# Thread: Subtracting Percents / Fractions

1. ## Subtracting Percents / Fractions

I feel so embarrassed... use to do geom/trig on the fly now I can't do simple 5th grade arithmetic. Trying to figure out:

$\displaystyle 8\frac{1}{4}$ % - $\displaystyle 5\frac{2}{5}$%

Into:
$\displaystyle 8\frac{5}{20}$ % - $\displaystyle 5\frac{8}{20}$%

Into (where does the 25 come from? I see 1 was taken away from the 8, please explain)
$\displaystyle 7\frac{25}{20}$ % - $\displaystyle 5\frac{8}{20}$% = $\displaystyle 2\frac{17}{20}$

Converting to decimal it's:
0.0825 -0.0540 = 0.0285 or $\displaystyle =\frac{285}{10,000}$ simplified... I gave up.

2. Originally Posted by pychon
Trying to figure out:

$\displaystyle 8\frac{1}{4}$ % - $\displaystyle 5\frac{2}{5}$%

is

$\displaystyle \frac{33}{4}$ % - $\displaystyle \frac{27}{5}$%

As % means divide 100

$\displaystyle \frac{33}{400}$ - $\displaystyle \frac{27}{500}$

Now find a common denominator and subtract.

3. I'm not familiar with your way... never made percentages into improper fractions, was taught to rename the fractional parts with the same common denominator. Keep in mind I'm looking for explanations.

The problem is solved... I just need to know where $\displaystyle 7\frac{25}{20}$ came from or an easier way to do these.

4. Originally Posted by pychon
I just need to know where $\displaystyle 7\frac{25}{20}$ came from or an easier way to do these.
I get,

$\displaystyle \frac{33}{4}- \frac{27}{5}$

$\displaystyle \frac{33}{4}\times \frac{5}{5}- \frac{27}{5}\times \frac{4}{4}$

$\displaystyle \frac{165}{20}- \frac{108}{20}$

$\displaystyle \frac{165-108}{20}$

$\displaystyle \frac{57}{20}$

5. Tried to PM, but ridiculous post count rules:

I know you're trying to help. But I need explanations to your solutions... not just how you devised it in your head and displaying the fractional equations.

It's been "years" since I've done any of this stuff... explanations of "how" you worked out the solution would be greatly appreciated!

6. Originally Posted by pychon
I feel so embarrassed... use to do geom/trig on the fly now I can't do simple 5th grade arithmetic. Trying to figure out:

$\displaystyle 8\frac{1}{4}$ % - $\displaystyle 5\frac{2}{5}$%

Into:
$\displaystyle 8\frac{5}{20}$ % - $\displaystyle 5\frac{8}{20}$%

Into (where does the 25 come from? I see 1 was taken away from the 8, please explain)
8= 7+ 1 and $\displaystyle 1= \frac{20}{20}$
$\displaystyle 8\frac{5}{20}= 7+ 1+ \frac{5}{20}= 7+ \frac{20}{20}+ \frac{5}{20}$

$\displaystyle 7\frac{25}{20}$ % - $\displaystyle 5\frac{8}{20}$% = $\displaystyle 2\frac{17}{20}$

Converting to decimal it's:
0.0825 -0.0540 = 0.0285 or $\displaystyle =\frac{285}{10,000}$ simplified... I gave up.

7. I'm sorry, but that doesn't explain anything to me. Like I said... would be nice for explanations, not worked out solutions.

8. I thought the explanations were very clear. If you are having trouble, please state which steps are confusing you? It would make it easier for us to help.

Would you accept that this is
$\displaystyle 7 + 1 + \frac{5}{20}$?

What a fraction means is 'top divided by bottom'.

So let's look at the 1.

This could be written as $\displaystyle \frac{2}{2}$ or $\displaystyle \frac{3}{3}$ and so on, as the top divided by the bottom will give one. It could also be written as $\displaystyle \frac{20}{20}$ then, because a fraction means top divided by bottom.

This means we have:
$\displaystyle 7+\frac{20}{20}+\frac{5}{20}$

This means '7, plus five out of twenty, plus twenty of twenty'.

Can you then see that this will equal

$\displaystyle 7 + \frac{25}{20}$?

'seven plus twenty five out of twenty'?