English Guide: Practical Tips for Better English Communication

How to make your point effectively in a meeting We understand that standing out in a meeting involving different people is very important. Everyone has their own ideas and wants to get their points across. So, getting noticed and making your point effectively is a difficult task, but not an impossible one. What you need to do is to know exactly what you want to say and say it in an effective manner. Of course, how you conduct yourself throughout the meeting is also important, because how well...
Job interview tips: How to convert your weak points into strengths? When applying for a job, the deal breaker is your resume and interview skills. With an impressive resume, you have a better chance at getting noticed and shortlisted for an interview. Then it depends on what impression you make on the interviewer during your interview, and that is what will decide your chances of landing the job. It is the responsibility of an interviewer to grill a candidate in such a way that they gauge the candidate’s strong and...
Avoid common English mistakes: How and when to use "one of", "some of" and "few of" One rule of English grammar that can confuse a new or amateur English speaker is the subject-noun difference. This shows mostly when you use phrases like ‘one of’, ‘some of’ or ‘few of’ in a sentence. If you think that all these phrases imply the same meaning, and can be used interchangeably, then that’s where you will be wrong. Knowing how to use a phrase correctly is what will help you be a flawless English speaker. Now these three phrases...
Difference between ‘how about’ and ‘what about’ and how to use it If you aren’t a native speaker, learning right English can be quite a task. The reason being, a lot of words and phrases we use are colloquial and don’t really adhere to the rules of English language. That is why the difference between how we use and understand certain phrases and why it would mean something entirely different to a native speaker. The biggest problem arises when we use certain words and phrases interchangeably. The most basic...
article thumbnail Idioms are a group of words whose meaning is different from the literal meaning.  Idioms are expression, a phrase. They have hidden meaning. For Example- “Kick the bucket”, it means to die. There are many other idioms too which are related to body. These are known as Body idioms.Some of the Body Idioms are:1. All ears:  full attentionExample- Her all ears were here when we were talking about that matter.Example- We should keep all our ears open while...
article thumbnail Most of us get confused between the usage of - I, me, mine and myself. Are you confused, what to use when? This blog will help clear your confusion.When to use I, me, mine and myself1. I and me‘I’ is used when you are referring to yourself. In this, you are the one who is performing the action.Example- I am going for the dance class with Shweta.Example- I submitted the project a little late.Me is used when someone else is going to perform a...
people waiting outside room In our busy work schedules, occasionally there arise situations where we have to keep people waiting for us. This situation, especially, when faced in an office environment, when you are busy with your work and someone requests you or your boss orders you to do something which is very urgent. So, at that time you have to speak to them politely and communicate that they have to wait for a while. These are the words which can help you.Words used to ask...
Difference between Sometimes,sometime and some time English is a language which sometimes has many confusions. There are some words with different meanings and different words with the same meanings. Example - smart, bright and intelligent or attractive, pretty and lovely. These words mean the same, right? Now we are going to look at words which are same but are used according to the situation or during a specific time.For Example -She looked around for some time.He sometimes comes here.I need sometime...
clarity Sometimes when we have a conversation with someone, we sway in our thoughts and tend to overlook what the other person just said.  This annoying situation can happen with anyone of us. But it is our duty to clarify the mistake or tell the person to repeat what he/she said. This situation can also be experienced by an employee during a meeting. In this particular blog, we would like to share some of the ways to ask for clarification. Words to be...
yes If suppose a person asks you, ‘Do you stay in Airoli?’, and if you need to say yes, you can say it in  different ways, something like, yes, you’re correct. This was just an example of how to say whether someone is right. There are some other ways or words you can use. 8 ways to say that whether someone is right 1. Yes that’s right - informal way of agreeing Example - Meena - I heard that you are shifting to Kerala? Is it? Reena- Yes that’s’...
sleeping Sleep is very important for our body. It keeps us fresh and energetic. Sometimes, when we do not get a good night’s sleep, we feel so irritated because our brain cannot function properly. And this may be a very common topic of discussion amongst our friends and parents and others too. So, here are some phrases which you can use.Phrases to discuss about sleep1. Tossing and turning: not being able to sleep properlyExample - Reena was tossing and turning...
Nice to Meet you As we all know, first impression is the last impression. Therefore, first impression should always be a positive and a good one, so that the person you are meeting feels good about you. There are some ways through which you can do this. Even in offices, when you have a meeting with your boss or with your clients there are some ways and manners which you need to follow. So, let us have look on interesting ways to say nice to meet you.Ways to say...
How to start Social Conversation in English at a party Have you ever been to a party where you do not know too many people? Or perhaps look back and recollect your first office party - where everyone around seemed to know everyone but YOU?  While some may have a natural flair for starting conversations in English with strangers or acquaintances, there are some others who feel out of place in such situations. This article shall quickly give you some valuable tips, to ensure that you can strike an...
spelling The ability to communicate our thoughts through words is a unique ability given to only one species on earth – human beings! A language allows us to express our mind and our feelings to another individual and “English” is the most universally accepted language. While we may pride ourselves on our English vocabulary skills, and believe that we rarely make mistakes in our written communication, it would still be a good idea to have a quick look at...
Reading News & articles There is no denying the fact that communication is a must for any kind of human interaction or collaborative efforts. The quality of your communication, however, be it written or spoken, depends on the strength of your vocabulary. Your ability to use the right words to convey exactly what you mean makes you a better communicator and holds you in good stead in general conversations.Here we shall look at a few tips that can help you improve your...
article thumbnail In our life, we all take decisions and make decisions on a daily basis. Some decisions are important that cannot be changed and some decisions can be changed according to the situation. There are some ways to  say that we have changed our decision. So let’s have a look:9 interesting phrases to express that you have changed your decision:1. I changed my mind: you had made a decision in past but you changed it.Example-  We decided to study...
make things happen In our life we all meet people who are little nervous, confused or who have lost hope in some or the other way. If you consider yourself as a true friend, you can help your dear ones by motivating them with your kind words. This can surely make a difference in their life.9 Phrases for motivationSo here are some phrases that you can use to motivate your dear ones.1. Give it a try: when someone is doing something for the first time but is...
extravagant Is your friend too extravagant? Did you understand the meaning of extravagant? No, right. It means a person who spends his/her money in a wasteful or careless way. There are many other words which can be used to describe a person who spends way too much money.9 words used to describe that you spend too much are:1. To splash out: to spend money on things which are not actually needed.Example- She is the one who always splashes out and then...
article thumbnail There are times when we get late for a meeting, or we miss our train or bus. These are all common situations which are faced by all. Sometimes you may get late because of your friend or because of someone else.  There is a certain way you can behave or communicate in these situations.  It is very important that you behave in a proper way so that you create a good impression of yourself on everyone.7 ways to say hurry up1. There’s no time to...
have a whale of time "This time she is going to hit the books”. Does that mean that she is going to beat a book? No, it means she is going to study hard this time. These sentences are known as idioms. Idioms are phrases which have a figurative or somewhat literal meaning They do not mean what exactly the words say. For Example- Best thing since slice bread – this means a new and a good invention. People also use idioms according to their moods like when they are...
article thumbnail Do you get confused between these words? They seem to be similar but they are used at different situations. For Example- The jeans which you bought for me yesterday from the market, is too loose. Do you think in this situation, the lose can be replaced with loose? No. So let us have a look at some more examples of the same kind and clear out our confusion between the uses of these words.Common mistakes to avoid between lose, loose, lost and...
thank you We all have certain people in our life to whom we are really thankful. It may be because they might have helped us or have been there when we needed their support.To show our courtesy, we must thank them in a good way. People give chocolates, gifts etc. to show the gratitude. The simplest form of expressing gratitude is by using the kind words. So, let us have a look at some of the best ways to thank someone. 8 Interesting ways to thank someone1....
sad baby In life, there are times when we feel low and upset. This situation comes when some unexpected things happen. We all, for sure, might have faced this kind of situation at least once in our lifetime. However, these things are very common and expressing them in English is not uncommon. In this blog, you will learn about some interesting slang words to express and describe disappointment.8 slang words to describe disappointment1. Bummer or Bummer...
Jam session In today’s competitive and busy world, it is not easy to get a job in an MNC company. As there are many candidates who apply on a daily basis, it becomes difficult for the HR to conduct the interviews. Hence, they conduct various rounds and the one who clears reaches the final round. These rounds include group discussions, written tests, and a JAM session. While you might be aware of tests and group discussions, JAM can be described as a short...
pronounce words English is the only language which is spoken widely all over the world as it can be easily learnt and understood. One of the old yet easiest way to learn English is by reading newspapers, books, novels etc. You might find range of vocabularies to learn. Pick up 10 new words and learn the meaning, spelling, pronunciation etc. Unfortunately, there are many words which are pronounced incorrectly. According to a recent research almost 82% of the people...

Solving Integers


Operations on integers

We have the following operations on integers:

Let’s discuss each one of them in detail:

Addition of Integers

We have three cases under this:

  • If both integers are positive:

We will learn this by using examples :

Add: 2 + 3

As we can see that both 2 and 3 are positive, so the answer to the above problem is 5.

  • If both integers are negative :

Add: (-2) + (-3)
Here, both -2 and -3 are negative integers, so we will add 2 and 3 that is we will get 5 and in the final answer we will put a negative sign before the answer.
So the final answer is -5

  • If one integer is positive and other one negative:

Solve: 2 + (-3)
In such case, we find the difference of their absolute values and prefix the sign of the integer whose absolute value is greater.
As in the above example, absolute value of -3 is greater than 2 so we get the answer as -1

Subtraction of Integers

Subtraction is the inverse of addition. Here also we have three cases:

  • If both integers are positive:

For example: Subtract 3 from 7.
7 – 3 = 4

  • If both are negative integers:

Suppose, we want to subtract -3 from -5
We proceed like this:
-5 – (-3)
Negative of a negative integer is the corresponding positive number.
-5 + 3 = -2

  • If one is negative and other one is positive:

For example: Subtract -3 from 5
5 – (-3) = 5 + 3 = 8

Multiplication of Integers

Multiplication is repeated addition. As in addition and subtraction, in multiplication also we have three cases :

  • If both integers are positive :

When both integers are positive, we multiply their absolute values and prefix plus sign to the product.
For example: Multiply 6 by 2
6 x 2 = 12

  • If both are negative integers :

When both integers are negative, we multiply their absolute value and prefix plus sign.
For example: (-6) x (-3) = 18

  • If one is negative and other one is positive:

When one integer is positive and the other is negative, we multiply their absolute values and prefix minus sign to their product.
For example: (-12) x 3 = 36

Division of Integers

Division is the inverse of multiplication. We have two cases under division of integers :

  • Division of integers with like signs :

To divide two integers of like signs, we divide their absolute values and prefix (+) sign.
Example 1 : Divide: 10 by 5
10 ÷ 5 = 2
Example 2 : Divide (-14) by (-7)
(-14) ÷ (-7) = 2

  • Division of integers with unlike signs:

To divide two integers of opposite signs, we divide their absolute values and prefix minus (-) sign.
For example: Divide: -15 by 3
-15 ÷ 3 = -5
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