SOLUTION: 406 1/2 what is it as an improper fraction

Question 594763: 406 1/2 what is it as an improper fraction
Found 2 solutions by in_the_math_vortex, math-vortex:
Answer by in_the_math_vortex(4) (Show Source): You can put this solution on YOUR website!

Answer by math-vortex(648) (Show Source): You can put this solution on YOUR website!
Hi, there:
Let's work through what 406 1/2 means, then I'll show you an algorithm for solving this type of problem.
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[I]
406 1/2 is a MIXED FRACTION. 406 is a whole number, and 1/2 is a fractional part. You have 406 whole things plus an additional half... for example, 406 whole cookies (yum!) and an additional half-cookie.
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An IMPROPER FRACTION is an equivalent fraction without the whole parts separated out. In the cookie example, imagine that we that we took all 406 cookies and broke them exactly in half. How many half-cookies would we have? Well, each whole cookie would break into two half cookies, or 812 half-cookies. Add the additional half-cookie we already had, and that's 813 half-cookies. Let's represent that as a fraction.
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In fractions, the number below the bar (the DENOMINATOR) tells how many pieces we broke each whole into. In our example, we broke each cookie into two pieces, so our denominator is 2.
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The number above the bar (the NUMERATOR) tells how many of those pieces we have. We have 813 half-cookies, so our numerator is 813. Therefore, our improper fraction is

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The big idea here is that the mixed fraction and the improper fraction are two different ways of representing the same quantity.
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[II]
Here's an algorithm for solving this problem.
1. We start with 406 1/2.
Since the denominator of the fractional part (1/2) is 2, let's also make the denominator of our improper fraction be 2.
2. To find the numerator, we multiply 406 by 2.

3. Now we add the additional half.

4. Our improper fraction is

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I hope that this helps! Feel free to email me if you still have questions about this solution
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Mrs. Figgy
math.in.the.vortex@gmail.com
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