ࡱ> )` R.bjbjUUZ??q8  866LLLTVVVVVV$Uhvz]dd@zLLׅRRR|LLTRTRR~j8rL* x |mXT0$nl3^3rr 3DRzzX$ by Jason Marshall In the last article, we discovered that integers alone are not sufficient to fully describe the world around uswe need the fractions existing between the integers too. (In learning that, we also learned that fractions are not integers.) In fact, eventually were going to discover that even fractions wont fully satisfy our needs! But well leave that for a future articletheres still much to learn about the fractional world first. In particular, today were going to take a deeper look at fractions and learn a few quick tips to help you understand exactly what numerators and denominators tell you. What Are Fractions? Before we get too far into the details of what the various parts of a fraction mean, lets briefly review their anatomy. First, a fraction is made up of two integersone on the top, and one on the bottom. VN The top one is called the numerator, the bottom one is called the denominator, and these two numbers are separated by a line. The line can be horizontal or slanted they both mean the same thing and simply serve to separate the numerator from the denominator. How to Pronounce Fractions in English If youve known about fractions for a while, its probably been some time since youve contemplated the names we use to describe them. But they arent exactly obvious, so its worth spending a minute or two thinking about them. Heres the quick and dirty tip to help you remember how to pronounce them all: The numerator is always spoken first, and you pronounce it exactly as you pronounce the number. For example, in 1/2 the numerator, 1, is just pronounced one; or in 45/77 the numerator, 45, is simply pronounced forty-five. Easy enough. But denominators are a bit trickier. They use the following convention: 2 is pronounced half 3 is pronounced third 4 is pronounced fourth (or quarter) 5 is pronounced fifth 6 is pronounced sixth 7 is pronounced seventh 8 is pronounced eighth 9 is pronounced ninth 10 is pronounced tenth, and so on. So, for the fraction written 1/2, the denominator, 2, is pronounced half, and the entire fraction is therefore one-half. A little less obvious: For the fraction 45/77, the denominator, 77, is pronounced seventy-seventh, so the entire fraction is forty-five seventy-sevenths. An easy way to remember this is that with the exceptions of half and quarter, the words used to describe the denominator of a fraction are the same used to put things in orderfor example, the order in which runners finish a race: third, fourth, fifth, etc. What Is a Denominator? Now lets take a closer look at the different parts of a fraction. First, the bottom partthe denominator. The word denominator is derived from the Latin word nomen, which means name (and also shows up in words like nominate and nomenclature). And thats pretty much what the denominator of a fraction does: it names, or indicates, the type of fraction that is described by the numerator (the top part). What Does the Denominator Tell You? Heres what I mean. The denominator of a fraction tells you how many parts a whole is broken into. It can be a whole pineapple, a whole song, or a whole anything. If the denominator of a fraction is, say, 4, then that indicates that the whole whatever is broken up into 4 equally-sized pieces. VN Or, if the denominator is 12, that means the whole whatever is broken-up into 12 equally-sized pieces. But how exactly does that name the type of fraction? Well, that leads us to the meaning of the numerator What Is a Numerator and What Does It Tell You? The word numerator comes from the Latin verb enumerate, which we still use in English to mean to count. So, the numerator of a fraction counts the number of equally-sized pieces identified by the denominator that are contained in the fraction. How then do we put this all together to understand the meaning of fractions? Heres the quick and dirty tip: Going back to our examples from before, the fraction 1/2 means one piece of a whole object divided into two equally sized parts. The denominator indicates that two parts make a whole, and the numerator counts off the fact that the fraction 1/2 contains one of those parts. Similarly, the fraction 45/77 means forty-five pieces of a whole object that is divided into seventy-seven equally sized parts. What Does It Mean if the Numerator is Bigger than the Denominator? In all the examples so far, the numerator has always been smaller than the denominator. In other words, in 1/2 and 45/77, 1 and 45 are smaller than 2 and 77, respectively. But what would it mean if the numerator were bigger than the denominator? Something like 7/4? Well, lets try interpreting this the same way as before. The denominator, 4, indicates that a whole is divided into four equally sized parts, and the numerator, 7, indicates that we have seven of those parts. So, if four parts make a whole, and we have seven, then we must have a whole object plus three more of the equally sized parts. So 7/4 is equivalent to 1 3/4also known as one and three-quartersand we now know that a fraction whose numerator is greater than its denominator represents a number that is greater-than one. In case youre wondering, that type of fraction is called improper, whereas fractions like 1/2 with numerators less-than denominators are called proper. What Does It Mean if the Denominator is Less than One? So far weve only talked about fractions with denominators that are greater-than one. At the end of the last article, I asked the brain-teaser question: Why cant the denominator of a fraction be zero? To find out the answer to that question, and take a peak at how fractions with denominators less-than one work, check out last weeks Math Dude Video Extra! episode posted to YouTube and the videos section of the Math Dudes Facebook page. Wrap Up Thats all the math fun we have time for today. But before I go, heres a brain-teaser problem for you to think about until next time: How can you tell if one fraction is bigger or smaller than another? Look for my explanation in this weeks Math Dude Video Extra! episode on YouTube and Facebook. Also, throughout the month of March, were giving away one free book each week to lucky Math Dude Twitter followers and Facebook fans. So please join our growing community of social networking math fans, ask questions, and#,-------------.&.@.D..............Ր|wqgqg\gqwhyKHmHnHujhKHU hKH ho(h5PJo(h5CJPJo(h5CJOJPJo(hCJOJPJo(hjhUmHnHsHtHhcjhcUhyh[3OJQJaJU)hyhy0J1B*CJOJQJaJph333%hyhyB*CJOJQJaJph333" ~",-------------B.D..... $ 9r a$gdydT-DM [$\$gdy-. chat with other math enthusiasts. Check it out and see how you can win a free book! Until next time, this is Jason Marshall with The Math Dude s Quick and Dirty Tips to Make Math Easier. Thanks for reading, math fans!      ,TRX,_>e_f[`Ns^Swww.TingClass.net f[ ~,TR N,TRX00MQ9,TR N}0www.tingclass.net -  PAGE 1 -  ...gdy0182P. A!"#$%S Fe(ᆆ5lE/JFIFC    $.' ",#(7),01444'9=82<.342C  2!!22222222222222222222222222222222222222222222222222" }!1AQa"q2#BR$3br %&'()*456789:CDEFGHIJSTUVWXYZcdefghijstuvwxyz w!1AQaq"2B #3Rbr $4%&'()*56789:CDEFGHIJSTUVWXYZcdefghijstuvwxyz ?]m_;Sw:AWm  Q1E~TbQpoa?*]'I1Ea?*7&( ~T\,. RbQpOʍ'I1Ea?*7&( ~T\,Oʍ'F( ~T\,. 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