The problem 2 ÷ 1/2 is asking you: ”How many halves are in 2?”  The answer is 4, because each unit (1) is made up of two halves, and there are 2 units total: 2 halves/1 unit * 2 units = 4 halves.  Try thinking about this same equation in terms of cups of water: How many half cups of water are in 2 cups of water?  You could pour 2 half cups of water into each cup of water which means you are basically adding them, and you have two cups: 2 halves/1 cup * 2 cups = 4 halves. All of this means that when the fraction you are dividing by is between 0 and 1, the answer will always be larger than the original number!  This is true whether you are dividing whole numbers or fractions by a fraction. Therefore, dividing by a fraction can be accomplished by multiplying by its reciprocal.  The reciprocal of a fraction (also called its “multiplicative inverse”) is just the fraction turned upside down, so that the numerator and denominator have switched places. In a moment, we are going to divide fractions by fractions by finding the reciprocal of the second fraction and multiplying them together, but let's look at some reciprocals first:  The reciprocal of 3/4 is 4/3. The reciprocal of 7/5 is 5/7. The reciprocal of 1/2 is 2/1, or 2. In order, the steps are:  Leave the first fraction in the equation alone. Turn the division sign into a multiplication sign. Flip the second fraction over (find its reciprocal). Multiply the numerators (top numbers) of the two fractions together.  This result will be the numerator (top portion) of your answer.    Multiply the denominators (bottom numbers) of the two fractions together. The result will be the denominator of your answer. Simplify your fraction by reducing it to the simplest terms. We will begin by leaving the first fraction alone, and changing the division sign to a multiplication sign:   1/3 ÷ 2/5 = becomes: 1/3 * __ = Now we flip the second fraction (2/5) over to find its reciprocal, 5/2: 1/3 * 5/2 = Now multiply the numerators (top numbers) of the two fractions, 1*5 = 5. 1/3 * 5/2 = 5/ Now multiply the denominators (bottom numbers) of the two fractions, 3*2 = 6. We now have: 1/3 * 5/2 = 5/6  This particular fraction cannot be simplified further, so we have our answer. "Dividing fractions, as easy as pie, Flip the second fraction, then multiply. And don't forget to simplify, Before it's time to say goodbye."  Another  helpful saying that tells you what to do with each part of the equation is: “Leave Me (the first fraction), Change Me (the division symbol), Turn Me Over (the second fraction).”

Summary: Think about what dividing by a fraction means. Understand that dividing is the opposite of multiplying. Memorize the following steps for dividing a fraction by a fraction. Work through these steps on the example 1/3 ÷ 2/5. Try remembering the following rhyme to help you remember:


” The main screen of Xend’s mobile app is designed to allow users to book pickups as quickly as possible. The Book Now screen lists all your addresses, with their proper categories (e.g., Home, Business, etc.) Booking a pickup can be with just one single tap of your finger. Scroll through your addresses and select the one where you want the pickup to be. Right underneath each address are two buttons. The first one is “Book Today.” Tap this button if you want the pickup to happen today.  Do note that the cutoff time is 2PM. If you need a pickup today, you must tap this button before 2PM. Otherwise, you’ll get an error message. If you’ve made the booking in time, you will see a success message with the pickup reference number. Wait for the courier to arrive at your doorstep. Scroll through your addresses and select the one where you want the pickup to be. Right underneath each address are two buttons. The second one is “Book Tomorrow.” Tap this button if you want the pickup to happen tomorrow. You will see a success message with the pickup reference number. Wait for the courier to arrive at your doorstep. Bookings from the mobile app can only be done for pickups happening today or tomorrow. Anything other than those need to be done from Xend’s website.

Summary: Go to “Book Now. Book for today. Book for tomorrow. Book for another date.


The simplest way to find out exactly how long your top piece needs to be is to subtract 2” (5cm) from the sill length. That way, you can ensure that the rest of the trim will be proportional to the sill. A window that’s 28" (71cm) wide might therefore have a head casing that’s between 30-33” long.  It’s common for the upper casing to be about an inch (roughly 2.5cm) shorter than the sill on either side. If you’re using the same casing for the top and sides of the window, the distance that the top piece extends on either side should be equal to the width of the trim. Draw a line with a pencil to indicate the appropriate length of the top piece. Make a perpendicular cut straight across the casing. Mark the length of the top piece from the end of the casing to save yourself an unnecessary cut. For windows with a uniform trim on the top and sides, you’ll need to cut the edges of the top piece at a 45 degree angle. This can be accomplished using a miter saw. Cut the casing one one side, then turn it over and make a second cut in the opposite direction.  Before you cut your sloped casing, mark your window measurements on your trim piece. Then, cut your 45 degree angle moving away from the measurement lines on both sides of your trim. The shorter part of your head casing piece needs to match your window measurement. The edges of the finished top piece should now fit together perfectly with those of the side casing. If you don’t have access to a miter saw, you can also use a miter box and a normal handsaw to achieve a precise angle. Rather than aligning the top piece flush with the upper edge of the window opening, raise it up by ⅛” (.32cm) to leave a subtle reveal line. Fasten the head casing using finishing nails, remembering to space them out every few inches across the length of the board.  Use a level to confirm that the top piece is even before nailing it down.  The reveal line will lend the appearance of added depth to the finished window. If your side and head cases look a little misaligned, you can fix this with a long finish nail. Drive the long finish nail into the top of the side casing and into the head casing, which should straighten them.

Summary: Determine a length for the head casing. Cut the head casing. Use a miter saw to cut sloped casing. Nail down the head casing.


Whether you like to save your essays locally, on a flash drive for your computer, or through a cloud service like Google Drive, iCloud Drive, or Microsoft OneDrive, set up a filing system for your classes ahead of time. Make one folder for each of your classes and subfolders for any recurring type of assignment, like a weekly writing exercise. You can even color code your digital folders to match your real life color-coding system for even more precise organization. You can set up filters to funnel messages from your professors into individual class folders as they come in. This way, you’ll never have to dig through your email trying to find that one special email your professor sent with an important addendum or due date change. Whether it’s an orientation meeting for freshmen or a one-on-one with a teacher, it can be helpful to schedule digital reminders for one-off events that might disrupt your normal schedule. Most phones have calendar features that will remind you of an upcoming event 5 minutes, 10 minutes, or 30 minutes beforehand. Use these to help yourself keep on top of new or last-minute meetings you might forget to consult your regular calendar about.
Summary: Create a computer filing system. Set up an email filter for your different subjects. Use your smartphone to create reminders for important events.