How to Understand Fractions
Fractions are a cause of a lot of frustrations in our everyday life, whether it be at home or at work. But there are some tricks to employ to simplify the process. The first comes in understanding that a fraction simply refers to parts of a whole, for example, a fraction of the cost (a term we hear all the time) is simply a part of the whole cost.
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Instructions
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Eliminate preconceived notions of fractions. A lot of the frustration is the result of past difficulty with such calculations. If you are already frustrated to begin with, that will make it that much more difficult to work your way through the problem. Look at it this way: A fraction is simply a part of a whole when that whole is cut into pieces. If a pie is cut into six slices, and you remove one slice, that one slice is 1/6 of the total pie.
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Simplify the problem. Sometimes you just see large fractions. You can simplify almost every fraction you have using basic numbers, one through nine, and determining what number is divisible for both the numerator (the top number which designates isolated parts) and denominator (the bottom number which refers to the total number of parts). For example, 9/27 is divisible by three. If you divide both 9 and 27 by three, the result is 3/9. You can divide that by three again, resulting in 1/3.
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Identify the common denominator. If the denominators are not the same, you cannot do more complicated calculations involving fractions, such as adding and subtracting fractions. For example, you can determine the common denominator in the problem 3/4 + 2/3 by multiplying the 3 by 4 and the 4 by 3 to achieve 12. You would then multiply the numerators by 3 and 4 respectively. The result has a lowest common denominator of 12. After the multiplication has taken place, you have 9/12 + 8/12 = 17/12 or 1 and 5/12.
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Think of division as a reciprocal relationship, which is a reverse relationship. For example, 1/2 divided by 1/3, will be multiplied by the reverse of the denominator. In this case, both the numerator and denominator will be multiplied by three. The goal is to eliminate the main denominator, which will give you one fraction instead of two. When that happens, you will focus solely on the numerator. 1/2 multiplied by 1/3 will be 3/2 or 1 and 1/2.
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Simplify to make the problem easier is the bottom line. When you look at big fractions if you don't simplify the problem, it will appear a lot more overwhelming than it actually is. Think of it as a big complicated part of machinery in front of you, and you are trying to simplify it by its parts and break it down to make it more manageable. In this way, you can better visualize the process in your mind and, in turn, better see a problem simplified to, say, 2/3 as two pieces of a pie which is split into three total pieces.
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