Fractions with like denominators can be added or subtracted by adding or subtracting the numerators and keeping the same denominator. The resulting fraction may need to be simplified by reducing if possible or changed to a mixed number if improper.
How can I add subtract a Rational NumberSolution .pdfamitseesldh
How can I add/ subtract a Rational Number?
Solution
Simplify all problems by turning fractions into decimals and minimizing operation
symbols where possible. Then you\'re just lining everything up with the decimals and doing
simple adding or subtracting. Remember the fraction is a portion of a whole number 1. Just to
clarify, Dividing the denominator (lower part) into the numerator (top part) will give you the
fraction in decimal form. In Mixed numbers, where you have a whole number and a fraction (i.e.
1 3/4) the whole number should remain unaffected in your conversion unless the numerator is
greater than the denominator (i.e. 1 5/2) thus the fraction results in a whole number to add to the
whole for your final decimal conversion. (i.e. 1 5/2 = 1+2.5 = 3.5 Here 5 divided by 2 = 2
remainder 1 which in fraction form would be 2 1/2 and 1/2 is commonly known to be .5 so 5/2 =
2.5 to add to the 1). just sharing for future help :) 1. 24.65 2. 0.875 - 1.375 = -0.5 (If you cant
use a calculator to convert this one, 7/8 - 3/8 = 4/8 which simplifys into 1/2 and then 1/2 - 1 = -
1/2. When subtracting mixed numbers, i deal with the fraction part first, the whole numbers
second, and then i combine both. In this equation the number we were subtracting was bigger
than the one we are subtracting from and there was nothing to subtract the 1 from so there was a
-1 which i subtracted from our positive 1/2) 3. -1.5 + 1.5 = 0 (changed to \"+\" because 2
negatives = a positive) 4. -0.2 5. -0.5 - 0.75 = -1.25 (little trick here, when adding 2 negatives,
ignore the negatives, add them like they are positives, and then just put a negative sign in front of
your final answer) You should be able to convert this one into a decimal without a calculator
since these are common fractions, but in case you want to do it with them still in fraction form,
still apply my trick by temporarily ignoring the negatives and play with multiples in the
denominator so that you can convert one, or both fractions if necessary, to have the same
denominator, in this case the denominator 2 is a multiple of 4 and goes into it twice, so multiply
the top and bottom of the fraction 1/2, so 2/4+3/4 = 5/4 this can still be simplified since the
numerator is greater than the denominator, so 5/4 = 1 1/4 because 4 goes into 5 one whole time
with a remainder of 1, and then throw in the negative that we had been ignoring all along, -1 1/4.
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Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
We all have good and bad thoughts from time to time and situation to situation. We are bombarded daily with spiraling thoughts(both negative and positive) creating all-consuming feel , making us difficult to manage with associated suffering. Good thoughts are like our Mob Signal (Positive thought) amidst noise(negative thought) in the atmosphere. Negative thoughts like noise outweigh positive thoughts. These thoughts often create unwanted confusion, trouble, stress and frustration in our mind as well as chaos in our physical world. Negative thoughts are also known as “distorted thinking”.
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http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
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The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
2. Terminology Like decimals, fractions represent parts of numbers. A fraction is usually a number that is between 0 and 1. Numerator - number on top Denominator - number on bottom
3.
4. Examples 1 5 + 2 5 = 3 5 This answer cannot be reduced any further.
5. 9 14 5 14 = 4 14 The GCF of 4 and 14 is 2, so we divide by 2 to reduce. ÷ 2 = 2 7
6. 8 9 + 3 9 = 11 9 This is an improper fraction (the top is bigger than the bottom), so we want to change it to a mixed number. To do this, divide the bottom into the top. 9 11 1 9 2 Answer: 1 2 9
