Questions tagged [fractions]

Questions on fractions, i.e. expressions (not values) of the form $\frac ab$, including arithmetic with fractions. Not to be confused with the tag (rational-numbers): fractions denote rational numbers, but the same rational number may be written in different ways as a fraction.

A fraction is simply an expression $\frac{a}{b}$, where $a$ and $b$ are typically integers (where $b\neq 0$). This tag may be used, when $a$ and $b$ are more general expressions or algebraic objects; however, consider adding a more specific tag also:

Fractions are distinct from rational numbers because they are a representation: $\frac 34$ and $\frac{30}{40}$ are different fractions that happen to represent the same rational number.

For arithmetic with fractions, this tag is appropriate along with .

2981 questions
0
votes
1 answer

Integral solutions to expression given below.

Given expression $xy=2^23^45^7(x+y)$ What are its integral solutions? I tried to solve it by converting it to $\frac{1}{2^2}\frac{1}{3^4}\frac{1}{5^7}=\frac{1}{x}+\frac{1}{y}$ But thereafter it got a li'l messy. I'd appreciate some help.
0
votes
3 answers

proving that given fraction is irreducible.

Prove that for every natural number n, fraction $\frac{21n+4}{14n+3}$ is irreducible. I deduced that if we can prove that numerator and denominator have 1 as their GCD, we can get the result, but I cannot get it from thereon.
0
votes
3 answers

Adding fractions (to find an equal) without known denominator

The question is "Find $v$": $$\frac {1}{20}=\frac {1}{30}+\frac {1}{v}$$ I have no idea what I'm really doing so if someone could explain in a somewhat easy-to-understand way I'd really appreciate it!
0
votes
1 answer

Removing a fraction in the denominator

What steps do I need to take to simplify $\frac{1}{\frac{1}{\sqrt{2}}}$ to $\frac{\sqrt{2}}{1}$? Can you please explain the steps i need to take in this problem and explain generally how to remove fractions from the denominator.
0
votes
4 answers

I can't understand the algebraic simplification below

I can't understand the last step of simplification in the following algebraic expression. I am aware that $\sqrt{3}=3^{\frac{1}{2}}$. Can't see how they get the $6$ in the denominator, and how $\sqrt{3}$ gets to the numerator. Any help will be…
Kasvan
  • 21
0
votes
1 answer

Fractions and decimals

Ten companies sponsored a tournament and decided to give M rupees collectively.Two companies dropped and remaing agreed on paying their share equally.What was the increase in share of each company? The answer is M/40.How this answer comes.Any help…
0
votes
1 answer

Trending proof for fairly simple fraction

(Please humour the physicist!) Why does $\left(\frac{1-a}{1-a^b}\right) \to \frac{1}{b}$ as $a \to 1$? This came from a calculation involving flow measurement of gases, and although I can see and compute the answer, I don't understand how this…
0
votes
3 answers

Ordering an even and odd fraction that are close

We know that $1/4 < 5/11 < 1/2$. I did it this way from small to large: $$\frac{1 \cdot 3}{4 \cdot 3} = \frac{3}{12}$$ $$\frac{5}{11}$$ $$\frac{1 \cdot 6}{2 \cdot 6} = \frac{6}{12}$$ It is hard for me to decide between 5/11 and 6/12 without a…
0
votes
2 answers

$\frac{6}{4 \times 2} + \frac{7}{5 \times 2} + ... + \frac{21}{19 \times 2}$

I got this exercise from school and I have no idea what notion to use, it resumes to Harmonic series, I can't find a generic answer. Do you have any idea? $\frac{6}{4 \times 2} + \frac{7}{5 \times 2} + ... + \frac{21}{19 \times 2}$ Which is the…
yonutix
  • 135
0
votes
3 answers

Adding fractions with exponents

$$3^5 + {1\over3^5}=?$$ My first instinct was to rewrite the second term as $3^{-5}$. Since the base is $3$, rewrite as $3^{5+-5}$. It simplifies to $3^0= 1$. Apparently this is incorrect. Can anyone please explain why?
Emma
  • 3
0
votes
2 answers

Adding drawnfractions (Very simple question)

I have been surprised not being able to solve this: +---------------------------+ | XXXXXXXXXXXX| | | XXXXXXXXXX| | | XXXXXXXX| | | XXXXXX| | | XXXX| | | X| …
JorgeeFG
  • 493
0
votes
1 answer

$5.30$ converted to a fraction or mixed number in lowest terms

$5.30$ converted to a fraction or mixed number in lowest terms The correct answer they got on my worksheet is $5 \frac3{50}$, but I get $5 \frac{15}{50}$.
0
votes
3 answers

Find the fractional representation $p/q$...

Been trying to get some sort of solution for this for hours now, with no avail. Find the fractional representation $p/q$, with $p \in \mathbb{N}$ and $q \in \mathbb{N}$, of the rational number whose decimal representation is: $22.521111...$ Any…
Liam
  • 39
0
votes
2 answers

Compare colon notation with fraction

I'm working on a job interview test and there is one answer which I just don't get. The test states that statement below is true. To me it just seems wrong. No box is provided to check. Then how do I check it correct or wrong? Am I missing something…
jeroen81
  • 103
0
votes
1 answer

Is there a value for $a$ other than a factor or a multiple of $c$ in $\frac{a}{b}=\frac{c}{d}$

Suppose $a,b,c,d$ to be whatever quantities whatsoever that satisfy the proportion $\frac{a}{b}=\frac{c}{d}$. Is there a value for $a$ other than a factor or a multiple of $c$. Or, is there a value for $b$ other than a factor or a multiple of $d$. I…
user126456