- Posted by Bertha in Grammar |
- November 2nd, 2009 |
The form of the noun that explains in what relation the noun is standing to some other word is denoted as its Case.
There are five cases of nouns;
- The Nominative
- The Genitive
- The Accusative
- The Dative
- The Vocative
The Nominative Case: The Nominative Case names the thing or the person that suffers or performs the action expressed by a Verb; for example,
“The tiger killed a deer.” In this sentence, the verb ‘killed’ expresses action of killing and the action is performed by ‘the tiger’. So, the ‘tiger’ is in its Nominative Case.
“The baby is fed by her mother.” In this sentence, the verb ‘is fed’ expresses the action of being fed. The person suffers the action is ‘the baby’. So, the ‘baby’ is in its Nominative Case.
To find out Nominative Case in a sentence, you have to consider the verb and ask: “What or who does this?” or “what or who suffers this?” The answer to the question is the noun or pronoun in its Nominative Case.
The noun or the pronoun is the Subject of the respective sentence.
The Genitive Case: The Genitive Case stands for relationship or possession; for example,
“The lion’s mane.” “ The baby’s mother.” Who is the owner of mane? The lion. Who has relationship with the mother? The baby. So, in these sentences, “lion’s” and “baby’s” are in their Genitive Case.
The Genitive Case is generally formed by adding apostrophe s to the noun; such as,
Singular – woman’s.
Plural – women’s.
However, if the plural word ends in s, or if last syllable of a singular starts and ends in s, then the Genitive Case is generally formed by just adding apostrophe.
Singular – Moses’ Law.
Plural – horses’ back.
Points to note:
- Genitive Case is mostly used when the nouns indicate any living thing; such as,
The lion’s mane; the man’s father; the horse’s back, the kid’s toy.
However, if the noun indicates any non-living thing, then the possession is mostly expressed by preposition “of”.
“The windows of the train” ; not “the train’s windows.”
“The heat of fire” ; not “the fire’s heat.”
- Unlike other cases, Genitive Case is indicated by change in the form of a noun.
The Accusative Case: The Accusative Case indicates Direct Object; the force of Preposition or the action of Verb is always directed to that object.
“The tiger killed a deer.” The action of the Verb killed directed to which object? The answer is ‘a deer’; so, ‘deer’ is in its Accusative Case.
The Dative Case: The Dative Case always indicates Indirect Object of the Verb, if there is any.
“I gave Sam a pen.” Sam = to Sam; “Sam” is the Indirect Object in this sentence. “Book” is the Direct Object in this sentence.
The Vocative Case: The Vocative Case always indicates the individual addressed; like,
John, please come here; John is in Vocative Case
Rita, give me the book; Rita is in Vocative Case.
- 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
