Calling all mathmeticians

[joyfulmomof2]

I am not sure where this question goes so you can move it if you want.

I am currently taking an algebra class, but I have a really fundamental math question. If you divide 120 by .04 why do you get a larger number. I cannot seem to wrap my mind around this concept for anything. :think It is hurting my brain. 120/.04 = 3000! Ahhhhhhhhhhh for the life of me, that makes no sense. Can anyone give me an illustration?

[Shining Light]

I don't know if this will help or just confuse you more but I'll give it a shot. Your problem is 120/0.04. Whenever someone is confused about math, I always recommend putting it into terms of money. For some reason most of us seem to get money more easily. So lets change 120 / 0.04 to
$120 divided by 4 cents. Except, to make it even easier, let's pretend it is $120 divided by 5 cents because that is pretty close to the original. So.... if you had $120 and you wanted to know how many nickels was in $120, wouldn't it be logical that you need more than 120 nickels to make $120 rather than fewer?
I'll stop explaining there and, hopefully, either that makes sense to you or someone else can pick it up from there. I shouldn't even be on GCM right now. I am just procrastinating instead of working so I'd better go.
Hope that helps :-)

[HuggaBuggaMommy]

You cannot have a divisor that is not a whole number, so you need to make .04 a whole number, and to do that, you multiply both numbers by 100 (whatever you do to one number you must do to another). So, now you have 12000 divided by 4, which is 3000. When you do the math on a calculator, the calculator automatically does that *silent* multiplication step for you.

Hope that helps!

[Teribear]

because you're dividing by a fraction.

.04 is 4/100

so in your example what you actually have is:

120 / (4/100)

which can also be expressed as

(120/1) / (4/100)

You have to multiply both factors by 100 to get the common denominator

so 120 X 100 = 12000 and 4/100 x 100 = 4

and you're left with

12000 / 4 = ?

12000/4 = 3000

Anytime you divide by a fraction you'll end up with a larger number than you started with and decimals are just a different way of expressing fractions.

Make sense?

[RubySlippers]

Starlene...that's a really good suggestion!
I advocate using manipulatives...so let's look at pennies.
If you had 100 pennies ($1) and you divided your dollar into piles of 4 pennies ($.04), you would make 25 little piles of pennies. If you had 12000 pennies ($120) and you divided your total into piles of 4 pennies ($.04), you would make 3000 little piles.

The number 1 divided by .04 gives you 25 increments of .04. Imagine if you made a number line of those increments. You would go from 0 to .04, to .08, to .12, to .16, to.20, to .24, to .28, to .32, to .36, to .40, to .44, etc., etc., till you get to a whole 1. Now imagine how many increments of .04 you would need to get to 120! Now 3000 doesn't seem so unreasonable. :)

Edited, to change my last sentence so it made more sense, maybe. :giggle

[Chris3jam]

Because .04 is less than 1 whole. That's why you end up with a bigger number. Plus, all the other answers. :mrgreen As in the one answer here, you could always level the playing field by changing into equal terms. . . . thus, .04 = 4 (that's just moving the decimal point by multiplying by 100) and what you do to one number you do to the other, so 120=12000 (120X100). So you get 12000/4 (as suggested below).

[joyfulmomof2]

Awesome thanks! You were all very helpful. I just could not picture it and therefore it made it difficult to do in my head because I was going the other way. I guess I am still thinking if you had 120 / .04 and you get 3000. I guess you are getting 3000 piles of 4 pennies that make 120 dollars, but it seems like it is saying that $120/$.04 = $3000. No?

Here is another thing. I am now entering the wonderful world of story problems!

Here is a story problem: (well I guess it really isn't a story, but anyway..)

How much of an alloy that is 40% copper should be mixed with 500 ounces of an alloy that is 60% copper in order to get an alloy that is 50% copper?

Rules of Problem Solving:

1. UNDERSTAND the problem. Choose a variable that represents the unknown and propose a solution.
2. TRANSLATE the problem into an equation.
3. SOLVE the equation.
4. INTERPRET the results: Check the proposed solution.

Ok, 3 and 4 are absolutely no problem to me. Once I have the equation I can totally solve it. My problem is understanding how to decide which variable should be represented by x and translating the problem into an equation. I just don't seem to get it. And this is a general question. That is just one of many examples and I have to take a test tonight. AHHHHHHHHHHHH! Is there a tearing hair out smiley? :lol So what I need to know is there a general rule to decide how to do that?

[Teribear]

Not exactly. When you're dividing by a fraction you're actually multiplying by the reciprocal of that fraction. Does that make any sense? In your example with the money you're forgetting to cancel out the units.

$120/$.04 = 3000 not $3000 because the unit $ cancels out

You see this a lot in scientific math.

[jghomeschooler]

I guess you are getting 3000 piles of 4 pennies that make 120 dollars, but it seems like it is saying that $120/$.04 = $3000. No?
Well, no. Think of it as .04 parts, 3000 times equals 120 whole pieces. or something like that. Just forget the $

[Shining Light]

How much of an alloy that is 40% copper should be mixed with 500 ounces of an alloy that is 60% copper in order to get an alloy that is 50% copper?

OK. I'm back, still procrastinating with my work.
I'll give this a shot and hope that I'm right and it makes sense to you.

First, figure out what the question is asking. Learn to interpret English words into "math" words. For example, when you see "how much of _____" that tells you what should be your variable - we'll use x. (That is a rule of thumb; sometimes you might use something else to be the variable but in this case you don't.) The other translation you can do is when you see "mixed" (another common word would be "combined"), you know that means you are adding something to get a sum.

If I haven't lost you yet, let's back up to what x is going to stand for. Since the problems says "How much of an alloy that is 40% copper..." you know that your unknown is just that -- x = the amount of 40% copper alloy (in oz.). I am using ounces because the other amount the problem mentions is ounces.

Now, it says how much of that (x) should you mix with (meaning add to) "500 ounces of an alloy that is 60% copper." So now we know we are going to add x ounces (that is 40% copper) to 500 ounces (that is 60% copper). Go back to the problem to see what happens when you mix the two together. It says you want to get an alloy that is 50% copper. That means that the combination of the two alloys will give you something that is equal to some amount of 50% copper alloy. So that brings up the question, how much will be 50% alloy and do you need to make that another variable (y)? NO. You don't want to put another variable in because you don't need one. You can just say that the number of ounces in the final alloy (50% copper) is equal to the number of ounces you combined (the number of ounces of 40% alloy + number of ounces of 60% alloy).

Let me try to summarize before I go on. (This is hard to explain in typing.) ---
We know that:
the number of ounces of 40% alloy + the number of ounces of 60% alloy must = the number of ounces of 50% alloy
In mathematical terms, that is x + 500 = x+500
Ha, ha! That's helpful, huh?

Well, we aren't done. We need to throw in the fact that
x ounces is 40% copper alloy,
500 ounces is 60% copper alloy, and
(x + 500) ounces is 50% copper alloy.
The way you show that is by multiplying the number of ounces by the percentage of copper in that amount. --->
(40%) times (x ounces) + (60%) times (500 ounces) = (50%) times (x + 500 ounces)

(Remember, to change a percent to a decimal, just move the decimal point over two places to the left --->
That means 40% = 40.0% = .400 = 0.4,
60% = 60.0% = .600 = 0.6, and
50% = 50.0% = .500 = 0.5.

So now the equation should say:
(0.4) times (x ounces) + (0.6) times (500 ounces) = (0.5) times (x + 500 ounces)
That can be written as 0.4x + 0.6(500) = 0.5(x+500) --->
simplify by multiplying 0.6(500) and distributing the 0.5 (x + 500) --->
0.4x + 300 = 0.5x + 250 --->
- 250 - 250
0.4x + 50 = 0.5x
-0.4x -0.4x
50 = 0.1x
divide each side by 0.1
500 = x

That means you need 500 ounces of the 40% copper alloy. And if you think about that, it ought to make logical sense,
If you combined 500 ounces of 40% copper alloy with 500 ounces of 60% copper alloy, you would end up with 1000 ounces of 50% alloy. They would even each other out.

I sure hope after all that that I didn't tell you how to do this the wrong way. (I hope, I hope, I hope! I'd be sooooo embarrassed.)

[birthchic]

Division asks : How many times is the divisor (.04) contained in the dividend (120)? How many.04s are contained in 120? Since .04 is less than 1 there will be more than 120...

[illinoismommy]

I am not sure where this question goes so you can move it if you want.

I am currently taking an algebra class, but I have a really fundamental math question. If you divide 120 by .04 why do you get a larger number. I cannot seem to wrap my mind around this concept for anything. :think It is hurting my brain. 120/.04 = 3000! Ahhhhhhhhhhh for the life of me, that makes no sense. Can anyone give me an illustration?


If you put 120 chunks of playdoh into groups of .04 (less than one) .... how many groups will you have? 3000. Because you have to take apart the chunks of playdoh to make them .04, thus making a whooooole lotta groups.

[RealLifeMama]

OhMy! This thread has me :( right now!
I was a mathematician in my "past life" so I eagerly opened this thread, and :eek
I couldn't for the life of me think how to explain it! I am blaming it on my huge 2 pound placentas!
I am glad you got the answers you needed. It was fun to read all the responses.

[joyfulmomof2]

Oh you guys are so awesome! Thank you all for all of your help. Starlene, I am coming back here to read your post, but my brain is fried for tonight and I just nearly failed my test. I couldn't even get back here to check on this thread before taking it. I tried so hard to get everything done, but I messed up. :( I may have a 0 on an assignment as well. I just don't get worded problems and it is so disheartening because I was averaging a 98% before this. Now I am going to have a B or possibly even a C! :( Anyway, I must sleep and tomorrow I probably will not be here either due to my schedule. But I will be back to try to get this. Thank you all! Goodnight for now.