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
38
votes
12 answers

How to make sense of fractions?

Can anybody explain what a fraction is in a way that makes sense. I will tell you what I find so confusing: A fraction is just a number, but this number is written as a division problem between two numbers! There is no answer to this division…
tony
  • 397
13
votes
2 answers

Can I split $\frac{1}{a-b}$ into the form $f(a)+f(b)$?

I was wondering if I can split apart the following fraction \begin{align} \frac{1}{a-b} \end{align} into the form: \begin{align} f(a)+f(b) \end{align} where $f(a)$ and $f(b)$ is some function in terms of $a$ and $b$
Gabe Love
  • 155
  • 1
  • 8
13
votes
4 answers

A question about neighboring fractions.

I have purchased I.M. Gelfand's Algebra for my soon-to-be high school student son, but I am embarrassed to admit that I am unable to answer seemingly simple questions myself. For example, this one: Problem 42. Fractions $\dfrac{a}{b}$ and…
mark
  • 313
13
votes
2 answers

Why do I get $0.098765432098765432...$ when I divide $8$ by $81$?

I got this remarkable thing when I divided $16$ by $162$, or, in a simplified version, $8$ by $81$. It's $0.098765432098765432\cdots$, or more commonly known as $0.\overline{098765432}$, with all the one-digit numbers going backwards...except for…
12
votes
5 answers

What is the 'physical' explanation of a division by a fraction?

For example, dividing by 2, means we cut something in two. But dividing by 0.5, can only be explained with multiplying something by 2. So, is there a "physical" explanation of dividing by 0.5? Is it "I divide by an entity that internally multiplies'…
j riv
  • 231
  • 2
  • 7
11
votes
7 answers

What happens when you add $x$ to $\frac{1}{3}x$?

I am dealing with an equation that requires me to add $x$ to $\frac{1}{3}x$: $x + \frac{1}{3}x$ = ?? I know this might be simple to any of you on this site, because you are all asking questions with symbols I have never seen, but this is confusing…
10
votes
3 answers

Why do these fractions give $99...9$?

Today, as usual, we were doing all those boring numerical computations in our calculators. It all started when my professor replaced $0.2$ with $\frac{1}{5}$. I got into calculating the unit fractions one by one. But soon, I got indulged in unit…
9
votes
3 answers

What makes this answer unsimplified?

Generally, what are the rules for simplifying answers? I had this question: Given $f(x) = \frac{1}{x}$, evaluate $\frac{f(x) - f(a)}{x-a}$. Why is the following a bad answer: $$\frac{\frac{1}{x} - \frac{1}{a}}{x-a}$$ The better answer…
Jwan622
  • 5,704
8
votes
1 answer

Does it make sense to multiply slopes?

Multiplying fractions is a regular occurance. If those fractions are considered slopes, does it make any sense? For example, if these fractions are slopes,$\frac{9}{8} \times \frac{49}{48},$ does the product have meaning in terms of slope?
7
votes
3 answers

Numbers whose self and reciprocal are finitely decimally expressable that are close to one?

How would I go about finding numbers x such that x and 1/x are finitely decimally reciprocal and are also close to 1? I'm not entirely certain how to phrase this question, but take for example 2. 2 and 1/2 can be represented with a finite number of…
Nolan
  • 73
7
votes
1 answer

Number to the exponent divided by exponent value

Can someone explain including working out how to solve this? $$\dfrac{5^x}{x} = 79.85957$$ I know that the answer is $x = 3.5$, but how does one normalise the equation so that the x is on one side?
6
votes
2 answers

Approximation of irrationals by fractions

If $\alpha$ is an irrational, and I'm trying to judge the suitability of of a rational $p/q$ as its approximation by the error $\Delta = |\alpha - p/q|$. For a given denominator $q$, I am finding a $p$ for which the error $\Delta$ is minimized. Why…
kuch nahi
  • 6,789
6
votes
8 answers

Why does the Denominator of the Denominator go to the Numerator?

Quite blindly I've learnt a basic rule about fractions: The Denominator of the Denominator goes to the numerator. I'm confused about it and I'll give an example as to why. Imagine the following: 1/2/2 Now, if the denominator of the denominator…
Nick
  • 6,804
6
votes
2 answers

Adding fractions of Groups of People

I understand the rules of adding fractions perfectly well. I know how to find common denominators, and understand why adding fractions without common denominators doesn't make sense. But, today someone asked me about adding $\frac{5}{6}$ and…
6
votes
3 answers

Ratios make me feel like an idiot - help me mix up some Coca-Cola

I may be over-complicating things, but something doesn't seem right (and I swear this isn't homework, I'm friggin 30 years old :P). I want to see what it will cost me to make a TWO liter of Coca-Cola using coke syrup and CO2 (assume the water is…
1
2 3
32 33