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April 13th, 2016, 07:05 PM   #1
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Wink I need help figuring out the answer to the addition of these mixed fractions

Ok, so the math problem is 7 1/2 + 5 1/3 + 3 1/4 = ?

How do I get the answer? I would really appreciate some help.
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April 13th, 2016, 11:15 PM   #2
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Have you managed any steps? I would tackle this by finding a common denominator and convert all the whole numbers into fractions.
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April 14th, 2016, 03:21 AM   #3
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Quote:
Originally Posted by Angelwngs26 View Post
How do I get the answer?
Is it acceptable to give the answer as a mixed fraction?
If so, you could start by calculating 1/2 + 1/3 + 1/4, producing a mixed fraction as the result, and then add 7, 5 and 3 to it.
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April 14th, 2016, 05:02 PM   #4
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I would start by converting to top heavy fractions.

$\displaystyle 7\frac{1}{2}=\frac{7}{1}+\frac{1}{2}=\frac{14}{2}+ \frac{1}{2}=\frac{15}{2}$

$\displaystyle 5\frac{1}{3}=\frac{5}{1}+\frac{1}{3}=\frac{15}{3}+ \frac{1}{3}=\frac{16}{3}$

Can you figure the last one using the method I have displayed? After this, look for a common denominator. A way to do this would be to look at the denominators that you have and then do prime factorisation and calculate the lowest common multiple, or do it by eye once you see what they have in common. You then can add the fractions.

So, for example, to add the two fractions above, what multiple do 2 and 3 have in common? Their LCM would be 6, so I would then convert the fraction so they both have a denominator of 6 as shown below:

$\displaystyle \frac{16*2}{3*2}=\frac{32}{6}$
$\displaystyle \frac{15*3}{2*3}=\frac{45}{6}$

Add the two together and what do you get?

This is the long way of going around it and skipjack's method is quicker.
Can you use the information above to to solve the actual question?

Last edited by skipjack; April 15th, 2016 at 09:54 AM.
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April 15th, 2016, 04:44 AM   #5
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Quote:
Originally Posted by skipjack View Post
Is it acceptable to give the answer as a mixed fraction?
If so, you could start by calculating 1/2 + 1/3 + 1/4, producing a mixed fraction as the result, and then add 7, 5 and 3 to it.
Of course, 1/2+ 1/3+ 1/4 is larger than 1 so an "improper fraction" and you will have to handle that.

(I don't believe I have ever seen "improper fractions" called "top heavy fractions" before, but I like it!)
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April 15th, 2016, 05:00 AM   #6
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(I don't believe I have ever seen "improper fractions" called "top heavy fractions" before, but I like it!)
I have always called them that; I really don’t know why. I just think the name is more fitting.

Last edited by skipjack; April 15th, 2016 at 09:55 AM.
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April 15th, 2016, 09:09 AM   #7
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Taylor_1989_2012, you mixed the multiplication (no sign) and the addition.

7 1/2 = (7x1)/2=7/2
5 1/3 = (5x1)/3 = 5/3

Now you can make the first addition, by setting to the same denominator 6=3x2
7/2 + 5/3 = (3x7)/6 + (2x5)/6 = 21/6 + 10/6 = 31/6

The last multiplication is:
3 1/4 = (3x1)/4 = 3/4

So, you have to add 31/6 to 3/4: you set to the same denominator 12=2x6=3x4:
31/6 + 3/4 = (2x31)/12 + (3x3)/12 = 62/12 + 9/12 = 71/12

Thus the result is 71/12…
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April 15th, 2016, 09:35 AM   #8
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Quote:
Originally Posted by Mathedu View Post
Taylor_1989_2012, you mixed the multiplication (no sign) and the addition.

7 1/2 = (7x1)/2=7/2
5 1/3 = (5x1)/3 = 5/3

Thus the result is 71/12…
a mixed number does not indicate multiplication between the whole number and fraction ...

$7\frac{1}{2} = 7 + \frac{1}{2} = \frac{15}{2}$


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April 15th, 2016, 10:36 AM   #9
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Have I misread the question?

Last edited by skipjack; April 16th, 2016 at 01:44 AM.
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April 15th, 2016, 10:38 AM   #10
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Originally Posted by taylor_1989_2012 View Post
Have I misread the question?
Quote:
I need help figuring out the answer to the addition of these mixed fractions
No.
Thanks from taylor_1989_2012

Last edited by skipjack; April 16th, 2016 at 01:44 AM.
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