1
vote
2answers
51 views

Definition of Rational/ Irrational Numbers reguarding denominators

The definition of a Irrational number is "Irrational numbers don't include integers OR fractions. However, irrational numbers can have a decimal value that continues forever WITHOUT a pattern." So ...
2
votes
3answers
76 views

can fractions be done on a regular caculator?

I am wondering if I can use me standard calculator to solve fraction problems which include: adding, subtracting, multiplying, and dividing fractions, or do I need to buy a scientific calculator to ...
1
vote
2answers
56 views

How do you simplify an algebraic expression?

Please explain how to simplify an expression that is similar to this one $\displaystyle\frac{a+3}{6}+\frac{a-4}{4}+\frac{a+2}{-3}$
0
votes
3answers
53 views

Splitting the numerator

Can someone explain how we can get the second fraction by splitting the numerator? $$\frac{x^3}{x^2+x+1}=x-1+\frac{1}{x^2+x+1}$$ I can get the LHS from the RHS but not the other way around. What ...
0
votes
2answers
30 views

I don't understand the expected result from an equation. [closed]

I came across this a while ago in my studies and let it pass however exams are closing in so I better figure it out. I am not sure why in the second equation 458 is the answer.
1
vote
3answers
54 views

Basic algebra, isolating the variable

So I have the equation $$\tan30=\frac{4.9t-\frac{10}{t}}{\frac{8.77}{t}}$$ And I want to find t, but my algebra has failed me. This is my working so far. ...
0
votes
2answers
33 views

Fractions with 3 diffferent variables

Calculate the values of $a$, $b$ and $c$ if: $$\frac{5}{13} = \frac{1}{a+\frac{1}{b+\frac{2}{c}}}$$ Can anyone give me a hint and not the answer? Thanks.
2
votes
3answers
126 views

Rules for cancelling fractions with exponents

I have an expression that I need to simplify, I know the answer (wolframalpha) but I'm not sure of the rule that gets me there. $\dfrac{(\alpha) X_1^{\alpha -1} X_2^{1-\alpha}}{(1-\alpha)X_1^\alpha ...
0
votes
0answers
68 views

difficult inequality to prove

I need help proving this inequality is correct for a homework assignment: $$\displaystyle \left(\frac{13}{4}\right)^{n} \leq ...
1
vote
3answers
127 views

How to work out this easy fraction?

I need help working out this fraction, I know it seems quite easy but I'm a bit stuck. The question is: $$\frac{5/2}{5/9}$$ My attempt was changing the denominators by multiplying by $2$ to make ...
1
vote
2answers
58 views

Simple algebra question - separating fractions

How does the following come about? I'm completely lost. Can anyone help me fill in the steps in between? $$ \frac{s+2}{s(s+1)} = \frac{2}{s} - \frac{1}{s+1} $$ I figured that $$ \frac{s+2}{s(s+1)} ...
0
votes
1answer
40 views

How to work out these fractions?

$\dfrac{-x^4 + 4x^2 + 6}{x}$ $\dfrac{7x^8 - 5x^5 + 9x^3 + x^2}{x}$ I have no idea how to do this. I was first thinking of doing $-x$ or collecting up the $x's$ but I'm not sure as I haven't dealt ...
0
votes
3answers
79 views

Ratio problem to find the woman weekly salary

A woman spend $5/8$ of her weekly salary on rent, and $1/3$ of the remainder on food, leaving $40 available for other expenses. What is the woman's weekly salary ? I have tried , i am really confused ...
0
votes
1answer
79 views

Finding percentage which is less

The number that is 50% greater than $60$ is what percentage less than the number that is 20% less than $150$ ? My try : I considered a number is 50% of $130$ which is greater than the $60$ and 20% ...
2
votes
2answers
244 views

How to prove the fraction identity without using calculator

How to prove without calculator that $$ \frac{1}{1001} + \frac{1}{3001} > \frac{1}{1000}$$
0
votes
2answers
199 views

Check my answers to these problems on rationalizing denominators? [closed]

I just need to check my answers for these problems. I did the work already on paper. I'm not trying to get free answers because I know that would hurt me in the long run. So here's the questions: ...
0
votes
1answer
61 views

Ring of fractions in $\mathbb{Z}/35\mathbb{Z}$

How can I determine $S^{-1}(\mathbb{Z}/35\mathbb{Z})$, where $S$ consists of of all elements of $\mathbb{Z}/35\mathbb{Z}$ except $0,5,10,15,20,25,$ and $30$?
0
votes
1answer
80 views

summation of fractions and inequalities

I am trying to prove that $\sum_{i=1}^{n}\frac{1}{a_i}\leqslant 2$, where all $a_i$ are less than 1000, and all $a_i$ have a lowest common multiple greater than 1000. This is what I have done so far: ...
0
votes
2answers
71 views

Simplifying $\frac{4}{2x-7}-\frac{3}{(2x-7)^2}$

A homework question asks me to "perform the addition or subtraction and simplify" $$ \begin{gather} \frac{4}{2x-7}-\frac{3}{(2x-7)^2}=4(2x-7)-3=8x-28-3=8x-31 \\ 8x=31 \\ x=\frac{31}{8} \end{gather} ...
1
vote
1answer
72 views

Problems with basic algebra

I'm studying for an exam in a digital communications course I'm taking, and the solution to one question has me totally lost. While finding the Inverse Fourier Transform of a function, there's one ...
2
votes
1answer
62 views

Problem with slopes.

I currently have a slope that looks like this: $\frac{-5}{10}$ However, I need to bring it down to it's lowest terms, so I divided the numerator and denominator by -5 and I got: $\frac{1}{-2}$ ...
2
votes
3answers
5k views

How can I convert this negative fraction to a positive one?

This question may be very simple, but I get confused on things like it. If I have a fraction like this: $-\frac{x}{-2}$ How can I convert this negative fraction to a positive one? It does not ...
1
vote
2answers
1k views

Problem with getting variable by itself in fraction.

I have a problem that looks something like this: The difference of the quotient of a number and $-2$ from $12$ is $15$. So I started off like this: $12-\displaystyle\frac{x}{-2}=15$ Then I ...
2
votes
1answer
178 views

Rationalizing fractions with multiple radicals

I am having trouble rationalizing $\frac{2}{\sqrt{2-\sqrt{2}}}$ I have tried multiplying the fraction by $\sqrt{2 + \sqrt{2}}$ and got $\frac{2\sqrt{2+\sqrt{2}}}{\sqrt{2}}$ I am not sure if that is ...
1
vote
1answer
273 views

Simplifying fraction with multiple radicals

I have an answer to a problem that I am working on but I have no idea how to rationalize the denominator because I have never worked with this type of problem before. The problem is: ...
0
votes
2answers
46 views

What is this technique called?

It's been a long time since I've done algebra. I remember how to do it, but I'm at a loss to explain it. For instance, my son has the following problem; $$\frac{3}{Q+1}+\frac{2}{Q}$$ So I say, you ...
4
votes
4answers
400 views

Of all the possible combinations of positive numbers that sum to 10, which has the largest multiplication?

Of all the possible combinations of positive numbers that sum to 10, which has the largest multiplication? I had also got a clue: it's related to e. Please help! ...
3
votes
1answer
113 views

How to solve this System of Polynomial Equations?

I have to complete a summer packet of 90 Algebra 2 questions. I have completed 89 of them, the only one I could not get was this. I know the answer is $y = \frac {47}2$, $\frac 17$ according to ...
0
votes
2answers
590 views

Graphing Fractional Exponents

$f(x)=x^\frac{5}{3}-5x^\frac{2}{3}$ is the same as : $f(x)=(\sqrt[3]x)^5-(\sqrt[3]{5x})^2$ Except, with the first equation, my calculator returns an error for negative values of $x$ (We are ...
-1
votes
1answer
133 views

Help with trinomial fractions [closed]

The denominator is $x-6$, and the numerator is a trinomial. I figured the trinomial out - $(x-3)(x-2)$; I'm not sure what to do after this step though. $$\frac{x^2}{x-6} - \frac{5x+6}{x-6}$$
5
votes
4answers
248 views

Writing a percent as a decimal and a fraction

I am having a problem understanding some manipulations with recurring decimals. The exercise is Write each of the following as a decimal and a fraction: (iii) $66\frac{2}{3}$% (iv) ...
3
votes
1answer
135 views

Is this a correct proof of a fact about rational numbers?

Prove the following statement: if $\frac{p}{q} (p \in \mathbb{N}, q \in \mathbb{N})$ is a rational number that corresponds to an infinite periodic decimal fraction $\alpha$, then the rational ...