- Posted by Paula in Divisibilty Rules, Maths |
- November 2nd, 2009 |
Crack That Exam with Flying Colors- Easy To Use Divisibility Rules
What is Divisibility?
What do you understand by divisibility? Well, it is really very simple. If you divide a number by another, and the result is a whole number, the number is divisible by the other. If you divide the two numbers, and get a remainder, then that number is NOT divisible by the other. Here’s an example
Suppose you divide 8 by 2. What is the result? It is 4. Are there any remainders after the division? No. Then, 8 IS divisible by 2.
But what if I divide 8 by 3 instead? You would get 2 as a quotient and 2 as a remainder! So, 8 is NOT divisible by 3!
How Do I Find Out If A Bigger Number Is Divisible By Another?
The examples above consisted of a single number only! But what if you have a number that is like 288? Do you sit and divide them? No, you don’t. There are simple steps that can tell you if a number is divisible by another. Take a look at them:
| |
|
| 2 |
If the last digit is 0,2,4,6, or 8 |
| 3 |
If the sum of the digits is divisible by 3 |
| 4 |
If the last 2 digits are divisible by 4 |
| 5 |
If the last digit is 0 or 5 |
| 6 |
If both the divisibility rules for 2 and3 apply |
| 7 |
If you double the last digit, subtract it from the rest of the digit and get something that is either 0 or divisible by 7 itself! |
| 8 |
If the last 3 digits are divisible by 8 |
| 9 |
If you can divide the sum of the digits by 9 |
| 10 |
If the last digit is 0 |
Let us take up an example. Consider the number 150. Let us find out if it is divisible by the other numbers:
- 150 is divisible by 2 because the last digit is 0.
- 150 is divisible by 3 because when we add the digits (1+5+0), we get 6 which is divisible by 3.
- 150 is NOT divisible by 4, since the last 2 numbers i.e., 5 and 0 are not divisible by 0.
- 150 is divisible by5 because the last digit is 0
- 150 is divisible by 6 because it is divisible by both 2 and 3
- 150 is not divisible by 7 because when we double 0 we get o again. If we subtract that from 15, we get 15, which is not divisible by 7.
- 150 is not divisible by 8 because the three digits 1, 5 and 0are not divisible by 8.
- 150 is NOT divisible by 9 because the sum of the digits 1+5+0=6, which is not divisible by 9.
- 150 is divisible by 10 because the last digit is 0.
Divisibility rules are very simple. Just make sure that you practice them for at least 10 minutes every day. You will soon be the new found genius in class and your teachers will be amazed by the speed you’ve developed!
Further Tips on Divisibility:
(i) A number divisible by 2 or 5
Any number ending in 0 or an even number is divisible by 2 e.g. 12, 256, 328, 2060. If the last digit of a number is 0 or 5, that number is divisible by 5 e.g. 150, 2025, 3175.
(ii) A number divisible by 4 or 25
Any number is divisible by 4 if the last two digits are divisible by 4, e.g. 132, 5276, 208. Similarly if the last two digits of a number are divisible by 25, that number is divisible by 25, e.g. 1375, 2500.
(iii) A number divisible by 8 or 125
For a number to be divisible by 8, its last three digits must be divisible by 8, e.g. 864, 1248, 3000. Similarly numbers ending with the last three digits divisible by 125 are divisible by 125, e.g. 4250, 12375, 12000.
(iv) A number divisible by 16 or 625
A number having its last four digits divisible by 16, will be divisible by 16, e.g. 31776, 28528. Similarly numbers having their last four digits divisible by 625 are divisible by 625, e.g. 83125, 125000.
(v) A number divisible by 3 or 9
If a number is divisible by 3, the sum of the digits is divisible by 3, e.g. 38451, 285612.
In the above numbers, sum of digits 3+8+4+5+1 = 21 and 2+8+5+6+1+2 = 24, which are all divisible by 3. Hence, the numbers are divisible by 3.
In a similar manner, a number is divisible by 9, if the sum of all its digits is divisible by 9, e.g. 1548, 653229.
In the above numbers, the sum of digits = 1+5+4+8 = 18, 6+5+3+2+2+9 = 27. Hence, the numbers are divisible by 9
(vi) A number divisible by 11
A number is divisible by 11 if the difference between the sum of the digits in the even places and the sum of the digits in the odd places is either 0 or a number divisible by 11, e.g. 65274, 538472.
In 65274, difference in the sum of numbers in the odd places and the sum of numbers in the even places = (6+2+4) – (5+7) = 0
In 538472, difference in the sum of numbers in the odd places and the sum of numbers in the even places = (5+8+7) – (3+4+2) = 20 – 9 = 11, a multiple of 11.
Hence the two numbers are divisible by 11
- Posted by Bertha in Grammar |
- October 21st, 2009 |
The difference in the type of a Noun that shows whether we are talking to a female or a male is denoted as Gender.
There are four types of Genders; the Masculine Gender, the Feminine Gender, the Common Gender and the Neuter Gender.
- Masculine Gender: Names of the males are of the Masculine Gender, such as man, hero, actor etc.
- Feminine Gender: Names of the females are of the Feminine Gender; such as woman, heroine, actress etc.
- Common Gender: Names that can be given either to a female or to a male are of the Common Gender; such as child, parent, student etc.
- Neuter Gender: Things with no life can’t be either female or male; so, names of those things are of the Neuter Gender; such as chair, table, book etc.
There are three different methods to distinguish the Feminine Noun from the Masculine Noun;
1) By a change of the word
2) By a change of the ending
3) By adding a word after or before.
Masculine – Feminine
Husband – Wife
Nephew – Niece
Brother – Sister
Cock – Hen
Wizard – Witch
Son – Daughter
King – Queen
Gentleman – Lady
Boy – Girl
Bull – Cow
- By a change of the ending
Masculine – Feminine
Author – Authoress
Lad – Lass
Hero – Heroine
Widow – Widower
Master – Mistress
God – Goddess
Duke – Duchess
Lion – Lioness
Shepherd – Shepherdess
Patron – Patroness
- By adding a word after or before
Masculine – Feminine
Land-lord – Land-lady
Grandpa – Grandma
Pea-cock – Pea-hen
Bride-groom – Bride
Man-servant – Maid-servant
He-goat – She-goat
Examples of Nouns in Common Gender
Singer – male or female
Parent – father or mother
Cat – male or female
Teacher – master or mistress
Deer – stag or hind
Bird- cock or hen
Cub – male or female
Fish – milter or spawner
Pupil – male or female
Servant – man or maid
Enemy (or friend) – male or female enemy (or friend)
Orphan – boy or girl whose parents are dead
Infant or baby – male or female infant or baby
- Posted by Paula in Maths |
- October 17th, 2009 |
Are you constantly confused by those divisibility questions? Do multiplication and tables leave you cold? Steady on. Mathematics can be fun too, once you realize the magic hidden behind those numbers. If you have always found the subject unfriendly, let us teach you a trick or two that will really impress you. Ready or not? Here we go…
• Let us go through a little tip about divisibility. Have you looked at a long number and wondered whether it was divisible by 4? There is an easy way of finding it out.
1. Just take the last digit in the number and
2. Add it to two times the second last number. You have the answer!
3. Let’s take up an example:
Take the number 212334436. Is it divisible by 4? Let’s see. Take the last digit in the number i.e. 6 and add it to twice the second last number i.e. 3. Then, 6+ (2X3) =12. Find out if this is divisible by 4. In the example above, it is. Therefore the number 212334436 IS divisible by 4!
4. You can even use this tiny trick to find out whether a particular year is a leap year or not. Try it out yourself, right now! We TOLD you it’s fun!
• Let’s try out another fun trick! Have you always been confused by the relation between kilos and pounds? There is a simple way out. Suppose you are trying to convert kilos into pounds. How would you go about it in the shortest manner possible? It’s simple.
1. Just double the kilos and add a decimal point to the answer.
2. Then, just add the two together.
3. Let’s take another example:
For instance, when you try to convert 86 kilos, just double it. That will give you 172. Now, add a decimal point to 172, (or just divide it by 10). That gives you 17.2. Now add the two numbers, i.e. 172 and 17.2. The result is 189.2. So, 86 kilos would give you 189.2 pounds. Ridiculously simple, isn’t it?
• Finally, a useful trick that will help you in temperature conversions! Here is an easy way to convert Fahrenheit to centigrade and vice versa. You’ve got to try this out!
1. When you are converting Fahrenheit to centigrade, just take away 30 from it and then divide by 2. You have your answer in a jiffy.
Want an example? Try this:
74 degree Fahrenheit -30=44. Divide this by 2 and you have 22. So, 74 degree is 22 degree centigrade.
2. If you want to convert a temperature from centigrade to Fahrenheit, just do the reverse. Just double the number and add 2 to it. Isn’t that fun?
There are a number of shortcuts you can use to make mathematics easier and fun. The easy steps we detailed above are just some of the tricks used by experts to get that edge over others. Try out these math shortcuts today and stun everyone with your speed!
- Posted by Paula in Reading and writing skills |
- October 15th, 2009 |
So you’ve done all your homework and are gearing up for that admission to your favorite college. You have all the grades required and all the documents ready. Are you going to zip off that essay in about five minutes? Spare a thought. College essays are meant to gain an insight into you as a person. So, handle them with care. Here are a few pointers you might like to go through:
The Approach to the College Essay
• Make it unique. If you are asked to write about your favorite book or character, try to make it personalized. For instance, the college is not looking for an abstract description of the book. Highlight your favorite parts of the book and describe why you like them. This should give the examiners a good idea about you as a person, so take some care. Remember, the essay and the interview can be used to express your individuality very effectively.
• Having said that, there is no alternative to directions, so follow them carefully. Read the topic carefully and try to understand what the college essay is about. If an essay is about your favorite activity, its purpose is to understand what you enjoy doing when you are not studying. Focus on that and not on a narrative about your favorite team!
• Let’s take up another example. If you are asked to write about a tragedy, try and focus on your experiences about it and not on describing it in detail. The purpose of every college essay is to find out how well you write. It is not really about how tragic a life you have had!
The Layout of Your College Essay
• It is very important to think about the pattern you are going to follow when you are writing. The best way to go about it is to have an outline ready. You can even brainstorm and think about the topic at first. Focus on what you know about it. If you are not very sure, read up. There is no shortcut to anything in life, and this is no different.
• Follow directives about spacing, margins and style very carefully. If you are asked to use white paper, make sure you do that.
• Your opening sentence needs to be compelling, so pay a lot of attention to it.
• Make sure you check the essay thoroughly. Pay attention to spelling, punctuation and grammar. You could even ask a friend to read it aloud, so that you can spot problems with it.
• Your essay should always have a thesis statement, main statements and the transitions. Once you have this layout in place, your job will be much easier.
• Pay attention to details. If you are repeating words, make sure you replace them well.
A college essay is all about creating a balance between your individuality and the specifications required. Take some time out for it and give it the right attention.
- Posted by Bertha in Grammar |
- October 12th, 2009 |
There are five kinds of Nouns; 1) Proper Noun, 2) Common Noun, 3) Material Noun, 4) Collective Noun and 5) Abstract Noun.
In this lesson, we will have a brief discussion on different kinds of nouns.
1) Proper Noun: When the noun denotes one specific thing, place, or person as distinct from all others, it is called Proper Noun; like, John (name of a person), London (name of a place), and Bible (name of a book).
N.B. – A Proper Noun should always be commenced with capital letter.
2) Common Noun: When the noun does not denote any particular person or thing; and is common to all things or persons of the same class, it is called Common Noun; like, ‘man’, ‘city’, ‘book’.
Here, ‘man’ denotes any and every man. ‘City’ denotes all the cities in this world and ‘book’ points out all books.
N.B. – Sometimes, a Proper Noun acts as a Common Noun, when it’s used in a general sense; like,
He is the Einstein (= the greatest mathematician) of this century.
3) Material Noun: A Material Noun denotes a substance or a matter of which a thing is made; like,
Air is lighter then water.
Fish is a good food.
Cow eats grass.
Rice is a staple food.
Fire burns.
Book is made of paper.
We write with ink.
All the italics words are examples of Material Noun.
N.B. – According to the sense, the same word can be used as a Common Noun or a Material Noun.
a) “Cow gives milk”. In this sentence, ‘milk’ is represented as a Common Noun.
b) “Milk is a balanced food”. In this sentence, ‘milk’ is a Material Noun.
4) Collective Noun: When the noun denotes a group or a collection of objects, considered as single complete whole, it is called Collective Noun. These objects can be animals, emotions, people, concepts, inanimate things or other things. For example;
A hive of bees; there can be millions of bees, but only one hive. In this sentence, ‘bees’ is the Common Noun that denotes all bees, but hive is a Collective Noun; since it stands for all bees in it and not for any particular bee.
5) Abstract Noun: When the noun denotes some state, action or quality apart from anything having quality, etc. Abstract nouns can’t be touched, smelt, heard, tasted or seen; like,
We know that milk is white. We also know that tooth is white. We can so talked about whiteness apart from tooth or milk or anything which is white. Therefore, whiteness is the abstract noun in both the sentences.
State – hardness, bondage, poverty, etc
Action – choice, laughter, sight, etc.
Quality – height, honesty, nobility, etc.
N.B. – A same word may act as an Abstract Noun or a Common Noun, as per the sense. If an Abstract Noun is used as a Common Noun, it means A) the person having the quality, or B) the thing to which the state, quality or action belongs:-
Instances of Persons
Witness – 1. Testimony or evidence (Abstract Noun)
2. The person who gives evidence (Common Noun)
Beauty – 1. The state or quality of being beautiful (Abstract Noun)
2. Who possesses beauty (Common Noun)
Instances of Things
Speech – 1. The sense of speaking (Abstract Noun)
2. The word spoken (Common Noun)
Judgment – 1. The act of judging (Abstract Noun)
2. The decision given by judge (Common Noun)
Formation of Abstract Nouns
Abstract Nouns may be formed from Common Nouns, Adjectives or Verbs.
Abstract Nouns from Common Nouns
Common Noun Abstract Noun
King Kingship
Rascal Rascality
Slave Slavery
Captain Captaincy
Agent Agency
Friend Friendship
Abstract Nouns from Adjectives
Adjective Abstract Noun
Cold Coldness
Wide Width
Sweet Sweetness
Proud Pride
Brave Bravery
Great Greatness
Abstract Nouns from Verbs
Verbs Abstract Noun
Serve Service
Please Pleasure
Protect Protection
Conceal Concealment
Expect Expectation
Free Freedom
In two ways, a Material, Abstract or Proper noun can be changed into a Common Noun; either by putting an article (“the” or “a”) before it, or by transforming it into plural number.
Proper Noun Common noun
Daniel was an educated Jew. 1. A Daniel came to decision.
2. There are hundreds of Daniels.
Abstract Noun 1. Abraham was the justice of peace.
Justice is a dignified virtue. 2. There were five justices present in the court.
Material Noun 1. I ate the mango on the table
Mango is a nutritious fruit. 2. Let me eat one of the mangoes.
- Posted by Bertha in Grammar |
- September 30th, 2009 |
A noun denotes a name to a person or a thing. There are five kinds of Noun; 1) Proper Noun, 2) Common Noun, 3) Collective Noun, 4) Material Noun, 5) Abstract Noun. However, we are not going to discuss all of them here.
1) Proper Noun – When the noun or the name is used for one particular thing or person, it is known as proper noun; like,
John is a good boy.
New York is a busy city.
John and New York, both are examples of proper noun.
2) Common Noun – When the noun or the name is common to every thing or person of same kind, it is known as common noun; like,
Tiger is a fierce animal.
Here, the noun Tiger denotes every tiger in any part of this world.
- When the common noun means only one person or one thing at a time, the common noun is in the Singular number; like, ‘goat’, ‘man’, ‘snake’ etc.
- When the common noun means more than one person or one thing, it is in the Plural number. In other words, when a common noun means several things or persons of same kind at a time, it is in Plural number; like, ‘goats’, ‘men’, ‘snakes’ etc.
N.B. – Since, a proper noun relates only one particular thing or person; it can be in the Singular number only. However, a common noun relates either one or more than one person or thing; and so, can be in both Singular number and Plural number.
Singular to Plural Conversion
1) Mostly, Plural numbers are formed by adding ’s’ to the Singular number; like,
Singular Plural
Boy Boys
Snake Snakes
Cap Caps
Flea Fleas
Hut Huts
2) When the nouns end in s, sh, ss, x, or ch, the Plural number is formed by adding es to the end of the Singular number; like,
Singular Plural
Class Classes
Fish Fishes
Compass Compasses
Box Boxes
Wrench Wrenches
3) The nouns ending in ‘y’ form the Plural by adding ‘s’ (if ‘y’ has any of the vowels going before it) to the Singular; like,
Singular Plural
Monkey Monkeys
Day Days
4) Nouns ending in ‘y’ form the Plural by adding ‘es’ (if ‘y’ has any of the consonants going before it) to the Singular; like,
Singular Plural
Army Armies
Butterfly Butterflies
5) When the nouns end in fe, or f, the Plural number is normally formed by changing fe or f into ves; like,
Singular Plural
Knife Knives
Life Lives
Leaf Leaves
Wolf Wolves
Some Exceptions
- There are some nouns that form the Plural number by changing some vowels in the middle of the word; like,
Singular Plural
Foot Feet
Goose Geese
Tooth Teeth
Louse Lice
Mouse Mice
Man Men
Mailman Mailmen
- There are few nouns that form their Plural number by adding en; like,
Singular Plural
Child Children
Ox Oxen
- There are some nouns that have same form in both the Plural and Singular; like,
Singular Plural
Sheep Sheep
Fish Fish or Fishes
Swine Swine
Dozen Dozen or Dozens
Quail Quail
Elk Elk or Elks
Cod Cod or Cods
- Posted by Bertha in Grammar |
- September 24th, 2009 |
There are hundreds of thousands of words in all languages. However, all the words do not perform the same job. Some of them express ‘action’ some denote a ‘thing’; some qualify a thing and so on. These words act as building blocks of a language including English. For an example: Well, he and little Tony walk to shop quickly.
In the above-mentioned sentence, you may notice that each of the words has its own job. Each of them explains how a word is used, not what a word is. These words can be categorized in different classes or types. These classes are known as “Parts of Speech”. There are eight Parts of Speech in traditional grammar and these are:
1. Noun
2. Pronoun
3. Adjective
4. Adverb
5. Preposition
6. Verb
7. Conjunction
8. Interjection
Below, we will discuss basics of each of the Parts of Speech.
1. Noun – Noun denotes a name to some thing or person; like,
Richard saw tigers in the zoo.
Here, Richard denotes name of a person, tigers denote name of a thing (animal); and zoo denotes name of a thing (place). Richard, tigers and zoo are nouns, in this sentence.
2. Pronoun – Pronoun is the word used instead of Noun; like,
I told Richard that tigers which he saw in the zoo would do no harm to him, as they are behind bars.
Here, I is used for the speaker; he and him denote ‘Richard’; and which and they are used for tigers. All these italics words are pronouns.
3. Adjective – Adjective qualifies a noun or a pronoun; like,
A brave man killed a ferocious bear.
Here, brave expresses the quality of ‘man’, and ferocious shows the quality of the ‘bear’. So, brave and ferocious are adjectives.
4. Adverb – Adverb qualifies meaning of an Adjective, Verb or Adverb; like,
An almost white cat jumped very quickly through the window.
Here, almost qualifies the adjective ‘white’; very qualifies the adverb ‘quickly’; and quickly qualifies the verb ‘jumped’. All these italics words are adverbs.
5. Preposition – Preposition is a word that placed before noun or pronoun to show what a thing or a person has to do with another thing or person; like,
The cat is sitting on the table.
Here, without the word ‘on’, the sentence ‘The cat is sitting the table’, makes no sense. The cat might also sit under the table or above the table. What the cat has to do with the table is not known until a preposition is positioned between them.
6. Verb – Verb expresses an action. In other word, we can say that a verb is used to say something about a person or a thing; like,
The boy fell from top of a building.
Here, the word ‘fell’ denotes the action of the boy or we can say something about the boy by the word ‘fell’. ‘Fell’ is the verb in this sentence.
7. Conjunction – Conjunction is used to join one word to another; or a sentence to another; like,
Tom and his sister came to the school before I reached.
Here, the noun ‘Tom’ is joined to the noun ‘sister’ by the word ‘and’. ‘And’ is the conjunction here. Similarly, the second sentence ‘I reached’ is joined to the first sentence ‘Tom and his sister came’ by the word ‘before’. The word ‘before’ is also a conjunction.
8. Interjection – Interjection expresses feelings of the mind; like,
Oops! I missed the train.
Hurray! We have won the match.
In the first sentence, ‘Oops’ expresses the feeling of regret; and, in the second sentence, ‘Hurray’ expresses the feeling of joy. Both of them are interjections.
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