0
votes
2answers
48 views

Rationalising the Surds

Please help me rationalise and simplify: $$ \frac{1}{\sqrt[3]{2} - 1} \ - \ \frac{2}{\sqrt{3} - 2} \ . $$ I have tried using the cube of the denominator and the square of the denominator on the ...
7
votes
2answers
147 views

Rationalizing the denominator 3

It is a very difficult question. How can we Rationalizing the denominator? $$\frac{2^{1/2}}{5+3*(4^{1/3})-7*(2^{1/3})}$$
0
votes
2answers
29 views

solve ratio word problem without algebra

Four gallons of yellow paint plus two gallons of red paint make orange paint. I assume this makes six gallons. So the ratio is 4:2, or 2:1. Question: how many gallons of yellow paint, and how many ...
0
votes
2answers
49 views

Converting fractions / decimals to percentages

Can someone show me the methodology on how to convert 1.2794 to a percentage form? If I multiply it by 100, I get 127.94%, which is the correct answer. I'm not really sure 'why' I multiplied it by ...
1
vote
4answers
120 views

change $0.684 210 526 3$ into a fraction

I am a non-mathematician who quit with math after middle school. Now I face a practical problem which I cannot solve. Suppose I want to turn $0.684 210 526 3$ into a fraction, how would I do that ...
0
votes
4answers
84 views

Why does $ \frac {\frac {1}{\sqrt{x}}}{x} = \frac {\sqrt{x}}{x^2} $?

A homework question recently asked for me to simplify: $\frac{1}{\sqrt{7}} \div {7}$ It's easy to see that this becomes $\frac{1}{7\sqrt{7}}$ But according to wolfram alpha this is also equal to ...
5
votes
3answers
286 views

What's the algebraic property where you can flip the fractions in an equation?

Earlier in algebra, we spent over 20 minutes trying to figure out $$ \frac{1}{R_1} + \frac{1}{R_2} = \frac{1}{R_e} \,\,\,\, \text{solve for }R_2 $$ when the teacher said "What you start out with is ...
1
vote
2answers
46 views

Calculating percentage to compensate for percent discount.

Missing something very basic here and cannot pin point it. We need to charge a client \$100 for a product. Let's say our payment processor charges us 10% on every transaction. We make this ...
0
votes
7answers
256 views

Why Not Define $0/0$ To Be $0$?

For every number $x$, $x\times 0=0$, hence $\dfrac{0}{0}$ can be any number! So $\dfrac{0}{0}$ "is knows as indeterminate" [1]. But what if we define it to be $0$? I already have an answer, but ...
1
vote
1answer
72 views

Simplifying square root with fraction

I'm not sure about this equality $$4(-3+\sqrt {15})/4)^2 = (9-6 \sqrt{15} +15)/4$$ Hope some one can enlighten me. I will be facing more of such fractions, please guide me on how to solve/simplify ...
0
votes
2answers
35 views

Percentage of Amounts

I'm studying and I'm not that sure how to answer this question. Is $97.1%$ $=$ $650,000,000$? I was going to find $2.9%$ of $650,000,000$ however this would be wrong as I would finding our the ...
2
votes
1answer
71 views

Percentage of an amount?

I'm totally confused, we were doing a question in class and there are two answers but I'm not sure why one works and the other one doesn't. For example; there are 6000 pandas now and over 10 years ...
6
votes
1answer
109 views

How to best understand Euclid's definition of equal ratios? How does it relate to Dedekind cuts?

This is something I've been wondering about. When I think of "ratios" $x/y$ and $z/w$ as being "equal", with $x$, $y$, $z$, and $w$ being real numbers, this means the results of dividing the real ...
0
votes
1answer
73 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% ...
1
vote
4answers
74 views

Simplifying compound fraction: $\frac{3}{\sqrt{5}/5}$

I'm trying to simplify the following: $$\frac{3}{\ \frac{\sqrt{5}}{5} \ }.$$ I know it is a very simple question but I am stuck. I followed through some instructions on Wolfram which suggests that I ...
0
votes
2answers
181 views

Ratio - Basic Question

If ratio of A:B = 1:2 if it is doubled , should it be not 2:4 i see many problems where they are simply multiplying numerator by 2 please can some one explain
16
votes
12answers
2k views

Why is $\frac{1}{\frac{1}{X}}=X$?

Can someone help me understand in basic terms why $$\frac{1}{\frac{1}{X}} = X$$ And my book says that "to simplify the reciprocal of a fraction, invert the fraction"...I don't get this because isn't ...
5
votes
1answer
195 views

Is it possible to rationalize a denominator containing two cube roots?

The fraction in question is $$-\frac{12}{\sqrt[3]{12\sqrt{849} + 108} - \sqrt[3]{12\sqrt{849} - 108}}$$ And was reached in calculating the solution to $x^4 - x - 1 = 0$. I've tried all the standard ...
1
vote
2answers
94 views

when the numerator is less than the denominator

when the numerator is less than the denominator the result is always between 0 and 1? for example if I have a number like x/y where x<y then the result will be ...
0
votes
2answers
95 views

When is a fraction simplified?

When is a fraction simplified? "A fraction is simplified if the numerator and denominator do not have any common factors other than 1." This is what I read on this website: ...
0
votes
2answers
83 views

Aproximate calculation in decimals

I am trying to refresh on precision of calculations. If we have the decimal fractions: $.234673$, $.322135$, $.114342$, $.563217$ each known to be correct to six figures why are each of the decimals ...
3
votes
1answer
495 views

How do I get the integer part of a number by using basic arithmetic?

While it is trivial to simply remove the fractional part of an irrational or rational number, and in programming I could just use the floor() or ...
0
votes
1answer
76 views

Find the set of all natural number that make $(n+1)/(n+3)$ reducible

Lets assume $d$ is a natural number which makes $(n+1)/(n+3)$ reducible, then $d|n+1$ and $d|n+3$. $d|[n+3-(n+1)] = d|2$ which means $d=1$ or $d=2$. $n+1$ and $n+3$ must be divisible by $2$ so all ...
2
votes
1answer
69 views

Fraction comparison and addition

On Monday, Leo memorizes $\frac{3}{5}$ of his trumpet solo. On Tuesday, he memorizes $\frac{1}{3}$ more. What fraction of his solo does he have left to memorize?
1
vote
3answers
60 views

Please explain how this ratio is being calculated

A,B and C are partners of a company. A receives $\frac{x}{y}$ of profit. B and C share the remaining profit equally among them. A's income increases by $I_a$ if overall profit increases from P% to ...
0
votes
1answer
389 views

Equivalency of percentage formulas

I know 3 methods for calculating percentages, one example, find 70% of 50: 1) 50/100 * 70 2) 70/(100/50) 3) 70/100 * 50 I do not undertand how this 3 methods can be equivalent, also conceptually ...
1
vote
1answer
87 views

Simplifying a fraction?

$$\frac {n-2}{n} \cdot \frac {n-3}{n-1} \cdot \frac {n-4}{n-2} \cdots \frac{2}{4} \cdot \frac{1}{3} = \frac {1}{n(n-1)}$$ Why is this true? Notice the denominators and numerators cancel out, but ...
1
vote
4answers
436 views

Fastest way to compare fractions

Which is the fastest method to compare the below fractions with minimum calculation possible and finding which is greatest and which the smallest?? $$\frac{26}{686},\quad \frac{48}{874},\quad ...
3
votes
1answer
91 views

How fast is a low denominator encountered, when using only mediants?

This question is (remotely) related to How to find a "simple" fraction between two other fractions?, but is not answered in that older post. Let $f_1=\frac{a}{b}$ and $f_2=\frac{c}{d}$ be ...
3
votes
1answer
92 views

Is there a direct proof of this inequality between quotients of integers?

Let $\frac{a}{b}$ and $\frac{c}{d}$ be two reduced fractions with $bc-ad > 1$ (and hence $\frac{a}{b} \lt \frac{c}{d}$) and $a,b,c,d$ positive. It is well known that there are integers $u,v$ ...
2
votes
1answer
243 views

How to calculate percentage of comment lines in a code?

I have a file within which I have 6 lines of code and 8 lines of comment. What's the formula to calculate how much percent of the whole file comments have?
3
votes
1answer
120 views

Ways to teach fractions

I'm tutoring elementary-level kids on equivalent fractions and am not doing a very good job of explaining it. I've tried using the example of a pizza or a pie and have shown them how they can come up ...
1
vote
6answers
363 views

Proof of dividing fractional expressions

For dividing two fractional expressions, how does the division sign turns into multiplication? Is there a step by step proof which proves $$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \cdot ...
0
votes
1answer
211 views

How would I solve this fraction division problem?

5/8 รท2 1/2 I understand how to divide it by flipping the numbers (reciprocal) and what not. I just don't know what to do with the 2 next to the division sign. Help?
0
votes
2answers
91 views

Solve $\frac{x-a}{b}-\frac{x+c}{d}=0$ for x

I need to solve $$\frac{x-a}{b}-\frac{x+c}{d}=0$$ for x. The answer is: $$x=\frac{ad+bc}{d-b}$$ But i can't figure out how to get there, I think i have to start by making the fractions have the ...
0
votes
1answer
94 views

Calculate percentage between two numbers

I have two numbers which summed up are considered to be $100\%$. The first number $n_1$ should decide the percentage amount. For e.g., $$n_1 = 5$$ $$n_2 = 15$$ so the percentage in this case ...
32
votes
7answers
1k views

Bad Fraction Reduction That Actually Works

$$\frac{16}{64}=\frac{1\rlap{/}6}{\rlap{/}64}=\frac{1}{4}$$ This is certainly not a correct technique for reducing fractions to lowest terms, but it happens to work in this case, and I believe there ...
4
votes
3answers
305 views

Fractions with radicals in the denominator

I'm working my way through the videos on the Khan Academy, and have a hit a road block. I can't understand why the following is true: $$\frac{6}{\quad\frac{6\sqrt{85}}{85}\quad} = \sqrt{85}$$
2
votes
1answer
142 views

How to add coins fast as fractions

When you have a problem that requires you to add coins together. Is it better to use fractions? For example, you have 14 one dollar bills, 24 quarters, 12 dimes, 78 nickles, and 20 pennies. So I ...
2
votes
1answer
290 views

Trivial: Rationalize fraction with a third-degree root

This is a pretty trivial question. How do you rationalize a function with a denominator that contains a third degree root? Edit: My expression is $\displaystyle{\frac{1}{\sqrt[3]{2}-1}}$.