Solving Rational Expressions

Solving Rational Expressions Expressions consist of one or more than one unknown variables with different coefficients and constant numbers. Rational expression is an expression which consists of terms in the fraction form i.e. p / q form. Here q cannot equal zero. There are various mathematical operations which are used to simplify and solve the given rational expressions. Example 1: Find the solution by simplifying the expression x2/ 2 - x2 / 6? Solution: The given question is on subtracting rational expressions. This question contains adding with the same polynomial x2. The first step is to calculate the LCM of the denominators 2 and 6 which is 6. Now 1 / 2 and 1 /6 can be subtracted with the LCM of the denominators as 6. This makes the solution x2 / 2 - x2 / 6 = 3 x2 / 6 - x2 / 6 = 2x2 / 6. Hence the solution is x2 / 3. Example 2: Find the solution by simplifying the expression x / 10 + 2 x/ 5? The given question is on Adding rational expressions. This question contains adding with the same polynomial x. The first step is to calculate the LCM of the denominators 10 and 5 which is 10. Now 1/ 10 and 2 /5 can be added with the LCM of the denominators as 10. This makes the solution x / 10 + 2 x /5 = x /10 + 4 x /10 = 5 x / 10. Hence the solution is x/ 2.

College Demands Critical Thinking

College Demands Critical Thinking There are many reasons why college is different than high school; however, the main reason is the different way you will be forced to think. High school teachers preach that you will think critically in their high school courses, but most students are not fully introduced to this type of thinking until college starts. High school classes do require some critical thinking, but not nearly as much as colleges do. The entire course curriculum can be different. High school classes rely on memorizing dates, definitions and other facts. However, college challenges students to know and apply the knowledge to the professional business world or everyday life. High school classes involve a lot of tests and tedious (sometimes mindless, thoughtless homework), where as college classes usually forego the repetitive homework in place for essays and other larger projects. Colleges do have tests; however they are not as frequent, and they are usually larger exams. Some classes only have a midterm and a final. Others will have three to five tests, rather than weekly or biweekly tests or quizzes. Also, the structure of the tests will be vastly different. College tests will utilize a lot of real world examples that are applied to their corresponding definitions, rather than the actual definition. Therefore, students need to not only memorize the definition but also understand its meanings and applications. Also, college professors love to assign group activities. College professors believe these are essential to the college learning experience because people will need to work well in groups in the professional world. Also, some professors will even assign groups knowing that there will be intense problems within the groups. Its crude; however, professors get a kick out of watching students work out their differences. They believe that it is vital for students to be able to work with people whom they do not get along with. Furthermore, sometimes a group project will be the only assignment for that class, and a students entire grade will depend on that one project. Usually this project will result in a class presentation that will last the entire length of the class, which could be anywhere from 45 minutes to two hours. College professors will engineer this project to be something very similar to what a young professional would accomplish in the professional work environment. This is not true for all classes, however. There are a lot of 100 level courses where students will find themselves memorizing trivial information. However, it is rare that a student will only do so. Most of these classes will be an introduction course that students will take during their first quarter/semester at college. Also, the further students get along into college curriculum the less they will memorize. Applying knowledge is especially prevalent in the upper-level classes that will pertain directly to students respective majors. Also, many college students and professors find it necessary that students go outside the classroom and get involved in organizations. These organizations will be a great asset to any student, and they will force him/her to further apply the knowledge he/she learned in the classroom. These organizations will not force students to memorize mindless dates and figures, but it will create an opportunity for students to transcend classroom knowledge to their respective majors. This is a great way for college students to display their abilities to their prospective employers and how they can apply it. Also, this benefits underclassman immediately because they can learn beyond the introduction courses within their majors and be better prepared for the larger class projects. Also, it ameliorates resumes and portfolios, which are vital to internships and entry level jobs.

Its Not about How Hard You Study- Online Tutoring Make Study Smarter

It’s Not about How Hard You Study- Online Tutoring Make Study Smarter 0SHARESShare If you’re looking for help to achieve the expected grade in Math,  Science Online Tutoring  Sessions are the most convenient and reasonable way to achieve those goals. TutorPace.com offers online private tutorial for every subject. Students’ k-12 may avail homework help, test preparation help from these sessions. Our home schooling sessions include latest tools to make the sessions interactive and interesting. Pre assessments are conducted to show you where you should focus, and post assessments confirms that you’ve the subject is well-read. Studying for hours, running for tuitions after school actually affects brain and at times become hectic.  Students however fail to stay away from the practice because of the tough competition.   Shorter but effective study sessions are actually more effectual way to prepare for exams. Nevertheless, this process requires adequate planning ahead to have sufficient time to study so as to achieve the required grade. We are committed to provide high quality guidance to every student. We offer wide-ranging Online Tutorial Courses for students’ k-12 to give them relief from their nerve-racking routine. [starbox id=admin]

Solving Inequalities With Absolute Value

Solving Inequalities With Absolute Value Absolute value of any number whether its negative or positive represents only its positive version. Absolute value is actually the distance of the number from the center and is denoted by | |(modulus sign). Hence absolute value is never negative. Absolute value is the magnitude of the number not the sign. Absolute value equation contains the variables and numbers with the absolute value sign in it. Example 1: Solve for the variable x in the inequality | 5x | 25? Solution: Given is the equation |5x| 25. Here the unknown variable which needs to be solved for is x. First step: The absolute value gives two cases; 5x 25; 5x -25. Dividing by 5 on both sides of the given equation. (5x)/ 5 25/5; (5x)/ 5 -25/ 5. This gives x 5; x -5. Hence the solution contains two intervals x 5 and x -5. Example 2: Solve for the variable x in the inequality | 2x + 4| 24? Solution: Given is the equation |2x + 4| 24. Here the unknown variable which needs to be solved for is x. First step: The absolute value gives two cases; 2x + 4 24; 2x + 4 -24. Subtracting 4 on both sides. 2x 20; 2x -28. Dividing by 2 on both sides of the given equation, x 20/2; x -28/2. This gives x 10; x -14. Hence the solution contains two intervals x 10 and x -14.

Latin Declensions Our Memorising Tips

Latin Declensions Our Memorising Tips How to Learn the Latin Declensions ChaptersWhat Are the Latin declensions?Latin Declensions: Learn Using Multiple IntelligencesMemorizing Techniques to Learn the Latin DeclensionsLatin Declensions: Doing Exercises to Boost MemoryLatin Declensions: Study with a Private Tutor!Latin can be complicated for beginners learning the language. Latin grammar is not necessarily obvious, especially because Latin nouns can be quite problematic.In fact, all nouns correspond to a Latin declension according to their position in the sentence. Learning Latin, therefore, requires you to memorise all the Latin declensions and cases.Don't fret, Superprof is here to give you some tips to help you remember these pesky grammar rules!For the masculine or feminine parisyllabic nouns, the example used is civis, civis, m (citizen):CaseSingularPluralNominativeCivisCivesVocativeCivisCivesAccusativeCivemCivesGenitiveCivisCiviumDativeCivisCivibusAblativeCiveCivibusFor neutral parisyllabic nouns, the example is mare, maris, n (sea):CaseSingularPlural NominativeMareMariaVocativeMareMariaAccusativeMareMariaGenitiveMarisMariumDativeMariMaribusAblativeMariMaribusFor the imparisyllabic masculine or feminine nouns, the example we've used is consul, consulis, m (consul):CaseSingularPluralNominativeConsulConsulesVocativeConsulConsulesAccusativeConsulemConsulesGenitiveConsulisConsulumDativeConsuliConsulibusAblativeConsuleConsulibusFor neutral imparisyllabic nouns, the example is corpus, corporis, n (body):CaseSingularPluralNominativeCorpusCorporaVocativeCorpusCorporaAccusativeCorpusCorporaGenitiveCorporisCorporumDativeCorporiCorporibusAblativeCorporeCorporibusFor the fourth declension, masculine or feminine, we will use manus, us, f (hand) as an example:CaseSingularPluralNominativeManusManusVocativeManusManusAccusativeManumManusGenitiveManusManuumDativeManuiManibusAlbativeManuManibusFor the fourth  declension for neutral nouns, we will use cornu, us, n (horn):CaseSingularPluralNominativeCornuCornuaVocativeCornuCornuaAccusativeCornuCornua GenitiveCornusCornuumDativeCornuiCornibusAblativeCornuCornibusAs for the fifth declension, there are only feminine nouns, with the exception of dies, ei, m (day) but which is also feminine when it means the date. We will use the example of res, rei, f (thing):CaseSingularFeminineNominativeResResVocativeResResAccusativeRemResGenitiveReiRerumDativeReiRebusAblativeReRebusYou can easily find all the Latin declensions in an English-Latin dictionary like the Oxford Latin Dictionary or even online.Latin Declensions: Learn Using Multiple IntelligencesMaking a colour-coded diagram can help you remember the declensions. Source: Visual HuntThe theory of multiple intelligences was explained by the psychologist Howard Gardner in 1983 and later developed in 1993.This theory is a tool used in educational science to allow every student to flourish, to learn to how to learn and help them think differently about their education.He suggests that there are several types of intelligence:Linguistic: the ability to use language to understand others and express what we think. In terms of Latin and the declensions, it may mean we comment on what we see and express what we think of declensions to memorise them better and simplify learning,Logical-mathematical: the ability to manipulate numbers and problem solve. By making diagrams of the declensions, pupils can appropriate them and retain them better,Spatial: the ability to find one's way and establish relationships between objects in space. Making colourful drawing can allow students to make the declensions more tangible and thus memorise them more easily.These first three types of intelligence are the ones most used in schools to help students memorise an abstract topic. Each student then gradually discovers which intelligence is most effective for them.There are also other strands of intelligence described by this theory that may prove useful to some students:Intra-personal: the faithful and realistic self-representation and proper use in everyday life,Interpersonal: the ability to understand others and anticipate behaviour,Body-kinesthetic: using your body to express an idea or carry out a given physical activity,Musical: the ability to perceive and create rhythms and sounds. This can be useful when learning declensions, you'll soon see why!Naturalist: understanding your environment and having awareness of living things,Existential (spiritual): the ability to question the origin and meaning of things.Test your knowledge of Latin history and culture by identifying these 20 quotes!Sing along to the video then before you know it you'll be singing it in the shower!To learn the declensions, a father and son created their own lyrics set to the music of Get Lucky by Daft Punk:Have you tried using any familiar tunes that you've come up with yourself? If not, use well known tunes like nursery rhymes you learned as a child or even your favourite pop song to help you learn.Discover also the history and evolution of the Latin alphabet...Latin Declensions: Doing Exercises to Boost MemoryAfter you've learned the declensions and you think you know all of them by heart, test yourself with Latin exercises. You will find tons of these on the internet which will allow you to read Latin texts to enrich your Latin vocabulary, improve your Latin syntax, but most importantly, make sure you know your declensions.On the website latinedisce.net, you can browse through basic Latin-English dictionary as well as do exercises and tests to practise Latin vocabulary, the verbs and declensions.Another great resource for Latin games and quizzes is latinteach.com which is a fun learning website for all levels. Learn through flashcards, crosswords, games and puzzles to master latin grammar.Do you know about Latin's linguistic legacy?Latin Declensions: Study with a Private Tutor!Traveling to Rome? You'll be able to understand all the engravings! Source: Visual HuntIf  you get stuck and find learning Latin a real ordeal, yo u should consider taking private Latin lessons for beginners.A private teacher is there just for you and to meet your needs as a student. If your difficulties come from learning the declensions, a tutor will have a range of learning techniques to help you memorise them.Learning Latin with a private teacher is usually more motivating too. You will have goals to reach every week and you have no excuses not to do the work. Generally, you will not want to disappoint your teacher, who you can form a relationship with and who is likely to be much more interesting than your Latin teacher at school!On Superprof, there are tons of Latin teachers offering lessons for all levels, as well as thousands of other teachers in all Latin languages. They each have a different experience, from retired teachers to classical literature students to passionate mythology, ancient Greek and Latin students.A private class doesn't have to break the bank! With Superprof, Latin prices start at around fifteen pou nds. Of course, it depends on your level, your location and the teacher's experience. A beginners class will definitely cost less than a college course in Latin anyway!So, are you ready to test yourself on the Latin declensions?Now find the answers to all of your questions about the Latin language...

Useful English Expressions with the Word THING - Speak Fluent English

Useful English Expressions with the Word THING - Speak Fluent English I covered this recently in a lesson with my students. You might be interested in reading about it or  refreshing your memory about the topic. The following are useful English expressions with the word THING.THING is often a word we use when we are stuck for (cannot remember) another more appropriate  word or we do not actually know what this THING is really called. For example, you often hear Pass  me that thing over there!! or Could you pass me that thing, you know the thing for opening this  bottle! So THING has many uses and people always seem to know what we are referring to.However, THING is also used in many English expressions with real meaning. Here are some of those  uses with examples. Useful English Expressions with the Word THING A THING OF THE PASTWe use this to describe something no longer in use or that is outdated.ex. The fax  machine is a thing of the past. Who uses them today? The typewriter is a thing of the past. Everyone  uses a word processor.TO HAVE A THING FOR SOMETHING (SOMEBODY)We use this expression when we remembersomething or somebody we really liked or enjoyed or still enjoy today.ex. When I was young I had a  thing for postage stamps and I had a huge collection. As I got older I lost interest. He has a thing for  Julia Roberts the actress. He really thinks she is beautiful and watches all her movies.JUST ONE OF THOSE THINGSWhen we cannot explain something fully but know it is an issue then we often use this expression. For example, if someone is trying to explain why he likes or dislikes something without being able to give a specific reason then you will hear them say ah its just one of those things”.ex. Why do you not like going on a rollercoaster? Are you afraid? No, not really I can not  explain it. It is just one of those things. Do you not like travelling on trains? Why? Is it the noise or the movement from side to side. I don’t really know it is just one of those things.ONE THING LED TO ANOTHERWhen a series of events take place resulting in an action then we can say.one thing led to another… ex. Why are you home so late? And you are a little drunk! I know, I am sorry. I met my old school friend we got talking then had a beer. Then one thing led to another and we decided to have a few more! English Collocations with THING Enjoyed this infographic? Here’s what you can do next: THE IN- THINGFashions come and go and come again or so it seems. When something is in fashion we  say it is the in- thing! So at the moment a particular hairstyle or a particular style or design of  clothes will be the in-thing.ex. Hi how are you? Wow, I love the shoes. Where did you get them? They were my Mum’s they are the in thing these days all the 70’s clothes are back in fashion.FOR ONE THINGA very popular way to give a reason or reasons why we like or dislike someone or  something.ex. Are you going to the match on Sunday ? No, for one thing the tickets will be a crazy price and I think I have to work as well.ITS A GOOD THING THATWe use this expression in situations where we are fortunate or lucky that we did something without really thinking about it.ex. Oh dear its raining really heavy outside. Well it’s a  good thing that I brought the umbrella! It’s a good thing we left early for the airport. The traffic is  terrible there must have been an accident.Now you know most of useful Englsh expressions with the word THING. And you know what we mean when we ask you to pass that THING over there!Check out my packages of Skype English lessons. My English lessons over Skype will give you an excellent opportunity to improve your English language skills in efficient and affordable way.

Im Thankful For... - Heart Math Tutoring

Im Thankful For... - Heart Math Tutoring Im Thankful For Im Thankful For November 9, 2016 November is a month of thankfulness! Throughout the month we will be asking students what they are thankful for. Heart has much to be thankful for volunteers who spend one hour per week with students building academic skills and confidence, students who are excited to learn and schools that partner with us! Read on to hear from some of our students who were eager to share! Im thankful for my family! -3rd grade student at Billingsville Leadership Academy Im thankful forboth my Heart tutors helping me in math. That’s why my mom signed me up!” 4th grade student at Montclaire Elementary Im thankful for my teacher! -3rd grade student at Billingsville Leadership Academy Im thankful for both my Heart tutors being awesome! -Student at Montclaire Elementary

Lindsaydoeslanguages Portuguese stuff giveaway!

Lindsaydoeslanguages Portuguese stuff giveaway! Lindsaydoeslanguages is blogging about her World Cup Language Challenge and we’re reposting here to share with the entire italki Community. This blog post  originally was posted  on  Lindsaydoeslanguages.com  website. It only seems appropriate, what with my italki Language Challenge in Portuguese coming to a close ‘n all, to give away some lovely Portuguese stuff! The lucky winner will get a Teach Yourself Portuguese kit complete with 2 CDs and a book, a Collins Portuguese dictionary, and a Chambers Portuguese vocabulary book. I used these myself last summer to get to grips with enough Portuguese to take me on holiday and they are great! Fancy it? All you have to do is leave a comment with a reason to learn Portuguese and if you win, I’ll post the goodies out to you free of charge. Who knows? Your reason may even feature in my inevitable upcoming video 9 Reasons to Learn Portuguese! Leave a quick comment below for your chance to win! I’ll pick the winner at random on the 5th August. Good luck! Entry closes on August 4th at 23.59GMT. One winner will be picked at random and contacted via the e-mail linked to your Disqus profile. If you wish to be contacted via a different e-mail, please state this in your comment. I will post the goods to you from the UK so if you’re international, please be patient. I will contact the winner when I have dispatched the prize and announce the winner on the blog and/or YouTube if you give consent for me to do so. Thank you.