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.
Question: What is a summary of what this article is about?
Multiply the numerator and denominator by the same number. Divide the numerator and denominator by the same number.

Problem: Article: Standing against a wall, measure your total height and record it in centimeters, as this is how road bike frames are measured. Through an online search or by borrowing a chart at a road bike store, find the bike height that is associated with your total height. Use the chart to find whether you need an extra small, small, medium, large, or extra large road bike frame.  You can convert your height from inches to centimeters by multiplying it by 2.54. Road bike height charts should not be used as the only resource for sizing a road bike, but are a good starting point for the basic frame size you should be looking for. Some road bike charts are more specific, with up to 6 or 7 categories of bike frame sizes. with measuring tape. Spread your feet 8 to 10 inches (20 to 25 cm) apart, like you're on a bike. Then, place a book vertically between your legs, touching your crotch to simulate a bike seat. While holding the book in place with your hands, have a friend measure from the top of the book to the floor and record these measurements for later.  The book should be held between your upper thighs, simulating a road bike seat. If you recorded your measurement in inches, convert the measurement to centimeters by multiplying it by 2.54. You can take this measurement several times and record the average for a more accurate number. This equation will produce your ideal vertical frame size, or the seat tube, in centimeters. You will use this number to find a seat tube that fits your body. Record this number in a notebook or on your cell phone, as it is what you will be using when visiting the bike shop or measuring your current road bike.  This formula will provide you with a suggested size, but it's not a guaranteed fit. Double check your math and if you feel that you have made a mistake start over, as this number is essential to sizing a road bike. For example, if your leg inseam is 80 centimeters, your frame size will be approximately 54 centimeters. Identify the top of the seat tube, where the seat clamp holds the seat post. Find the center of the bottom bracket, which is where the axle binds to the road bike’s the crank arms. With a tape measure, record the distance between these 2 points to find the length of your seat tube. This distance should match your inseam measurement for a proper road bike frame size. This measurement is known as a C-T measurement and is used to identify the frame size. Identify the correlation between the inseam measurement and the seat tube measurement and record their correlation. The difference between these measurements should be within 2.54 centimetres (1.00 in) for a properly-sized road bike frame.  If you are buying a new road bike, choose a frame that has a seat tube measurement matching your inseam. If you are measuring your current road bike, consider purchasing a new frame if the bike’s seat tube measurement differs from your inseam.
Summary: Use your total height and a road bike sizing chart for a basic guideline. Measure your inseam Multiply your inseam measurement (in centimeters) by 0.67 for a suggested size. Measure your road bike’s seat tube. Compare your inseam measurement to the road bike’s C-T measurement.

INPUT ARTICLE: Article: Most people naturally have an overbite, which means their lips are not lined up on top of each other. Moving your jaw forward situates your bottom lip directly under your top lip. Be sure not to push your jaw too far forward. The right spot aligns your top and bottom teeth straight up and down.  Practice moving your jaw forward and backward while you buzz your lips to hear how this affects the buzz. You can also feel how it directs the airflow either down to your chin or up to your nose. Aligning your teeth directs the airflow straight forward into the mouthpiece for maximum airflow. Do not clamp your teeth together as this will hinder the airflow. Your teeth should be at least ¼” (6 mm) and at most ½” (12 mm) apart. Your jaw should feel like it is hanging loosely. Get the feel for this placement by putting the narrow end of the mouthpiece between your teeth. You can also use a pen or pencil, or a straw, which can help you test your airflow. Proper embouchure allows just the right amount of air to pass through your lips. If your tongue is on the roof of your mouth or moving around your mouth, it will block the airflow. Your tongue will move and tap your lips as you play the notes, but when you aren't tonguing notes, it should rest low in your mouth.

SUMMARY: Push your jaw forward to line up your lips. Leave about ¼” (6 mm) between your teeth. Keep your tongue low in your mouth.

A pixie cut can provide short straight hair with a lot of volume and movement. To achieve a voluminous pixie, keep the sides cropped, the top long, and add lots of layers throughout your short locks. The pixie is a versatile haircut. You can wear it slightly tousled, slicked backed, or with edgy spikes. The classic bob and its modern variations are chic, timeless, and flattering. These haircuts are easy to style and maintain. By opting for a short to  shoulder length haircut, you will reduce the weight of your hair, increasing your ability to add volume to your locks.  The severeness of the blunt bob creates the illusion of fullness and volume. When teased, the stacked bob adds movement and volume to fine, limp hair. A lob, or long bob, is ideal for fine, thin hair—it allows you to maintain some length while getting rid of stringy ends. As straight hair grows, the ends can appear stringy and unkept. To avoid this ragged look, opt for a long, blunt cut. A blunt cut will allow you to maintain your hair’s length while creating the illusion of full, thick hair.  If you prefer a less severe look, ask your stylist to add a few face-framing layers. Too many layers will cause fine, straight hair to look thin and stringy.
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One-sentence summary --
Opt for a pixie cut. Try a bob. Cut your long hair bluntly.