Please help! How would I solve 12 5/8 + 9 2/3?? Thank you!

- anonymous

Please help! How would I solve 12 5/8 + 9 2/3?? Thank you!

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- schrodinger

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- theEric

Hi! Well, adding 12 and 9 are easy. Adding those fractions is a little trickier. Would you agree that \[12\frac{5}{8} + 9\frac{2}{3}\] is the same as\[12+\frac{5}{8} +9+\frac{2}{3}\]?

- anonymous

yes, I would

- theEric

Alright, and it is also the same as \[12+9+\frac{5}{8}+\frac{2}{3}\]right?

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## More answers

- theEric

So 12+9, piece of cake. I can count it on my fingers (and I need some friend's fingers too). Anyway...
Both fractions have to have the same bottom part, called the "denominator" if you care to remember.\[\frac{numerator}{denominator}\]

- theEric

Lets look at JUST \[\frac{5}{8}+\frac{2}{3}\]

- anonymous

alright! (:

- theEric

Now, five-eighths can't just be added to two-thirds.
You have some fractions of 8 and some fractions of 3.
And since an eighth is different from a third, you can just add the top numbers.

- theEric

You have to have two fractions with the same bottom number. So they're both fractions of 24, or whatever. If you have some pieces of 24 and some other pieces of 24, you can easily know how many pieces (of 24) you have!

- theEric

So make the bottom numbers the same with simple algebra!

- anonymous

so 15/24 + 16/24?

- theEric

Say we did want to make \[\frac{5}{8}\] a fraction of 24.
Here's what we'd do:
Multiply 5/8 by 1. It's the only way were not actually changing it.
But that doesn't look helpful. But we can't change it.
Here's the trick:\[1=\frac{1}{1}=\frac{2}{2}=\frac{3}{3}=\frac{9999}{9999}\]

- theEric

\[\frac{5}{8}*1=\frac{5}{8}*\frac{3}{3}=\frac{5*3}{8*3}=\frac{15}{24}\]

- theEric

You see how that helps?
\[\frac{2}{3}*1=\frac{2}{3}*\frac{8}{8}=\frac{2*8}{3*8}=\frac{16}{24}\]

- theEric

Now its easier too add.

- anonymous

So 21 31/24?

- theEric

Yep, but 31/24 doesn't look good. What else can it be?

- anonymous

reduce it?

- theEric

Yeah! Wll, if by reduce it you mean turn it into a compound number and then make the numbers whole but as close to 0 as possible.. I don't remember big words like "reduce" :P Sorry!

- theEric

Go ahead and show me what you get, if you want. Or we can work it out together.

- anonymous

Yeah I have no idea what a compound number is...

- theEric

Oh! That's one I remember! Repeat usage, I guess.
It's just a number that has a whole number and a fraction.
I think\[21\frac{31}{24}\] actually counts, but I know it's not a simple-looking as it can be!

- theEric

Another example is like\[5\frac{3}{4}\]

- theEric

31/24 is greater than 1, so it can be a whole number plus a fraction.

- theEric

The first step in the general way to make a fraction into a compound number is to see how many whole numbers you have. That's \[31\div24\] but not including the remainder (remainder is whatever is left over). The remainder will be written as a fraction.
I know 24 goes into 31 only once. But a calculator will back me up:
\[31\div24=1.2916666666666666667\]

- theEric

So there is 1 whole number in 31/24.

- theEric

Anyway..... After you take that "1" out of\[\frac{31}{24}\]it's
\[\frac{31}{24}-1=\frac{31}{24}-\frac{24}{24}=\frac{31-24}{24}=\frac{7}{24}\]

- theEric

\[21+\frac{31}{24}=21+1+\frac{7}{24}=22+\frac{7}{24}=22\frac{7}{24}\]

- theEric

So you started with\[\frac{5}{8}\]and\[\frac{2}{3}\]
I seemed to just randomly choose "24" as the denominator for them both, and I also seemed to just randomly choose how to multiply each fraction. But really, I multiplied each fraction by the other's denominator over itself.
\[\frac{5*2}{8*3}=\frac{15}{24}\]and\[\frac{2*8}{3*8}=\frac{16}{24}\]
so the "24" kinda just happened.

- theEric

I hope I've helped more than I've hurt! I feel like my response has been jumpled, so I'm sorry. Ask me any questions you have, and I'll try to be more clear.

- anonymous

thank you so much!

- theEric

You're welcome. I hope you can do the problem on your own now!

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