:

  • Step 1: Find the last digit of the given number and double it.
  • Step 2: Subtract the number (double that you just got) from the remaining of the numbers.
  • Step 3: If the result of step 2 is either 0 or multiples of 7, then it will be divisible by 7.

Example: Now will apply the divisibility rule of 7 on the number 3969.

  • Step 1: The double of the last digit is 2*9=18
  • Step 2: The number formed by the remaining digits is: 396. So we will subtract 18 from it. We get 396-18=378.
  • Step 3: The number 378 is a multiple of 7 (5*47). Hence the number 3969 is divisible by 7.

Divisibility rule for 8

A given number will be divisible by 8 if the last 3 digits of the number are divisible by 8.

Example: When applying the divisibility rule of 8 on the number 2345048, we can find that the last 3 digits are 048 which is divisible by 8. Hence, the number 2345048 will be divisible by 8.

Divisibility rule for 9

The divisibility rule for 9 is similar to the divisibility rule of 3. A number will be divisible by 9 if the sum of all its digits is divisible by 9.

Example: While applying the divisibility rule of 9 on the number 111111111 we can find that the sum of digits is 9 which is divisible by 9. Hence the number 111111111 will be divisible by 9.

Divisibility rule for 10

The divisibility rule of 10 is the simplest rule you will ever know. A given number will be divisible by 10 only if it has 0 in its one’s position.

Example: The number is 123540 is divisible by 10 as it has 0 in its one’s position while the number 10005 is not divisible as it does not have a zero in its one’s position.

Divisibility rule for 11

There are various rules to decide if a given number is divisible by 11.

Rule 1: A given number will be divisible by 11 when the difference between the sum of the digits in the odd place value and even place value is 0 or a multiple of 11.

Example: Let’s check if 13574 is divisible by 11. So as per the above divisibility rule of 11, the sum of digits in odd place is 1+5+4=10 and the sum of digits in even place is 3+7=10. The difference is 10-10=0. Hence, the number 13574 is divisible by 11.

Rule 2: Add the digits in blocks of two from right to left. The result must be divisible by 11. If we apply this rule in the same example number 13574, we get 1+35+74=110 which is divisible by 11. Hence, the number is divisible by 11.

Rule 3: Subtract the last digit from the rest. The result must be divisible by 11. For example, in number 13574, we get 1357-4=1353, Again we can apply the same rule for 1353 and we get 135-3=132 which is divisible by 11 (11*12). Otherwise, we can apply the same rule again on 132 and we get 13-2=11. So, the number 13574 is divisible by 11.

Divisibility rule for 12

A given number will be divisible by 12 if the number is divisible by both 3 and 4.
Example: For example, the number 1476 is divisible by 12 as it is divisible by 3 (as the sum of digits is divisible by 3=18/3=6) and by 4 (as the last two digits are divisible by 3 76/4=19).

There is one more rule for the divisibility of 12. Subtract the last digit from the twice value of the remaining. If the result is divisible by 12, it will be divisible by 12. If we apply this rule in the above example we get 2147-6=288. Again applying the same rule in 288, we get 228-8=48 which is divisible by 12. Hence, this rule also certifies that the number 1476 is divisible by 12.

Divisibility rule for 13

A given number will be divisible by 13 if the number formed by subtracting 9 times of the last digit from the remaining is divisible by 13.

Example: Let’s check if the number 1469 is divisible by 13 using the above rule. 146-9*9=65 which is divisible by 13. Hence, the number 1469 is divisible by 13.

There is one more rule for divisibility of 13. A number is divisible by 13 if adding 4 times the last digit to the remaining is divisible by 13. Applying this rule in the number 1469 we get, 146+36=182. Reapplying the same rule on 182 we get 18+8=26 which is divisible by 13. hence, it is proved that the number 1469 is divisible by 13.

Divisibility rule for 14

There are two divisibility rules for 14. They are

  • Rule 1: A given number will be divisible by 14 if the number is even and divisible by 7.
  • Rule 2: A number is divisible by 14 if the result obtained after adding the last two digits with twice of the remaining is divisible by 14.

Example: Let’s check if 2744 is divisible by 14. As per the first rule, 2744 is even and divisible by 7 (7*392). So, it is divisible by 14. But this rule seems to be time-consuming as I have to perform division by 7. So, let’s apply rule 2 on this number. We get 2*27+44=98 which is divisible by 14. Hence, the number 2744 is certified to be divisible by 14.

Divisibility rule of 15

A number will be divisible by 15 if the number has 0 or 5 at the one’s position and the number is divisible by 3.

Divisibility rule of 16

A given number is divisible by 16 if the last four digits of the number are divisible by 16.

Divisibility rule of 17

There are two rules for checking the divisibility of 17.

  • Rule 1: A given number will be divisible by 17 if the number formed after subtracting 5 times the last digit from the remaining is divisible by 17.
  • Rule 2: If the number formed by subtracting the last two digits from twice of the remaining is divisible by 17, then the number will be divisible by 17.

Example: Let’s now apply the above two rules on the number 3978. Applying rule 1 we get 397-5*8=357, Applying the rule again we get 35-5*7=0. So, the number 3878 is divisible by 17.

Now, Applying rule 2 we get, 2*39-78=0. Hence, the number is divisible by 17.

Divisibility rule of 18

If a given number is even and is divisible by 9, it will be divisible by 18.

Divisibility rule of 19

A given number will be divisible by 19 if

  1. After adding twice of the last digit to the rest is divisible by 19 or
  2. The result after adding 4 times the last two digits to the remaining is divisible by 19.

Divisibility rule of 20

A number is divisible by 20 if the last two digits are divisible by 20.

4 Amazing Tips That Makes the Math Fun

It is a fact that many students worldwide are scared of mathematics. But it is also the fact that there are many fans of this subject too. That is why we witnessed several mathematical formulas and calculation methods developed by mathematical scientists. Whether it is the calculation circumference of circles or the length of a line, math is involved everywhere.

So, it is an important subject to learn and acquire mathematical knowledge. However, as we mentioned, most learners find this subject challenging and are unable to score good marks in their higher studies. Thus, we brought this post highlighting a few practical tips that make Mathematics a fun-loving subject to learn. Read on.

Tricks to Make Math A Fun-Loving Subject

1. Understand the real-life application

No doubt, math is dependent on calculation. So, many of you think that there are no real-life applications of such calculation. However, the reality is different. Why so? It is because, from a grocery list to designing massive engineering structures, math has its influence everywhere. Hence, students need to understand the real-life application of this subject first.

In lower classes, you had questions like 20 fruits in one basket, 5 apples, 6 oranges, 9 bananas, and calculate the sum of apples and oranges. So, while buying fruits, follow this application and calculate appropriately to know how many fruits are you buying. In this manner, math is also applied, and you also understand the additional phenomena.

2. Art lessons to learn

Who said, drawing, sketching, and painting are only limited to art lessons? In fact, it is the best way to learn mathematics also. The research shows that the visualization of concepts is an effective medium for acquiring sophisticated knowledge. Therefore, follow the same pathway to learn mathematical concepts.

For instance, sometimes, understanding the double bar graph questions is not an easy task to learn. In that case, we recommend students draw and learn. Draw the x and y-axis, sketch the graph, and enter values. Now, prepare some imaginary questions on your own and start solving the bar graph question. Hence, you will learn the vital concept in a very short time. Also, artistic skills will help in knowledge retention for a long time.

3. Learn in a competitive environment

Striving hard to achieve something great is also an excellent way to learn. If students do not understand theoretical concepts, it is better to provide them with games, puzzles, and other interactivities that develop their interest in the subject. Besides, games and puzzles will create a competitive environment where students put their best to learn mathematical concepts.

Motivating students to learn concepts will reduce the teaching effort. Reward winners and runner-ups to boost their motivational levels. There are several online games, quizzes, and puzzles of Math questions that enhance the knowledge power of learners. As a result, there would be more participants in these activities, and it would increase the fan base of mathematics.

4. Integrate technology

Finally, technology is a daily part of the new normal. Hence, adding computers and the internet in the classroom will give exposure to students to learn something beyond bookish knowledge. Today, technology is playing a crucial role in streamlining education. Online resources like eBooks, PDFs, and video lectures grab the attention of students.

Thereby, more students will start studying maths in an engaging manner. Also, online resources are helpful for differently-abled students who are having physical challenges. In a nutshell, technology is a positive learning tool that overcomes traditional learning challenges. Hence, many institutions opted for the same.

So, these were a few tips that make math a fun-loving subject. Hopefully, you have enjoyed it!

General Knowledge Worksheet on Great Women’s of Indian History (PDF)

Indian history is full of great Indian women who broke the gender barrier and proved themselves as winners. They all worked hard and made great progress in the fields of arts, science, law, politics, etc. In this article, we will learn about some of these extraordinary Indian women who have glorified our history with their presence.

Anandibai Gopalrao Joshi

She was the first female doctor in India and the first Indian woman to receive education abroad to obtain a medical degree in the United States.

Indira Gandhi

Indira Gandhi was the first and only woman to become the Prime Minister of India. She was also known as Iron lady. Daughter of Jawaharlal Nehru Indira Gandhi was the first prime minister of India. 

Justice Anna Chandy

She was the first female judge in India.  In fact, she was one of the first female judges in the British Empire.

Kalpana Chawla

She was the first Indian woman in space and died tragically in the Space Shuttle Columbia disaster.

Mother Teresa

She dedicated her life to helping the poor and was the first woman to win the Nobel Peace Prize in 1979.

Kiran Bedi

She is the first female Indian Police Service (IPS) officer and currently, she is Lieutenant Governor of Puducherry.

Anna Rajam Malhotra

Anna Rajam Malhotra became the first woman Indian Administrative Service (IAS) officer of India. In the year 1989, She was awarded the Padma Bhushan award.

Priya Jhingan

Priya Jhingan was the first Indian woman who joined the Indian Army in 1993.

Harita Kaur Deol

Flight Lt Harita Kaur Deol was a pilot in the Indian Air Force. She was the first woman pilot in the Indian Air Force to fly solo in 1994. She died in an air crash in Andhra Pradesh. 

Bachendri Pal

Bachendri Pal is the first Indian woman mountaineer who reached the summit of Mount Everest. She was awarded the fourth highest civilian award Padma Shri by the Indian Government in 1984. She was awarded the third-highest civilian award Padma Bhushan by the Government of India in 2019.      

Saina Nehwal

Saina Nehwal became the first Indian to win a medal in Badminton at Olympics in 2012. She became the first Indian woman to become number 1 in the world ranking in 2015. Nehwal is the first Indian badminton player to have won an Olympic medal and the first Indian to win two singles gold medals (2010 and 2018) in Commonwealth Games.                                                                                                                                           

Arunima Sinha

She is an Indian mountain climber and sportswoman. She is a seven-time Indian volleyball player. She is the world’s first female amputee who climb Mount Everest in the year 2013. She is the first female amputee to climb Mount Vinson, the highest peak of Antarctica. In 2015 the govt. of India honored her the fourth highest civilian award, the Padma Shri award.

Arati Saha

Arati Saha was an Indian long-distance swimmer. She was the first Indian and Asian woman who swim across the English Channel in the year 1959. Arati Saha was the first female sportsperson who received the Padma Shri award- the fourth highest civilian award in India in 1960.

Asima Chatterjee

She is the first female scientist in India, who conduct research in organic chemistry and medicinal plant.

Captain Prem Mathur

First female commercial pilot in India. She won the National Air Race in 1949. She was the first British-Indian woman pilot license holder.

Cornelia Sorabji

She is the great woman advocate in India and the first woman advocate. She is the first female who studies law at Oxford University in 1892. She was practicing low in India and Britain.

Mary Kom

The first Indian woman boxer, Mary Kom has won a medal in each of the six World Championships. In 2014, She became the first Indian female boxer who win a gold medal in the Asian Games.

Sania Mirza

Sania Mirza is the first-ever Indian woman to win a Women’s Tennis Association title in 2005. She became the first Indian woman to be ranked no.1 in WAT’s doubles rankings.

Mithali Raj

Mithali Raj is the first Indian woman cricketer. The first woman to complete 20 years in International cricket, Mithali Raj becomes the first player from India to score 2000 runs in T20-s. She is the highest run-scorer in women’s international cricket. She was awarded the Arjuna Award in 2003 and the Padma Shri in 2005.

Sushmita Sen

Sushmita Sen is the first Indian woman to win Miss Universe in 1994 at the age of 18. She is an Indian actress and model.

Santosh Yadav

She is an Indian mountaineer and the first woman to climb Mount Everest twice in 1992,1993.

Arundhati Roy

She is the first Indian author to win the Booker Prize for her book The God of Small Things.

Kiran Mazumdar Shaw

Kiran Mazumdar Shaw is an Indian billionaire entrepreneur. Popularly known as an Indian biotech queen, Kiran Mazumdar Shaw is listed as the 65th most powerful woman in the world by Forbes.

Karnam Malleshwari

Malleswari is the first Indian woman weightlifter to win an Olympic medal. She was a two-time weightlifting world champion with 29 international medals, including 11 gold medals. She received the Rajiv Gandhi Khel Ratna and in 1999 she received the Padma Shri award.

General Knowledge Worksheet on Great Women’s of Indian History

Q1. Choose the answer to the following questions.

  1. 1.Who is the first Woman Prime Minister of India?
    a. Sarojini Naidu
    b. Mrs. Indira Gandhi
    c. Rekha Sain
  2. Who is the first woman governor of a state?
    a. Sarojini Naidu
    b. Rajia Sultana
    c. Lakshmi Devi
  3. Who is the first woman to swim across the English channel?
    a. Sushmita Sen
    b. Leila Seth
    c. Arti Shah
  4. Who is the first woman to climb Mount Everest?
    a. Kiran Bedi
    b. Anna Chandi
    c. Bachenndri Pal
  5. Who is the first woman IAS officer?
    a. Anna Chandi
    b. Anna Malhotra
    c. Ujwala Rai
  6. Who is the first woman IPS officer?
    a. Anna Chandi
    b. Kiran Bedi
    c. Leila Seth
  7. Who is the first woman Advocate?
    a. Cornelia Sarabjit
    b. Fatima Beevi
    c. Kadambini Ganguli
  8. Who is the first woman weightlifter?
    a. Saina Nehwal
    b. Karnam Malleswari
    c. Sania Mirza

Q2. Fill in the blanks to complete the below statements.

  1. _____________ is the first woman cricketer.
  2. _____________ is the first woman miss Universe in 1994.
  3. _____________ is the first woman Scientist.
  4. _____________ is the first woman badminton player.
  5. ______________is the first woman President.
  6. ______________ is the first Miss India.
  7. ______________ was the first women musician to get Bharat Ratna.
  8. ______________ was the first Indian woman who reached space.
  9. ______________ was the first women to win Dadhasaheb phalke award

Answers to the above Questions:

A1: 1-b, 2-a, 3-c, 4-c, 5-b, 6-b, 7-a, 8-b

A2. 1-Mithali Raj, 2-Sushmita Sen, 3- Asima Chatterjee, 4- Shaina Nehwal, 5-Prativa patil, 6-Pramila Esther Abraham, 7-M S Subbulashmi, 8-Kalpana Chawla, 9-Devika Rani Roerich