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

Each way odds calculations.

apologies if this is the wrong board. I am working on a program to help with calculating odds in horse racing, however I am getting different results to all online each way odds calculators. I think it must be an issue with my understanding of odds…
Thomas G
  • 1
  • 1
0
votes
2 answers

Converting fractions to repeating decimals

I understand how to convert a repeating decimal into a fraction. For instance, let us look at $0.555555...$. We set $r = 0.5555...$, multiply it by ten then subtract $r$ from that to get $$9r = 5 \implies r = \frac{5}{9}.$$ How do I go the other…
HMPtwo
  • 433
0
votes
1 answer

How much must be taken from each slice of a pie cut into 3rds to be able to share equally between 4 people

Theoretically, if $3$ people were to split a pie evenly amongst themselves, only to have a $4$th person join them, how much or what fraction of each of their $\frac{1}{3}$ slices must be taken and given to the $4$th person, so that everyone has an…
0
votes
2 answers

How should I think about the relationship between numerator and denominator?

I've been thinking lots about the nature of fractions; of what exactly they are and what they tell you. I searched for a similar question as the one I have about fractions on this fourm, and found this thread, which I think summarizes my pondering…
0
votes
2 answers

Is it possible to split this fraction?

I am puzzled with this problem. $\cfrac{1}{b+c}=\cfrac{x_o}{b}+\cfrac{x_1}{c}$ Is it possible to define $x_0$ and $x_1$ in terms of $b$ and $c$? If so, could I at least get a hint?
0
votes
1 answer

Rules for simplifying algebraic fractions

I'm new to maths and I'm working on simplifying the fraction below: x^2+xy y^2+xy The answer is x over y but i want to know why i cant simply cancel everything out as it is from the start. I have been taught to cancel out like terms, so can't i…
Cookies
  • 45
0
votes
1 answer

Writing recurring decimals as a fraction

When writing recurring decimal to fraction why do we move the decimal place equal to the number of digits in the repeating string? For example, to write $0.10\overline{4357}$ as a fraction, we let $x= 0.10\overline{4357}$, we then multiply both…
Cal
  • 1
0
votes
1 answer

Can we compare fractions with same numerator and different denominator

If we are given the 2 fractions 4/7 and 5/7 5/7 is greater What if we had 1/8 and 1/9 Can I say that the fraction with a greater denominator is less
0
votes
0 answers

Recognizing infinite sets in set theory

I am learning set theory and one of my questions was this: Is the set of fractions between 0 and 1 an infinite set? I initially thought the answer was yes, but one of this possible answer confused me: The statement is false; the set of all real…
0
votes
0 answers

The Simplest Fraction for a Decimal

Is there a way to find the simplest fraction for a decimal? For example, let us say that I am trying to find the simplest fraction that rounds to $93\%$. I could easily say that $\frac{93}{100} = 0.93 = 93\%$. However, this misses $\frac{13}{14} =…
0
votes
0 answers

How to convert an improper fraction with variables to a mixed number?

I have fractions like these: $$\frac{12000x}{41}\qquad (1)\\\frac{12000+x}{41}\qquad (2)\\$$ What is the process to convert these to a mixed number (example: $5\frac12$)?
0
votes
0 answers

How to write "concave" equals sign in latex

I am reading a mathematical paper and they use this concave looking equals sign: I was unable to find how to write this in LaTeX. I don't even know what this sign is called. They use it to denote that the fraction of the two quantities is bounded…
0
votes
1 answer

What is the shortest and most preferred way of writing the result?

Let's say I have to calculate 6/4 (i know, it's simple). Would the preferred answer be 3/2 or 1.5? Same with square roots: is sqrt(2) a better answer than 2^(1/2)?
yrjarv
  • 101
0
votes
1 answer

How to solve $\frac{8x+3}5-\frac{11x-9}6+\frac{4x+3}{15}=\frac{11x+15}{10}$

Here's an equation: $$\frac{8x+3}5-\frac{11x-9}6+\frac{4x+3}{15}=\frac{11x+15}{10}$$ It looks simple, and I know the answer $- 3/4$, but can't arrive at it. Instead, I arrive at $1.75$ by reducing all the fractions to a common denominator $- 30$.…
Yan
  • 9
0
votes
2 answers

Are these fractions all equal?

Are the following expressions all equal to one another? (2ab+c)/y (2ab)/y + c/y (2a)/y * (2b/y) + c/y $$\dfrac{2ab+c}{y}=\dfrac{2ab}{y}+\dfrac{c}{y}=\dfrac{2a}{y}×\dfrac{2b}{y}+\dfrac{c}{y}$$
Jorh
  • 11