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Question:

roeboy
roeboy
Student
High School - 11th Grade

What changes this improper fraction, 5/3, to a mixed number?

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Posted by roeboy on Wednesday November 4, 2009 at 2:11 PM and tagged with fractions, improper fraction, math, mixed number.

Answers:

  1. ophelious
    ophelious Teacher
    Vocational

    eNotes Editor

    A "mixed number," in math terms, is a whole number with a fraction attached to it. What you have posted in your question is essentially an "improper fraction," a situation that occurs when the top number is bigger than the bottom number. In the math universe, that just 'aint right. It should be converted into a "mixed number" to make things right with the universe.

    So how do you do it?

    Okay, here we go. First, you divide 3 into 5, keeping the remainder (and not making a bunch of decimals out of it like you would in other math problems.) What you end up with, in this case, is 5/3=1 with a remainder of 2. The whole number you came up with (in this case "one") goes in front of the fraction in your answer. To get the fraction part, take the remainder and stick it on top of the denominator (which in this case is 3.) The answer you end up with is 1 2/3.

    Good luck!

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    Posted by ophelious on Wednesday November 4, 2009 at 2:52 PM

  2. zetalyte
    zetalyte Teacher
    Elementary / Primary

    Dividing the bottom number 3 (denominator)  into the top number 5 (numerator) will change the improper fraction 5/3 into a mixed number. 

    1. 3 goes into 5, once

    2. 3 x1 is 3

    3. 5-3 = 2

    This number 2 instead of being written as a remainder becomes part of a fraction. Your answer when you divided "1" becomes your whole number and the fraction is the remainder "2" over your original denominator "3". Thus your final answer is 1 2/3

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    Posted by zetalyte on Sunday December 6, 2009 at 10:29 AM

  3. reveille
    reveille Teacher
    Middle School

    I am a fifth grade math teacher.  This is the way I explaing it to my 11-year old students... nearly all of them understand it the first time around.  I also use the following terminology when I tutor high-school and college students, simply because it is honestly the easiest way to understand fractions.

    First of all, you have to understand that math is a language.  It is one of the few truly universal languages.  As such, you have to understand that everything in math can take multiple forms.  In reality, what you are doing when you "solve" any math problem is simply TRANSLATING the "expression" (act of conveying an idea to someone outside myself) into another format... which retains the same meaning, but just looks different.  It's the same idea as translating from English into Spanish (or any other language).  What makes or breaks a math student is the ability to be able to recognize the information as it is seen in different forms on paper.

    In the case of fractions, what most students don't understand is that the fraction itself is actually telling you what to do - it is a form of communication.  In the case of your "improper" fraction, 5/3 tells the reader that an "operation" (something we do) needs to be performed.  Operations, in math, are always things we do to numbers.  The expression 5/3 contains two number symbols and one "operation" (action) symbol.  The fraction bar in a fraction (whether the fraction is proper or improper) always tells the reader that the writer of the expression intends the reader to divide something (convenient, since the bar physically "divides" the two numbers into their own little spaces on the paper, huh?)

    When you see an expression with one number over a fraction bar... all of which is over another number (some sort of fraction), you always need to think DIVIDE.  You can re-write the "fraction" into a division problem that looks more familiar to you.  You can use what I call the long-division "house" format.  The top number (numerator) will always go inside the house, and the bottom number (denominator) will always go outside the house.  When you translate the "fraction" into a familiar-looking operation, you can simply work out the long division and further translate the original question into either a decimal (standard format) or a mixed number.

    The only difference between the expression 1/3 and 5/3 is that 1/3 means that it is a value less than one... when you work out the long division problem, you will find that the number "translates" to approximately 0.333 (notice the zero in front of the decimal... that means that there are ZERO wholes in the value... it is less than one).  When you work out 5/3, it "translates" to approximately 1.666 - Notice that this is MORE than one.

    Either way, the fraction bar is a "command" in math.  It tells the reader to divide.  Hope this helps with fractions in general!

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    Posted by reveille on Saturday December 26, 2009 at 3:32 PM