Antonyms/SynonymsThe words which are opposite in meaning' to the given words are known as Antonyms and the words which are same in meaning to the given words are known as Synonyms.
Elementary Idea of TensesRead the sentences in each column and try to find the difference in these columns of same row. The words orgroup of words shown in bold letters give us an idea about the time i.e. past, present or future. Here, a short detail of tenses is given and rest you will study in higher classes.
They study science every day.
(Simple Present)
Two years ago, she studied science in U.S.A.
(Simple Past)
If you are having problems, she will help you.
(Simple Future)
She is studying science now.
(Present Continuous)
She was studying science when you called yesterday.
(Past Continuous)
She will be studying science when you will arrive tonight.
(Future Continuous)
She has studied science in several different countries.
Jumbled Sentences and WordsJumbled SentencesSentences have been divided into parts. The parts are named P, Q, R and S. Rearrange the parts P, Q, R and S to form meaningful sentences. Let us look at some examples:
Example 1
P: sings Q: she R: very S: sweetly(a) PQRS (b) QPRS(c) RQPS (d) PRSQAns. (b)She sings very sweetly.
Example 2
P: of using abusive wordsQ: in the habitR: he isS: when he speaks(a) PQRS (b) QPRS(c) RQPS (d) PRSQAns. (c)He is in the habit of using abusive words when he speaks.
Example 3
P: he is Q: everything R: careless in S: doing(a) PQRS (b) QPRS(c) RQPS (d) PRSQAns. (d)He is careless in doing everything.
Example 4
P: walk Q: carefully R: on S: road(a) PQRS (b) QPRS(c) RQPS (d) PRQSAns. (a)Walk carefully on road.Jumbled wordsIn jumbled words, the letters of the alphabet are placed randomly you are supposed to rearrange those letters to make a meaningful word.
Story ConstructionWriting a story is an art and an enjoyable task. While writing" a story you should describe the events one by one. Try to make the starting and end of story interesting. Some stories are given below, read them and learn how to make a story.ArchieAlthough it may seem impossible for Archie to exhibit a personality you will find that lie is usually saying what he shouldn't and is getting unexpected reactions from the crowd wherever he goes. Nothing ever bothers Archie. He's a happy go-lucky little guy who really isn't serious about anything. His outlook is one of that's okay with me whatever it is/' If he is right about an issue, he becomes elated with himself If it is revealed that lie is wrong, that's okay too. He never gets hungry never has bills to pay never gets tired and never sleeps. You see, Archie is a puppet.He plays many roles. One day, he's a baseball player. Another day he's a South American bandit, a leader of the parade or a stock broker. Sometimes, he's a teacher, trying to teach what he doesn't know. Other times, he's a student, trying not to be taught. He seldom gets his facts straight or understands how to conduct himself. Most of what he says has little or no value. But, he doesn't care. Archie is an entertainer. He just has fun and helps others to do the same. He gives a thrill to small kids and entertains adults of all ages. He has a lot of help though. His help comes from those whom he entertains. From time to time, it's good to stop for a while and just relax with a little bit of fun and laughter. That's what Archie is all about.As you continue to read, you will see how Archie's antics in entertainment came to be and the positive and wholesome affects that the reading of good short stories can have on the entire family.A Smart BlondOne afternoon, a beautiful, young blond lady entered a major bank in New York City and asked for a loan of $5,000. When asked why she wanted the money, she explained that she needed the money for a trip to Europe. She would be in Europe for no more than two weeks. The bank manager explained that the young lady would need something of value to be used as collateral to secure the loan.The lady pointed out of the window at a car. She asked, "Will that new Rolls Royce be sufficient?" "Well, of more...
Essay ConstructionA Scene in an Examination HallExamination is a terror and a curse. It is a very dreadful experience one goes through. Great scholars have said: "We have been examiners as well as examinees. We can well understand how terrible an examination is/ Even Jesus Christ said, "Let no one be put to test.The fear of examination mars the charms of students life. Life in itself is a huge test and we are always put to trial in one form or the other. No one is spared and I was no exception.I was in the examination hall and English paper was before me. The very first and second questions made me nervous. I raised my head and saw all were tensed. There was pin-drop silence in the hall. Then all of us started attempting the paper somehow. Those who had been working hard were doing the paper well and calmly. Those who had been cramming were heaving deep sighs. The clever among them were looking for an opportunity to cheat and copy.I have heard the teachers are supposed to be impartial and honest but I found that those who had been posted to prevent the candidates from using unfair means, were themselves becoming a part of it. Such things will make coming generations educated illiterates and I doubt how our coming generations, can progress when both the teachers and the taught were taking to unfair means.Soon the time of examination was over. The bell rang and the teachers started collecting the answer sheets. One could see joy on the faces of those who had attempted the paper brilliantly but sorrow on the faces of those who had not studied and failed to attempt the paper properly.The Children's DayOur first Prime Minister Shri Jawaharlal Nehru or Chacha Nehru was very fond of children. His birthday falls on 14th November. So in his memory his birthday is celebrated as Children's Day. On this day, the schools and colleges remain closed, so that the children can enjoy this day to the fullest.Chacha Nehru adored children, he himself used to become a child while playing with them. Pandit Nehru used to set free white pigeons on his birthday: The number of pigeon depended on the age of Pandit Nehru. He used to set them free in the football stadium where the school children used to organize songs and dances in his honour.Now-a-days this day is mostly celebrated in schools too. On this day usually the principal of the school distributes sweets to the children. The cultural activities are also organized in schools on this day the significance of this day more...
CompositionLetterLetter writing is a form of composition for communicating between the writer and the leader. In a letter, we express out feelings and ideas to another person who is away from us Letters are divided into two parts: 1.Formal Letters: These letters are written to businessmen, teachers, editors etc.2.Informal Letters: These letters are written to friends, family, relatives, neighbors etc. Formal LetterWrite a letter to the sub-inspector of police station reporting about the theft of your bicycle. Sender's \[\leftarrow \] B -118, Safdarjung Enclave Address New Delhi-110017 Date \[\leftarrow \] 26th December 2016 Receiver's \[\leftarrow \] Sub-Inspector of Police Address Hauz Khas Police Station New Delhi-110016 Subject \[\leftarrow \] Subject: Theft of bicycle Salutation \[\leftarrow \] Sir,Introduction \[\leftarrow \] I study in Hauz Khas Public School. I would like to inform you about the theft of my bicycle which is missing from the school parking lot since yesterday.Main Body \[\leftarrow \] I parked it at aroid 7.3 am, also, I had locked it for safety. However, when I returned there at 3?o? clock, it was a not there. The school authorities have been reported and are looking into the matter, but I found it agreeable to vile on F.I.R as well. It was a bright green Hercules MTB with my name etched near the seat. I purchased it from Naman Brother, Green Park in July 2015.Conclusion \[\leftarrow \] I hope these detail will help you in your investigation. I will be grateful to you if you help me with the matter. Regard \[\leftarrow \] yours faithfully Name \[\leftarrow \] vinay Full name more...
Factors and
Multiples
Introduction
We have studied
about the operations on numbers, in this chapter, we will study two important
terms, that is, ?factors? and ?multiples?. They are related to the operations
of multiplication and division.
Factors
Factors of a number
is the number, which divides the given number completely. If a, b, c, d ?. are
factors of ?m? then ?m? will be exactly divisible by a, b, c, d?.
How to Get
Factors of a Number
To find all
possible factors of a number, we have to find all the numbers, which divide the
given number exactly.
Rules of
Divisibility
(i)The numbers which have 0, 2, 4, 6, or 8 at the unit place is divisible
by 2. Ex: 24545666, 69965654, 5484542130 are divisible by 2.
(ii)If sum of digits of a number is divisible by 3 then the number is
divisible by 3. Ex: Sum of the digits of 25441215 = 2 + 5 + 4 + 4 + 1 + 2 + 1 =
24. 24is divisible by 3, therefore, 25441215 is divisible by 3.
(iii)If the number formed by its last two digits (ones and tens) is divisible
by 4, the number is divisible by. Ex: 348568928 is divisible by 4 as 28 is the
last two digits which are divisible by 4.
(iv)If a number has the digit 0 or 5 at unit's place, the number is
divisible by 5. Ex: 5 is at the unit place in the number 544598265645,
therefore, 544598265645 is divisible by 5.
(v)If a number is divisible by 2 as well as by 3, the number is divisible
by 6. Ex: the number 6345822 is divisible by 6, since it is divisible by 2 as
well as 3 as 2 is at unit?s place and sum of the number is 6 + 3 + 4 + 5 + 8 +
2 + 2 = 30, which is divisible by 3.
(vi)If the number formed by its last three digits is divisible by 8, the
number is divisible by 8. Ex. 548602136 is divisible by 8. As the number formed
by its last three digits is 136, which Is divisible by 8.
(vii)If sum of digits of a number is divisible by 9, the number is divisible
by 9 Ex: sum of digits of 786545883 = 7 + 8 + 6 + 5 + 4 + 5 + 8 + 8 + 3 = 54
and 54 is divisible by 9. Thus 786545883 is divisible by 9.
(viii)If a number has the digit 0 at unit?s place, the number is divisible by
10 Ex: 0 is at the unit place in the number 2549896980, 2549896980 is divisible more...
Factors and Multiples
Introduction
We have studied about the operations on numbers, in this chapter, we will study two important terms, that is, 'factors' and 'multiples'. They are related to the operations of multiplication and division.
Factors
Factors of a number is the number, which divides the given number completely. If a, b, c, d ?. are factors of 'm' then 'm' will be exactly divisible by a, b, c, d?.
How to Get Factors of a Number
To find all possible factors of a number, we have to find all the numbers, which divide the given number exactly.
Rules of Divisibility
(i)The numbers which have 0, 2, 4, 6, or 8 at the unit place is divisible by 2. Ex: 24545666, 69965654, 5484542130 are divisible by 2.
(ii)If sum of digits of a number is divisible by 3 then the number is divisible by 3. Ex: Sum of the digits of 25441215 = 2 + 5 + 4 + 4 + 1 + 2 + 1 = 24. 24is divisible by 3, therefore, 25441215 is divisible by 3.
(iii)If the number formed by its last two digits (ones and tens) is divisible by 4, the number is divisible by. Ex: 348568928 is divisible by 4 as 28 is the last two digits which are divisible by 4.
(iv)If a number has the digit 0 or 5 at unit's place, the number is divisible by 5. Ex: 5 is at the unit place in the number 544598265645, therefore, 544598265645 is divisible by 5.
(v)If a number is divisible by 2 as well as by 3, the number is divisible by 6. Ex: the number 6345822 is divisible by 6, since it is divisible by 2 as well as 3 as 2 is at unit?s place and sum of the number is 6 + 3 + 4 + 5 + 8 + 2 + 2 = 30, which is divisible by 3.
(vi)If the number formed by its last three digits is divisible by 8, the number is divisible by 8. Ex. 548602136 is divisible by 8. As the number formed by its last three digits is 136, which Is divisible by 8.
(vii)If sum of digits of a number is divisible by 9, the number is divisible by 9 Ex: sum of digits of 786545883 = 7 + 8 + 6 + 5 + 4 + 5 + 8 + 8 + 3 = 54 and 54 is divisible by 9. Thus 786545883 is divisible by 9.
(viii)If a number has the digit 0 at unit?s place, the number is divisible by 10 Ex: 0 is at more...
Fractions
Fractions
Fraction is a number, which in used to represent the part of a whole. It is expressed in the form of \[\frac{P}{Q}\] where P and Q are natural numbers. The upper part of the fraction is called numerator and the lower part is denominator. For \[\frac{5}{9}\] is a fraction, where 5 is numeration and 9 is denominator.
Example:
Represent the shaded part of the figure as a fraction.
Solution:
\[\frac{1}{4}\]
Like Fraction
The fractions, which have the same denominators are called like fractions.
Example:
\[\frac{5}{17},\frac{8}{17},\frac{12}{17},\frac{19}{17}\] are like fractions
Unlike Fraction
The fractions, which do not have the same denominators, in other words, the fractions with different denominators are called unlike fractions.
Example:
\[\frac{8}{9},\frac{4}{13},\frac{9}{8},\frac{10}{12}\] are unlike fractions.
Unit Fraction
The fractions which have the numerator 1 are called unit fractions.
Example:
\[\frac{1}{3},\frac{1}{5},\frac{1}{8},\frac{1}{15}\] are unit fractions.
Proper Fraction
If the numerator of a fraction is smaller than the denominator, the fraction is called proper fraction.
Example:
\[\frac{5}{7},\frac{7}{9},\frac{4}{15},\frac{9}{16}\] are proper fractions.
Improper Fraction
If the numerator of a fraction is greater than the denominator, the fraction is called improper fraction.
Example:
\[\frac{178}{128},\frac{321}{65},\frac{712}{100}\] are improve fractions.
Mixed Fraction
Mixed fraction is the sum of a whole number and a proper fraction. Both the whole number and the fraction are written together, but the sign of the addition (+) does not appear between them.
Example:
\[4\frac{5}{7},9\frac{1}{3},7\frac{8}{12},8\frac{6}{13}\] are mixed fractions.
Equivalent Fractions
Two or more fractions are said to be equivalent fractions/ if they have the same value. In other words, when equivalent fractions are reduced into their simplest form, they give the same fraction.
Example:
The equivalent fractions of \[\frac{8}{13}\] are \[\frac{16}{26},\frac{24}{39},\frac{32}{52}.\]
Comparison of Unit Fractions
If the numerators of two fractions are same and their denominators are different, then the fractions having smaller denominator will be the greater one. To take an example, \[\frac{1}{P}\] and \[\frac{1}{Q}\] are unit fractions where P and Q are natural numbers. If Q < P then \[\frac{1}{P}<\frac{1}{Q}.\]
Example:
Compare between \[\frac{1}{13}\] and \[\frac{1}{15}.\] Which fraction is greater than other?
Solution:
\[\frac{1}{13}\]>\[\frac{1}{15}\]
Because 13 < 15, therefore \[\frac{1}{13}\]>\[\frac{1}{15}\].
Comparison of Like Fractions
Like fractions have same denominator. The fraction which more...
Operation on Fractions
Operation on the Fractions
In the previous chapter, we have studied about the fractions. In this chapter we will study operations on the fractions, like addition, subtraction, multiplication and division on fractions.
Addition of Fractions
Make the denominator of fractions same by multiplying a suitable number of the numerator and denominator of both fractions. The common denominator is the denominator of the resultant fraction and addition of numerators is the numerator of the resultant fraction.
Example
Add \[\frac{12}{16}\] and \[\frac{13}{16}.\]
Solution:
\[\frac{12}{16}\,+\,\frac{13}{16}\,=\,\frac{12+13}{16}\,=\,\frac{25}{16}\]
Example
Add \[\frac{10}{9}\] and \[\frac{9}{10}.\]
Solution:
\[\frac{10}{9}\,=\,\frac{10}{9}\,\times \,\frac{10}{10}\,=\,\frac{100}{90}\]
\[\frac{9}{10}\,=\,\frac{9}{10}\,\times \,\frac{9}{9}\,=\,\frac{81}{90}\]
Therefore, their sum = \[\frac{10}{90}\,+\,\frac{81}{90}\,=\,\frac{100+81}{90}\,=\,\frac{181}{90}\]
Subtraction of Fractions
Make the denominator of each fraction same by multiplying a suitable number to the numerator and denominator of both fractions. The common denominator is the denominator of resultant fraction and result of numerators after subtraction is the numerator of the resultant fraction.
Example
Subtract \[\frac{23}{27}\] from \[\frac{30}{27}.\]
Example
Subtract \[\frac{16}{17}\] from \[\frac{18}{19}.\]
Solution:
\[\frac{16}{17}\,=\,\frac{16\times 19}{17\times 19}\,=\,\frac{304}{323}\]
\[\frac{18}{19}\,=\,\frac{18\times 17}{19\times 17}\,=\,\frac{306}{323}\]
Therefore, difference \[=\,\frac{306}{323}\,-\,\frac{304}{323}\,=\,\frac{2}{323}\]
Multiplication of Fractions
Numerator is multiplied to numerator and denominator is multiplied to denominator on multiplication of any two fractions.
Example
Find the product of \[\frac{13}{20}\] and \[\frac{16}{19}.\]
Solution:
\[\frac{13}{20}\times \frac{16}{19}\,=\,\frac{13\times 16}{20\times 19}\,=\,\frac{208}{380}\]
Example
Find the product of \[\frac{23}{15}\] and \[\frac{175}{207}.\]
Solution:
\[\frac{23}{25}\times \frac{175}{207}\,=\,\frac{23\times 175}{25\times 207}\,=\,\frac{7}{9}\,\]
\[\{\because \,23\,\times \,9\,=\,207\,and\,25\,\times \,7\,=\,175\}\,\]
Multiplication of a fraction and a Whole number
Simply, numerator of a fraction is multiplied by a whole number and denominator remains same as the denominator of a fraction.
Example
Find the product of \[\frac{26}{15}\] and 22.
Solution:
\[\frac{26}{15}\,\times \,22\,=\,\frac{26\times 22}{15}\,=\,\frac{572}{15}\]
Example
Find the product of 25 and \[\frac{127}{140}.\]
Solution:
\[25\times \,\frac{127}{140}\,=\,\frac{25\times 127}{140}\,=\,\frac{635}{28}\]
Division of Fractions
For division of fractions, we use following steps:
Step 1: Reverse the order of divisor fraction so that denominator becomes numerator and numerator becomes denominator and put the sign of multiplication in place of division.
Step 2: Multiply numerator by numerator and denominator by denominator.
Example
Divide \[\frac{15}{28}\] by \[\frac{15}{28}\]
Solution:
\[\frac{15}{28}\,\div \,\frac{7}{3}\,=\,\frac{15}{28}\,\times \,\frac{3}{7}\,=\,\frac{45}{196}\]
Example
Divide \[\frac{20}{33}\] by \[\frac{5}{11}.\]
Solution:
\[\frac{20}{33}\,\div \,\frac{5}{11}\,=\,\frac{20}{33}\,\times \,\frac{4}{3}\]
Division of a Fraction by a Whole Number and Vice more...
Solution:
\[\frac{1}{4}\]
Like Fraction
The fractions, which have the same denominators are called like fractions.
