INPUT ARTICLE: Article: For example, 120 × 120 =  Count the total number of zeros on the end. (In this case, 2). Do the rest of the problem.  12 × 12 = 144 Append the number of zeros counted to the end of the number;   14400 You might then be able to use some of the techniques below.  For example: Instead of 14 × 6  break 14 down into 10 and 4, and multiply both by 6, then add them together...14 × 6 = = 6×(10 + 4) = (10 × 6) + (4 × 6) = 60 + 24 = 84. For example:  Instead of: 35 * 37 = ?  do this: 35 × (35 + 2) =  =  352 + (2 × 35) = 1225 + 70 = 1295 Using; 352 = ?  Ignoring the 5 on the end, multiple the number (3) by the next highest number (4).   3 × 4 = 12 Append 25 to the end of the number.  1225 Using 412 = ? and 392 = ?  Figure the square you already know.  402 = 1600 Decide if you need to add or subtract. You will add with a larger square and subtract with a smaller one. Add the original number that was squared to the next number to be squared.  40 + 41 = 81  40 + 39 = 79. Make the addition or subtraction.  1600 + 81 = 1,681  --->   412 = 1,681  1600 - 79 = 1,521   ---->   392 = 1,521  This only works for numbers one unit above or below the original. Using 39 × 51 = ?  Find the number that is equidistant of both numbers.  In this case, 45, which is 6 away from both numbers. Square that number.  452 = 2025 Square the distance the numbers are from the central number.  62 = 36 Subtract that number from the first square.  2025 - 36 = 1989  If you have taken algebra, the formula is expressed as:  51 × 39 = (45 + 6)×(45 - 6) = 452 -6 2( x + y )×( x - y ) = x2 - y2  For a more complete explanation, see How to How to easily solve math problems using difference of squares. Using 25 × 12 = ?  Multiply by 100 by appending two zeros to the end of the other (not 25) number.  25 × 12   1200 Divide by 4.  1200 ÷ 4 = 300  25 × 12 = 300 For more details, see How to Multiply by 25 in your head.

SUMMARY: Manage numbers ending in 0 (zero). Use the distributive property of multiplication to convert difficult to multiply numbers to easy to multiply numbers. Square numbers ending in 5 (five). Square numbers one less or more than a square you already know. Simplify multiplication by using "Difference of Squares". Multiply by 25.


INPUT ARTICLE: Article: One of the best ways to keep your liver healthy is to eat a balanced diet that is low in trans fats and fructose (as in "high fructose corn syrup").  These substances are found in many processed foods, including chips, soda, fried foods, etc., and have both been shown to contribute negatively to liver function.  Processed foods also include a host of other chemicals to maintain freshness and appearance, which your liver has to work to filter out. Your best bet for maintaining liver (and overall!) health is to minimize your consumption of prepackaged and processed foods, and prepare food from scratch using fresh ingredients whenever possible. Organic food is produced using minimal pesticides in the case of produce, and minimal or no added hormones or antibiotics, in the case of animal products.  This translates to less chemicals and additives that your liver has to filter out. It is important to note that organic foods still may contain some residual pesticides, and the jury is still out on how much of a health benefit they provide.  However, if you can afford to go organic, it certainly won't harm your liver, and you will be helping the environment, as well. A recent study published in Hepatology found that coffee drinkers, including those who drank decaf, were up to 25 percent less likely to have abnormal liver enzyme levels.  Researchers do not yet know why this is the case, but drinking coffee may be helping your liver out. Regular exercise not only helps you maintain a healthy body weight, it does good things for your liver, as well.  Studies have shown that just 150 minutes of activity per week (that’s just 1/2 an hour, five days per week) is enough to improve liver enzyme levels, and overall liver function. It can also reduce your chances of developing fatty liver disease. As if you didn't have enough reasons to quit already: numerous studies have shown that smoking drastically increases the risks of contracting both cirrhosis (scarring) of the liver, and liver cancer. Hepatitis is an inflammation of the liver that is usually caused by a virus.  There are three main types of hepatitis: A, B, and C, and all are contagious, however hepatitis C is usually only spread by sharing intravenous needles.  Vaccines are available for hepatitis A and B.  Practice good hygiene: remember to wash your hands after using the restroom or changing a baby's diaper. Hepatitis B is commonly spread through unprotected sex, so always wear a condom. Do not share drug needles with another person, or come in contact with another person's blood. Get vaccinated for hepatitis A and B.

SUMMARY:
Eat a healthy diet. Consider choosing organic foods to limit your exposure to pesticides and other chemicals. Drink coffee. Exercise regularly. Quit smoking. Protect yourself from hepatitis.