# Thread: Brushing up... simple algebra question

1. ## Brushing up... simple algebra question

As title states, I need to brush up on my algebra... been a few years.

This is the question:
the number of half-pound packages of tea that can be made up from a box that holds 10 1/4 pounds of tea is.

This is the formula and answer:
Code:
10¼ lbs ÷ ½ = 41/4 x 2/1 = 20½

What I need to know, in order for my brain to dig up those lessons in the recesses of my brain, is how this is determined. Where does 20½ come from 41/4 x 2/1? I see division, but multiplying that number I just can't grasp.

I also seen a few videos on youtube regarding algebra, maybe someone knows a specific example they could direct me to.

Thanks

2. Edit: nevermind, I understand now. I'll edit this post again.

Here's a full answer:

$\displaystyle 10\frac{1}{4} = \frac{41}{4}$ because $\displaystyle \frac {40}{4}=10$ with $\displaystyle \frac {1}{4}$ left over.

To divide fractions, an easier method is to 'flip' the second fraction and then times. That's what changes it into:

$\displaystyle \frac {41}{4} \times \frac{2}{1}$

Just times the top by the top and the bottom by the bottom:

$\displaystyle =\frac{41\times2}{4\times1}$

$\displaystyle =\frac{82}{4}$

This is just another way of writing '82 divided by 4'

$\displaystyle =20\frac{1}{2}$

3. Thanks for the reply. fixed the formula... its also the answer. I'm looking how it was solved.

4. Is that what you were asking? I made several mistakes so had to edit my post around 5 times.

5. Thanks, it does solve the question I had with how the answer was found. But where was the formula $\displaystyle \frac {41}{4} \times \frac{2}{1}$ derived?

6. I must apologize: I forget that you're here to ask for help, not for an inconsistent ramble. It's a difficult question to explain, actually. The method for dividing fractions is to 'flip' the second and times.
One way to think about it is that you're 'doing the opposite twice'.

If I take the sum:

$\displaystyle \frac {1}{10} \div \frac {1}{2}$
This means
'1,divided by 10, divided by 1, divided by 2'
If I flip the second fraction, it becomes:

$\displaystyle \frac {1}{10} \div \frac{2}{1}$
which is to say
'1, divided by 10, divided by 2, divided by 1'
I have reversed the sum completely.
Therefore, if I change it to:
$\displaystyle \frac {1}{10} \times \frac {2}{1}$
I have now reversed the sum completely again. As we have done the opposite twice, we'll get the same result.

I have explained that very badly. Perhaps this link will do a better job.
Fraction (mathematics) - Wikipedia, the free encyclopedia
although it may just make it seem more confusing.

7. I got it. Thanks.

Another question:
$\displaystyle (x +3)(x +3) = x{^2} + 6x + 9$

How is that worked out? I seriously need a rudimentary class to brush up on this, but atm need basics to open a door I haven't used for years... cramming for a test next Tues.

8. That should be a little easier to explain.
What that means is
'EVERYTHING in bracket one multiplied by EVERYTHING in bracket two'
The easiest method to do this with is called the 'FOIL' method.
F: First
O: Outside
I: Inside
L: Last

So, using your example of $\displaystyle (x+3)(x+3)$
First: (x+3)(x+3)

Outside: (x+3)(x+3)

Inside: (x+3)(x+3)

Last: (x+3)(x+3)

To start, times the terms in bold red.

This gives:
F: $\displaystyle x^2$
O: $\displaystyle 3x$
I: $\displaystyle 3x$
L: $\displaystyle 9$

Add up the result:

$\displaystyle x^2 + 3x + 3x + 9$
$\displaystyle = x^2 + 6x + 9$

Edit: And please don't feel as though you're behind: quite a lot of people, who don't necessarily have this knowledge, can pass their maths G.C.S.E with a C grade and then drop the subject permanently, without ever gaining an understanding of it. Two of my friends were in this situation.

9. Thanks, your help has definitely recalled some portions.

10. I'm sorry that I couldn't be more helpful. You probably know of these links already but they contain resources to aid your maths revision.
BBC - GCSE Bitesize - Algebra
S-Cool | Maths

11. NP... help is appreciated. Heads not as twisted.

Another:
$\displaystyle (3+2)(6-2)(7+1)=(4+4)(x)$

Solved:
$\displaystyle (5)(4)(8)=8x$
$\displaystyle 160=8x$
$\displaystyle 20=x$

Answer:
8+12

Now, my the issue I'm dealing with is... where does 8+12 come from?

12. I don't think the 8+12 has any relevance to that at all. $\displaystyle x=20$ is correct, and is the final answer. To say $\displaystyle x=8+12$ is true, but not necessary to answer the question completely.