Q: In our first example, using 9/11 and 2/4, we decided to use 44 as the common denominator. But remember, we can't just change the denominator without multiplying the numerator by the same amount as well. Here's how we turn it into an equivalent fraction:  We know 11 x 4 = 44 (this is how we found the number 44 to begin with, but you can solve 44 ÷ 11 if you forgot). Multiply both sides of the fraction by the same number to get the result: (9 x 4 ) / (11 x 4) = 36/44 Here's the second fraction in our example, 2 / 4, transformed into an equivalent fraction using 44 as the denominator:  4 x 11 = 44 (2 x 11) / (4 x 11) = 22/44. Once both fractions use the same denominator, you can add or subtract the numerators to get the answer:  Addition: 36 / 44 + 22 / 44 = (36 + 22) / 44 = 58/44  Or subtraction: 36 / 44 - 22/44 = (36 - 22) / 44 = 14 / 44 If the numerator ends up larger than the denominator, you have a fraction larger than 1 (an "improper fraction). You can make these into a mixed number, which is easier to read, by dividing the numerator by the denominator, and keeping the remainder as a fraction. For example, using the fraction 58 / 44, we get 58 ÷ 44 = 1, with remainder 14 left over. This means our final mixed number is 1 and 14/44.  If you're not sure how to divide the numbers, you can keep subtracting the bottom number from the top, writing down how many times you've subtracted. For example, convert 317 / 100 like this: 317 - 100 = 217 (subtracted 1 time). 217 - 100 = 117 (subtracted 2 times). 117 - 100 = 17 (3 times). We can't subtract any more, so the answer is 3 and 17/100. Simplifying a fraction means writing it in its smallest equivalent form, to make it easier to use. Do this by dividing the numerator and denominator by the same number. If you can find a way to simplify the answer even further, keep doing it until you can't find another. For example, to simplify 14/44:  The numbers 14 and 44 are both divisible by 2, so let's use that. (14 ÷ 2 ) / (44 ÷ 2) = 7 / 22  There are no numbers that divide evenly into both 7 and 22, so this is our final, simplified answer.
A: Change the first fraction to use the common denominator. Do the same for the second fraction. Add or subtract the numerators of the fractions to get the answer. Convert improper fractions into a mixed number. Simplify the fraction.

Article: Many graduate students have degrees in engineering or other fields. If you found your passion for physics later in life, you can still catch up and have a successful graduate school experience. You do not need to be a genius to get a PhD. Graduate school is hard work, but success depends on your dedication more than on your ability. Like undergraduate, you'll often need to take entrance exams to get into a graduate program. The GRE is the main test to take in the United States. The three primary sections of the GRE are quantitative reasoning, verbal reasoning, and analytical writing. Like the SAT and ACT, you can find any number of prep courses and prep materials for the GRE. You can also find practice tests to take online. Look into physics talks for the general public in your area or contact a physics department directly. Most places will be happy to give you information and point you to resources about graduate programs.
Question: What is a summary of what this article is about?
Don't be discouraged if you haven't focused on science earlier in your academic career. Work on your GREs. Try to meet and talk to physicists.

Q: Failure is a necessary part of the creative and learning experience. Embrace it as such, and commit yourself to learning from your failures and your mistakes. This way, you'll grow to see every failure as an opportunity for improvement and innovation rather than an obstacle or a limit on your success. Sometimes we get ideas that seem to vanish before we’ve committed them to paper. Many thoughts are seemingly random and disconnected. Try drawing a mind map on a piece of paper. Now, because you can see your ideas, you might be able to understand them and their relationships better.  List your seemingly random ideas. Pick some of your most intriguing ideas, and write them on various places on a sheet of paper. Place them according to how you think they are connected. Draw lines connecting ideas. Draw spur lines of important ideas and connect them to lesser ideas. Taking a little time to contemplate the world or to reflect on things will help expand your horizons. Spending time alone will also enable you to consider problems you’ve been trying to work through and find new solutions that you might not have thought about before. Having an open mind will enable you to think about problems that you might not have thought about before. You’ll also be able to engage ides and ways of doing things that you were previously hesitant about.  Part of this is accepting the position that there are often many ways to solve a problem or achieve a goal. Accept that there are many ways to view the world. Then you can see that there are many ways to be creative and solve problems. Understand that you don’t know everything, and every activity is a learning experience. Consider unpopular or even “weird” ways of viewing things or solving problems. These unconventional ideas or views might just give you a creative spark. Actual creating is the best practice to train your brain for creativity. There are a number of things you can do to train your brain in this way:  Drawing. If you enjoy drawing, draw. It does not really matter if you think you're good at it. Writing. If you enjoy writing, write. Actual writing (fiction or non-fiction) is the best way to hone and develop your thoughts and your creative impulse. Build. If you enjoy building things, whether it be abstract art or basic carpentry, you should build. This will stimulate your creative juices, and you might wind up building something really cool! Try to get outside of your comfort zone and the “box” you typically function within. Think about a problem you are trying to solve in different ways. Embrace different perspectives, and maybe try to view the problem as an opportunity. For example:  If your goal is to build a fence, think about the purpose of building a fence. Then focus on what you hope to achieve by building a fence. If you’re trying to keep deer from eating your prize flowers, maybe consider other options like spraying your flowers with organic soap to deter the deer. If you’re trying to solve the problem of fuel efficiency in car, perhaps think about it as a transportation problem instead. Instead of just trying to build a more fuel efficiency engine, you can scale down the size of a car or even identify alternate modes of transportation for people. Don’t fear starting all over if you think a line of inquiry or something you’ve been working on has failed you. Just start over and re-conceptualize. Remember, being productive and creative are different. You just need to judge for yourself when you need to be creative and when you need to achieve productivity, or both.  Someone can be highly productive while not being creative at all. Creativity entails finding new ways to solve problems and making or creating things that are unique. Productivity entails producing something, but can often be done in a non-creative and workman-like way.
A:
Embrace your failures. Make a mind map that will help you visualize your thoughts. Reserve some time alone so that you can think about stuff. Dedicate yourself to having an open mind. Work with your hands and/or your head to create new things. Re-conceptualize problems. Differentiate between creativity and productivity.