TheXSquaredFactor

Here's a method to convert any repeating decimal to a fraction. 

The first step is to set it equal to a variable; I'll use the standard one, x.

\(7.428571428571...=x\)

Next step is to get only one portion of the repeating portion to the right hand side of the equation. I will demonstrate this:

\(\begin{align} 742857.428571&=100000x\\ 7.42857142857...&=x\\ \end{align}\)

Subtract the equations together to get the following:

\(7428564=999999x\)

Divide by the coefficient of x on both sides.

\(x=\frac{7428564}{999999}\)

This is your final answer. I do not believe the numerator and denominator have any common factors. 

I don't understand why Gh0sty was unable to complete the challenge. What you said is contradictory to your original post.

I have highlighted, in red, where Gh0sty thought it was unnecessary to use every number:
 

Hi everybody,  {nl} Who's up for a challenge? I chose these numbers at random.  {nl} PUZZLE 1  {nl} 10,50,5,25,and 500.  {nl} {nl} Use these numbers to make the number 575.  {nl} {nl} Rules:  {nl} Use only these numbers  {nl} No number can be used twice  {nl} You do not have to use all the numbers  {nl} You can use + - x or divide.  {nl} You can use brackets.  {nl} {nl} First one to respond with exact answer wins. If you post later but you have a substantially different answer, you win too.  {nl} If no-one gets the exact answer then closest answer after 24 hours wins. (competition closes in 48 hours)  {nl} {nl} You will be expected to explain how you got your answer. {nl} {nl} Use a name other than 'guest' and your wins will be recorded.  {nl} If enough people are interested we will keep playing with different numbers.  {nl} Any questions?  {nl} (I have copied this game from the previous number puzzles.)  {nl} Have fun.

To solve this problem, we must figure out how much square feet the entire room is. We know the length and the width of the room. Since, this room is rectangular, we can use that information to figure out how much square feet this room covers. 

We aren't done yet, though! The question is asking how much carpet is remaining after covering the entire floor. This requires the subtraction operator.

Therefore, after completely covering the \(\left(8\frac{3}{4}\right)^{'} * \left(9\frac{1}{3}\right)^{'}\)rectangular room in carpet, Rodger will have  \(\frac{10}{3}ft^2=3\frac{1}{3}ft^2=3.\overline{33}ft^2\) of carpet left. 

I understand, I think! I will simplify \(36\div12+5-(4)(6)+(16-8)\).

It is possible that, after all of this solving, that you have a question. If you do, just ask! I (or any other active member of this forum) will be happy to answer. Don't hesitate.

#5

I have the same issue as #3 because it can be subject to more than one interpretation, too.

When your use "divided by," do you mean that 36 is the numerator and the quantity of 12 + 5 - (4)(6) + (16 - 8) is the denominator. In other words, do you mean  \(\frac{36}{12+5-(4)(6)+(16-8)}\)?

Thanks for responding quickly! I will evaluate it, to your choice, as the latter one of \(f(7)=\frac{6(x+3)}{11(x+7)}\).

#4

I will evaluate \(6^2+4(17+5)-50-(36-10)\) now

For #3, this one contains some ambiguity in which interpretation you mean. You're question is one of the following.

1. \(f(7)=\frac{6(x+3)}{11}*\frac{(x+7)}{1}\)

2. \(f(7)=\frac{6(x+3)}{11(x+7)}\)

While I solve the next 2, please clarify which one you want me to do. In the future, use parentheses (or brackets) to disambiguate any mathematical input.

For example, if the interpretation is #1, use (6(x+3)/11)*(x+7) 

For the second interpretation, use 6(x+3)/(11(x+7))

Time to do #2. Now, I will simplify the expression, as I interpret it to be, \(\frac{6*4}{7}+\left(\frac{5}{6}+\frac{1}{3}\right)\):

Of course, the parentheses are unnecessary in this expression as any order of adding is allowed by the associative property of addition. There is also one for multiplication.

I'll solve each one in a different comment. 

#1

Simplify the expression \(\frac{5}{9}+\frac{2}{3}+\frac{1}{4}+5\).