Math Is Fun Forum

I dunno. I would think that paper (partly) digested by an animal would make a pretty good fertilizer.

Hail to the king, baby.

I remember the one for Natural numbers. The definition of the set of Natural numbers goes something like this:

1 is in the Natural set
For every x in the N set, there is an x' which is the successor to x
(There's some more, but I think that's all the important parts for 1+1)

By the definition of addition in the Natural set, x + 1 = x'
So in the set of Natural numbers, 1 + 1 = 1'

ooh! I love Mastermind

Guess2: 645

The other use for a Useful Percentage is to find out the answer to questions like "What is 30% of 150?"

To obtain the Useful Percentage from the Pretty Percentage you must divide the Pretty Percentage by 100.
So 30% is our Pretty Percentage. To make it useful we divide by 100 like this:
30 ÷ 100 = 0.3

Now here's how we use it. We want to know what 30% of 150 is. To get the answer you multiply the number (150) by the Useful Percentage.
150 × 0.3 = 45

So 30% of 150 is 45.

Taking your example, you know that 20% of the cars belong to the police. What is 20% of 140?
First, obtain the Useful Percentage: 20 ÷ 100 = 0.2
Second, multiply it to your other number: 140 × 0.2 = 28

That means 28 of the cars belong to the police. That means the rest must belong to other people.
140 cars - 28 belonging to police = 112 cars belonging to other people

Does it help if you know that, according to Taylor\Maclaurin:

In cases where |x-1| ≤ 1?

As long as you assume that m and n are the same sign and m ≤ 2n, then you could substitute in m/n for x in the above formula. You might need to convert the 1s in the equation to "fancy" 1s (ie n/n, m/m, or nm/nm)

Couldn't remember the LaTeX codes for them at the time. They would have made more sense if they weren't just bold.

I was referring to the set of prime numbers, P, and the real numbers R. Both contain infinite elements (points?) and if you remove the elements of P from R, R still remains infinite.

A better example might have been the set of all whole numbers and the set of all even whole numbers, but Prime and Real was what sprang to mind at the time.

THAT would be an interesting game. Let it run for infinite games and the scores are both equal and infinitely different....
2p - p = d

As p -> ∞, d -> ∞
And as p -> ∞, 2p -> ∞

It's like P and R all over again.

Math is a tough subject and a lot of people do have trouble understanding the methods involved. You may never get over your blockage, but it is very much worth the effort to try. We'll help however we can and I'm willing to bet that it's just a matter of teaching method for you to get over your hurdle.

Try having a look at the material on the website. You can access it via www.mathisfun.com or by clicking on the "Math Is Fun" link just below the "Useful Symbols" at the top of the page. There's very good visual examples of how to do Long Division. That may be a good starting place as knowing how to divide will make fractions so much easier to understand.

I hope you learned long division or else this might be right over your head, Musiqkid.

I'll walk through 300÷990 for you.
First, you need to add a few zeroes onto the end of the first number. You should know that every whole number can also be written with as many 0s after it's decimal place as you want.
For instance, 300 is the same as 300.0 and 300.00 and 300.000 and 300.00000000

When you divide a positive number by a larger positive number, it's necessary to write the smaller number like this. So you might write it down on your paper like this:
       _________
990 ) 300.0000

Just ignore the decimal for now and pretend we're doing 3000000÷990. You can see that your first step is to find 3000÷990. The answer is 3 remainder 30.
Just ignore the remainder as usual and write your first answer above the problem, then subtract 3x990 from 3000 to work out the next step. Keep your answers lined up! This is very important! Your paper should look like this:

       ____ 3___
990 ) 300.0000
         2970
            30

Now bring down the next 0 and you have 300 as the next number to work with. 300÷990 is 0 remainder 990. Again, ignore the remainder and write your answer above the problem and subtract 0x990 from 300. Your problem should look like this:

       ____ 30__
990 ) 300.0000
         2970
            300
               0
            300

Bring down the next 0 and you have 3000 as the next number to work with. 3000÷990 was 3 remainder 30, so subtract 3x990 from 3000. Your problem should now look like this:

       ____ 303_
990 ) 300.0000
         2970
            300
               0
            3000
            2970
                30

You might be able to see a pattern forming here. We'll continue getting 0s and 3s for as long as we continue, so I'll stop now and show you how to get your final answer. Remember how I put in bold text that you should keep all this lined up? This is why.

The final step is to take the decimal point and move it straight up into the answer we obtained by our dividing. In this case, if you moved it straight up, it would go before the first three in our answer. After this final step, here's what your workings should look like:

       ___  .303_
990 ) 300.0000
         2970
            300
               0
            3000
            2970
                30

This is your final answer: 300÷990= .303 (with the 0 and 3 repeating)

...and then curls up in the fetal position and makes a recovery.