Problem: Article: You should use your introduction to identify the major themes or ideas of the work and to state your reaction or reactions to these themes.  For a four to five page paper, your introduction can extend to one or two paragraphs. For a shorter paper, though, restrict it to a short paragraph made up of three to five sentences. Introduce the work by describing how the work to which you are responding fits in within the broader topic it addresses. You could also introduce the work by explaining your own beliefs or assumptions about the topic the work agrees with before explaining how the work challenges or supports your beliefs. Your response paper should not focus on a summary of the work. There is some debate as to the proper length a summary should be for this type of paper, but as a general rule, the summary should only span half of the body paragraphs if not less.  For a four to five page paper, this section should only take up about two to three paragraphs. Describe the content of the work and present the author's main arguments, especially as they affect your response. The summary should be somewhat analytical in nature instead of a strict retelling. As you present the details of the author's work and argument, you should use an analytical tone and discuss how well the author managed to get those points across. This is the point at which you must explain how you react, on an intellectual level, to the work you are responding to. You can include separate paragraphs explaining where you agree and where you disagree, or you can focus on agreement or disagreement alone, and write out as many paragraphs as needed to cover your response.  Note that this response format is best to use when you are focusing on a single major theme or argument in a work. It does not work as well if you are discussing multiple ideas presented by a work. Back up your analysis with quotes and paraphrases. Make sure that each example is properly cited. If you took the time to find textual evidence to support your responses during the prewriting stage, this portion of your paper should be fairly easy. All you really need to do is arrange your argument in a coherent manner and write in the details of the support you have already gathered. At this point, you need to restate your stance to the reader and briefly defend the significance of your stance.  Even for a four to five page paper, you only need one standard paragraph to accomplish this. For a shorter paper, make this paragraph only three to five sentences long. State how this work has a broader effect on you and to the genre or community in which it is a part.
Summary: Write your introduction. Summarize the work. Present and discuss your organizing argument. Write your conclusion.

Problem: Article: While you’re doing your thing on the floor, search the crowd for someone to dance with. Holding eye contact, smiling, and frequent touching are all strong signs that someone wants to dance. Once you’ve selected a partner, move in and prepare to get physical.  If you’re not sure whether the person is picking up on your signals, just walk right up to them and ask, “Hey, wanna dance?” Sometimes, someone may shoot you a fleeting glance or brush up against you by accident. If they spend the next few moments ignoring you or migrating to another part of the floor, don’t assume they’re playing hard to get—they’re probably just not interested. Once you’ve gotten up close and personal with your partner, time your movements to the tempo of the song. Move your hips back and forth against your partner’s. Coordinate the “upswing” of your hips to the beat to increase and decrease the pressure in turns.  Try grinding at different speeds to match whatever music is playing. You can move faster during songs that are upbeat and energetic, then slow things down with the music for a more sensual experience. Remember, grinding is a form of dancing, so the more rhythmic you make it, the more enjoyable it will be for both you and your partner. Once you’ve been dancing for a moment, try putting your hands on your partner’s hips and ask them if it’s okay. If they move your hands away, or tell you not to put your hands on them, just remove your hands. You can still dance, while moving your arms to the beat of the music. Don’t get touch them places other than their hips unless they move your hands there. You don’t want to creep out your partner! Face your partner squarely and pull your shoulders back so that your chest presses into theirs. Then, move your body away from your partner. Do this a few times and see if your partner catches on.  You can also mix up the chest bump by doing a wave motion with your upper body.  Do your best to synchronize your movements with your partner’s. Jut your hips forward to one side. As you do, your partner will pull theirs back on the same side. Keep your lower bodies locked together as you continue rolling to the opposite side, then change directions—they’ll stick their hips out and you’ll pull yours back.#*You can roll whichever way feels most comfortable, but most people will instinctively move in a clockwise direction. The circular motion of hip rolls is similar to the one you’ll use when grinding on your partner from the back.
Summary: Find a willing dance partner. Rub your hips against your partner’s with the rhythm of the music. Try putting your hands on your partner's hips. Add some light chest bumps. Work in some hip rolls to switch things up.

Problem: Article: Two fractions that are different but equivalent have, by definition, numerators and denominators that are multiples of each other. In other words, multiplying the numerator and denominator of a fraction by the same number will produce an equivalent fraction. Though the numbers in the new fraction will be different, the fractions will have the same value.  For instance, if we take the fraction 4/8 and multiply both the numerator and denominator by 2, we get (4×2)/(8×2) = 8/16. These two fractions are equivalent. (4×2)/(8×2) is essentially the same as 4/8 × 2/2 Remember that when multiplying two fractions, we multiply across, meaning numerator to numerator and denominator to denominator. Notice that 2/2 equals 1 when you carry out the division. Thus, it's easy to see why 4/8 and 8/16 are equivalent since multiplying 4/8 × (2/2) = 4/8 still. The same way it’s fair to say that 4/8 = 8/16. Any given fraction has an infinite number of equivalent fractions. You can multiply the numerator and denominator by any whole number, no matter how large or small to obtain an equivalent fraction. Like multiplication, division can also be used to find a new fraction that's equivalent to your starting fraction. Simply divide the numerator and the denominator of a fraction by the same number to obtain an equivalent fraction. There is one caveat to this process--the resulting fraction must have whole numbers in both the numerator and denominator to be valid. For instance, let's look at 4/8 again. If, instead of multiplying, we divide both the numerator and denominator by 2, we get (4 ÷ 2)/(8 ÷ 2) = 2/4. 2 and 4 are both whole numbers, so this equivalent fraction is valid.
Summary:
Multiply the numerator and denominator by the same number. Divide the numerator and denominator by the same number.