INPUT ARTICLE: Article: Exercise is a very important aspect of dealing with a mood disorder, as it helps to balance your teen’s hormones.  Exercise allows the body to release more feel-good hormones, such as dopamine and endorphins. These hormones provide the body with a natural high, meaning that your teen will feel happy and energetic. What is more, mood disorders are often provoked by a poor body image, especially during the teen years, so getting enough exercise can help to solve  that aspect of the problem as well. Relaxation techniques are another important part of dealing with a mood disorder. Relaxation techniques such as yoga and meditation help to bring down anxiety levels in people of all ages, teens included  These activities normalize your heart-rate and breathing, which is very helpful because your mind and body are constantly interconnected and physical reactions such as heavy breathing and fast heart-rate can increase anxiety levels. Teens might sometimes feel a bit negative towards relaxation techniques, so make an effort to do them together. This could also be a nice way for you and your teen to bond. A healthy balanced diet will not cure your teen's mood disorder in and of itself, but it will help to give them more energy, allow them to concentrate better in school and make them feel better about themselves physically.  Make sure your teen is getting three healthy meals a day, which include a good balance of whole grains, fruits, vegetables and healthy proteins. Don't allow your teen to skip breakfast - it really is the most important meal of the day as it kick starts the metabolism and gives your teen the energy they need to face the day. Limit the amount of junk food your teen eats. Too much junk food can lead to weight gain, which can exacerbate issues with body image, particularly amongst teen girls. Junk food is also devoid of important vitamins and minerals, which could leave your teen susceptible to other healthy issues. It's very important to educate your teen about the dangers of drugs and alcohol. These substances have a more profound effect on people with disorders and can make manic or depressive episodes worse.  For example, alcohol is a depressant and can easily trigger a depressive episode in a teen who suffers from a mood disorder. Stimulant drugs like cocaine, on the other hand, may trigger a manic episode in certain people. Of course, it will be impossible for you to monitor your teen at all times, and they probably won't appreciate you checking up on them all the time. Therefore, it's important that you calmly and clearly communicate the rules regarding drugs and alcohol to your teen, then give them some space and trust that they will make the right decision. Getting enough sleep is absolutely essential for teens who suffer from mood disorders, in order to keep them emotionally balanced. Teenagers should be getting at least 8 hours sleep per night and should aim to go to bed and wake up at the same time each day.  This can be very difficult for teens who prefer to stay up late surfing the internet or talking on their phones. Therefore, it may be necessary for you to enforce a bedtime or at least remove distractions such as computers or TVs from your teen's room. Also make sure that your teen's sleeping environment is conducive to a good nights sleep - it should be dark and quiet, and maintained at a comfortable cool temperature.

SUMMARY: Encourage your teen to exercise. Get your teen to try some relaxation techniques. Help your teen to follow a healthy, balanced diet. Educate your teen about the dangers of drugs and alcohol. Make sure your teen gets enough sleep.


INPUT ARTICLE: Article: As is true of any ratio, an algebraic ratio compares two quantities, although in this case variables (letters) have been introduced into one or both terms. You will need to simplify numerical terms (as shown above) as well as any variables when finding a ratio's simplified form.  Example: 18x2:72x{\displaystyle 18x^{2}:72x} Remember that factors can be whole numbers which divide evenly into a given quantity. Look at the numerical values in both terms of the ratio. Write out all factors for both numerical terms in separate lists.  Example: To solve this problem, you will need to find the factors of 18 and 72.  The factors of 18 are: 1, 2, 3, 6, 9, 18 The factors of 72 are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 Go through both factor lists and circle, underline, or otherwise identify all of the factors shared by both lists. From this new selection of numbers, identify the highest number. This value is the greatest factor common to both of the numerical terms. Note, however, that this value represents only part of the  greatest common factor within the ratio. (We still have the variables to deal with.)  Example: Both 18 and 72 share several factors: 1, 2, 3, 6, 9, and 18. Of these factors, 18 is the greatest. You should be able to evenly divide both numerical terms by the GCF. Do so now, and write down the whole numbers that you get as a result. These numbers will be part of the final simplified ratio.  Example: Both 18 and 72 are now divided by the factor 18.  1818=1{\displaystyle {\frac {18}{18}}=1} 7218=4{\displaystyle {\frac {72}{18}}=4} Look at the variable in both terms of the ratio. If the same variable appears in both terms, it can be factored out.   If there are exponents (powers) applied to the variable in both terms, deal with them now. If the exponents are the same in both terms, they cancel each other completely. If the exponents are not the same, subtract the smaller exponent from the larger. This completely cancels the variable with the smaller exponent and leaves the other variable with a diminished exponent. Understand that by subtracting one power from the other, you are essentially dividing the larger variable amount by the smaller one.  Example: When examined separately, the ratio of variables was:  x2:x{\displaystyle x^{2}:x}  You can factor out an x{\displaystyle x} from both terms. The power of the first x{\displaystyle x} is 2, and the power of the second x{\displaystyle x} is 1. As such, one x{\displaystyle x} can be factored out from both terms. The first term will be left with one x{\displaystyle x}, and the second term will be left with no x{\displaystyle x}. x(x:1){\displaystyle x(x:1)} x:1{\displaystyle x:1} Combine the GCF of the numerical values with the GCF of the variables to find the full GCF. This GCF is the term that must be factored out of both terms of the ratio.  Example: The greatest common factor in this example is 18x{\displaystyle 18x}. 18x⋅(x:4){\displaystyle 18x\cdot (x:4)} After you remove the GCF, the remaining ratio is the simplified form of the original ratio. This new ratio is proportionally equivalent to the original ratio. Note again that the two terms of the final ratio must not share any common factors (except 1).  Example: x:4{\displaystyle x:4}

SUMMARY:
Look at the ratio. Factor both terms. Find the greatest common factor. Divide both sides by the greatest common factor. Factor out the variable if possible. Note all of the greatest common factor. Write the simplified ratio.