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When you have a problem that requires you to add coins together. Is it better to use fractions?

For example, you have 14 one dollar bills, 24 quarters, 12 dimes, 78 nickles, and 20 pennies.

So I know that I can just take: $\begin{align*} 14 \times 1 &= \$14\\ 24 \times .25 &= \$6\\ 12 \times .10 &= \$1.20\\ 78 \times .05 &= \$3.90\\ 20 \times .01 &= \$0.20 \end{align*}$

Easy stuff, but I'm trying to figure out the best way to add these up. Assuming I have only 15-30 seconds to get this addition done without calculator. I figured the best way is to use fractions.

ps. Can someone tell me how to write real fractions in here instead of using slash? I just want to write them to look better in the future, I tried to look for a way in FAQ but didn't see anything on formatting.

Thanks

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    The [MathJax tutorial/reference is here](http://meta.math.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference).2014-06-04

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I would try to "simplify" the problem a little. For instance, you know 4 quarters is a dollar, so 24 / 4 is 6 dollars. 10 dimes to a dollar, so you have 1 dollar and twenty cents. 20 nickels to a dollar, so you have 3 dollars (60 nickels), and 18 nickels left over.

So now we're at 14 + 6 + 1 + 3 = 24 dollars (and don't forget the remaining 2 dimes, 18 nickels, and 20 pennies).

Simplifying the problem like this might make it easier - at least, that's how I would do it in my head.