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
4
votes
3 answers

Remainder and long division

I have been thinking about this. Lets say we take 7 divided by 3, we know the remainder is 1. However, if we let x=7 and x-4=3, and we take x/(x-4), after performing long division the remainder is 4. Why is it not 1?
Jus
  • 285
4
votes
3 answers

Is it possible to have a fraction wherein the numerator and denominator are also fractions?

For example: $$ \frac{\ \dfrac{3}{5}\ }{\dfrac{7}{8}} $$ I was wondering if such a situation had a name, wherein both the numerator and the denominator of a fraction consist of fractions themselves. I was also wondering if this was something…
Tom
  • 41
  • 1
3
votes
2 answers

Show that for every integer $n ≥ 1$, $1 + \frac{1}{4} +\frac{1}{9} + · · · + \frac{1}{n^2} ≤ 2 − \frac{1}{n}$

I can just think of trying to prove $\frac{1}{4} +\frac{1}{9} + · · · + \frac{1}{n^2} ≤ \frac{1}{n}$, but remains stuck.
Benjamin
  • 123
3
votes
2 answers

Adding a different constant to numerator and denominator

Suppose that $a$ is less than $b$ , $c$ is less than $d$. What is the relation between $\dfrac{a}{b}$ and $\dfrac{a+c}{b+d}$? Is $\dfrac{a}{b}$ less than, greater than or equal to $\dfrac{a+c}{b+d}$?
wajih
  • 51
3
votes
1 answer

How to go from 1/6 to 16 2/3

A VCR is programmed to record a TV show that lasts for a half hour. If the cassette tape used can accommodate 180 minutes of programming, what percent of the tape is used for this recording? I did 30/180, reduced to 1/6. I know the answer is 16…
3
votes
3 answers

confusion related to elementary operation on numbers

Let's take for example an fraction: $\dfrac{1+4}{2-4}$ and another fraction $\dfrac{1*4}{2*4}$. In the second fraction we can cancel 4 from both numenator and denominator but on the first we cannot do so.I have learnt how to do this but I do not…
3
votes
4 answers

Simplify this complex algebraic fraction

I'm stumped on this problem, I need to know how this answer was arrived at but my text book doesn't show this. $$\frac{\frac{1}{x+y}}{\frac{x}{y}}$$ The text book says the answer is this: $$\frac{y}{x(x+y)}$$ I think the problem is that I lack the…
James
  • 205
3
votes
4 answers

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: $$\frac{\frac {5}{2}}{\frac{5}{9}}$$ My attempt was changing the denominators by multiplying by $2$ to make $18$ and then changing the same way…
itshanks
  • 532
3
votes
2 answers

Understanding relationships between distance, time, speed.

I'm studying basic algebra through Khan Academy at a late age (I'm in my 30s, but what I'm learning now is probably elementary to middle school). The reason I didn't study math when I was younger was simply because I was stupid, and even though I'm…
3
votes
3 answers

Lottery Odds as Multiples of Fractions

I run a Lottery syndicate for the UK lottery, and we play 30 lines per draw. The odds of winning £10 (3 matching numbers) is deemed to be 1 in 56.7 (or 1/57 for the purposes of this question). I'd loosely determined that the odds of getting 3…
3
votes
4 answers

Express $x=0.\overline{31}_5$ as a fraction in lowest terms

Given $x=0.\overline{31}_5$, find the value of $x$, expressed as a fraction in lowest terms. I tried to change it into base $10$, but I don't think it's possible with fractions. So please help I'll appreciate it. Also I'm in 7th grade (easy…
user691889
3
votes
1 answer

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 number $10^{k} \frac{p}{q} (k \in \mathbb{N})$…
3
votes
2 answers

Fraction rules A/B/C vs B/C/A

I have all my fraction rules written down, but these two confuse me... $$ \frac{\;\;A\;\;}{\frac{B}{C}} \equiv{\frac{\;AC\;}{B}} $$ and $$ \frac{\frac{B}{C}}{\;\;A\;\;} \equiv{\frac{\;B\;}{CA}} $$ These do not give the same answers, and I am…
3
votes
2 answers

Explaining fractions in a consistent way

I'm trying to explain fractions to a keen 8 year old. I could think of two approaches: (1) Total Parts divided among Some People (Numerator = no. of pizza) $\frac{1}{2}$ is the slice if 1 pizza is divided among 2 people $\frac{12}{4}$ is 12 pizza…
3
votes
6 answers

The division of a fraction - Whole or Part?

My example is 1/2 divide by 8. The correct answer given : 1/16 However, in my mind this answer is 1 divide by 16, which to me is not what the question is asking. When I construct the argument, it seems it should equal 1/8 as the question is asking…
Joseph
  • 63
1 2
3
32 33