Simplification of Rational Numbers
Simplification of Rational Numbers
Simplification of Rational Numbers:
In order to simplify rational expressions involving the sum or difference of three or more rational numbers, we may use the following steps:
Step I: Find the LCM of the denominator of all the numbers involved.
Step II: Write a rational number whose denominator is the LCM obtained in Step I and numerator is computed as follows:
Divide the LCM obtained in step I by the denominator of first rational number and get a quotient. Multiply the numerator of first rational number by this quotient. Repeat this procedure for all rational numbers. Retain the given signs of addition and subtraction between the given rational numbers and get an expression involving integers. Simplify this expression to get an integer as the numerator.
Step III: Reduce the rational number obtained in step II to the lowest form if it is not already so. This rational number so obtained is the required rational number.
Simplify: -3/4 + 9/8 - (-5)/6
Solution:
We have,
-3/4 + 9/8 - (-5)/6 = -3/4 + 9/8 + 5/6, [Since, -(-5)/6 = 5/6]
Clearly, denominators of the three rational numbers are positive. We now re-write them so that they have a common denominator equal to the LCM of the denominators.
In this case the denominators are 4, 8 and 6.
The LCM of 4, 8 and 6 is 24.
Now, -3/4 = (-3) × 6/4 × 6 = -28/24,
9/8 = 9 × 3/8 × 3 = 27/24 and
5/6 = 5 × 4/6 × 4 = 20/24
Therefore, -3/4 + 9/8 - (-5)/6
= -3/4 + 9/8 + 5/6
= -28/24 + 27/24 + 20/24
= (-28 + 27 + 20)/24
= 19/24
Thus, -3/4 + 9/8 - (-5)/6 = 19/24
What is the reciprocal of | |||
| Right Option : D | |||
| View Explanation | |||
By what rational number should | |||
| Right Option : B | |||
| View Explanation | |||
If a=7, then the value of | |||
| Right Option : C | |||
| View Explanation | |||
Students / Parents Reviews [20]
Abhyas is an institute of high repute. Yogansh has taken admission last year. It creates abilities in child to prepare for competitive exams. Students are motivated by living prizes on basis of performance in Abhyas exams. He is satisfied with institute.
Yogansh Nyasi
7thAbhyas institute is one of the best coaching institute in the vicinity of Ambala Cantt area. The teachers of the institute are well experienced and very helpful in solving the problems of the students.The good thing of the institute is that it is providing extra classes for the students who are w...
Aman Kumar Shrivastava
10thWe started with lot of hope that Abhyas will help in better understnding of complex topics of highers classes. we are not disappointed with the progress our child has made after attending Abhyas. Though need to mention that we expected a lot more. On a scale of 1-10, we would give may be 7.
Manya
8thAbout Abhyas metholodology the teachers are very nice and hardworking toward students.The Centre Head Mrs Anu Sethi is also a brilliant teacher.Abhyas has taught me how to overcome problems and has always taken my doubts and suppoeted me.
Shreya Shrivastava
8thIt has a great methodology. Students here can get analysis to their test quickly.We can learn easily through PPTs and the testing methods are good. We know that where we have to practice
Barkha Arora
10thAbhyas is good institution and a innovative institute also. It is a good platform of beginners.Due to Abhyas,he has got knoweledge about reasoning and confidence.My son has improved his vocabulary because of Abhyas.Teacher have very friendly atmosphere also.
Manish Kumar
10thIn terms of methodology I want to say that institute provides expert guidence and results oriented monitering supplements by requsite study material along with regular tests which help the students to improve their education skills.The techniques of providing education helps the students to asses...
Aman Kumar Shrivastava
10thA marvelous experience with Abhyas. I am glad to share that my ward has achieved more than enough at the Ambala ABHYAS centre. Years have passed on and more and more he has gained. May the centre flourish and develop day by day by the grace of God.
Archit Segal
7thMy experience was very good with Abhyas academy. I am studying here from 6th class and I am satisfied by its results in my life. I improved a lot here ahead of school syllabus.
Ayan Ghosh
8thAbhyas is a complete education Institute. Here extreme care is taken by teacher with the help of regular exam. Extra classes also conducted by the institute, if the student is weak.
Om Umang
10thI have spent a wonderful time in Abhyas academy. It has made my reasoning more apt, English more stronger and Maths an interesting subject for me. It has given me a habbit of self studying
Yatharthi Sharma
10thAbhyas academy is great place to learn. I have learnt a lot here they have finished my fear of not answering.It has created a habit of self studying in me.The teachers here are very supportive and helpful. Earlier my maths and science was good but now it has been much better than before.
Barkha Arora
10thAbhyas institute is one of the best coaching institute in the vicinity of Ambala cantt.The institute provides good and quality education to the students.The teachers are well experienced and are very helpful in solving the problems. The major advantages of the institute is extra classes for weak...
Shreya Shrivastava
8thIt was good as the experience because as we had come here we had been improved in a such envirnment created here.Extra is taught which is beneficial for future.
Eshan Arora
8thWhen I have not joined Abhyas Academy, my skills of solving maths problems were not clear. But, after joining it, my skills have been developed and my concepts of science and SST are very well. I also came to know about other subjects such as vedic maths and reasoning.
Sharandeep Singh
7thOne of the best institutes to develope a child interest in studies.Provides SST and English knowledge also unlike other institutes. Teachers are co operative and friendly online tests andPPT develope practical knowledge also.
Aman Kumar Shrivastava
10thUsually we see institutes offering objective based learning which usually causes a lag behind in subjective examinations which is the pattern followed by schools. I think it is really a work of planning to make us students grab the advantages of modes of examination, Objective Subjective and Onli...
Anika Saxena
8thThird consective year,my ward is in Abhyas with nice experience of admin and transport support.Educational standard of the institute recumbent at satisfactory level. One thing would live to bring in notice that last year study books was distributed after half of the session was over,though study ...
Ayan Ghosh
8thBeing a parent, I saw my daughter improvement in her studies by seeing a good result in all day to day compititive exam TMO, NSO, IEO etc and as well as studies. I have got a fruitful result from my daughter.
Prisha Gupta
8thMy experience with Abhyas academy is very good. I did not think that my every subject coming here will be so strong. The main thing is that the online tests had made me learn here more things.
