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 .

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Can someone explain how this linear equation was solved [proof provided]

Can someone please explain to me the steps taken in the proof provided to solve the linear equation? [1]: https://i.stack.imgur.com/gQwxb.png "Proof" What I don't understand is how he removed the denominator of both fractions (3,5 respectively). I…
Wish
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A problem with rounding

Short version of the question: when rounded variable is used to calculate another variable, should I use rounded or unrounded value? Longer version: say I have two calculations: a / b = c and c + d = e (for the sake of clarity, a, b and d are known…
muszek
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help with simple order of operations in fractions?

first time poster here, so please be kind. :) I am working on an issue that I can't see past. I've got a worksheet with a multiple choice set of answers, but i KNOW they are all wrong! But maybe I am missing something? It's a simple fraction to…
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Help Reducing simple fraction

This has got to be easy, but for some reason I just don't see it, probably because it's late. Solution key to a quiz we took online says that: $\frac{A^2 + A + AB}{(A + B)(A + B + 1)}$ can get reduced down to $\frac{A}{A+B}$ but I can't seem to get…
late
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Why is $1 / x^y = x ^ {-y}$

I've known this rule for a long time, but I never got to understand why is that and how it works, could anyone explain to me how it is done? Any help is appreciated.
user95523
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How to shorten this fraction?

How to shorten this fraction? $R_1+R_2$ divided by $\frac1{R_1} + \frac1{R_2}$ The answer is $R_1R_2$. I just don't know how to get there.
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Equation with fractions

If $P=\frac{h}{1-h}$ then $h$ is equal to? Answer is: $\frac{P}{1+P}$ I understand that $\frac{P}{1+P}$ is the right answer for when I replace $\frac{P}{1+P}$ for h the answer solves the equation, but what I can't do is find the answer by myself,…
Jose
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Simple algebra question - separating fractions

How does the following come about? I'm completely lost. Can anyone help me fill in the steps in between? $$ \frac{s+2}{s(s+1)} = \frac{2}{s} - \frac{1}{s+1} $$ I figured that $$ \frac{s+2}{s(s+1)} = \frac{s}{s(s+1)} + \frac{2}{s(s+1)} =…
user12279
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Is the product of two numbers both less than one less than one

I'm bad at mathematics, and I wanted to know something. Say there are two numbers $a$ and $b$ where $a, b \in \Bbb R$ $-1 < a < 1$ and $-1 < b < 1$ Is it necessary that $a \times b < 1$? Edit: I was in hurry and didn't notice the big mistake I did
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Finding the number of fractions with unique values where the range for the denominator and numerator is in $\{1,2,\dots, n\}$

Imagine that you have a fraction, where both the numerator and denominator take values in the set $\{1,2,\dots, n\}$. Let us assume that the fraction is smaller then and or eqal to 1. The question is how many unique values can you get with every…
jurcistan
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Compute operations with fractions using calculator

I have a CASIO fx-350MS, and I need to make fraction computations, like $\frac{7}{2} \cdot \frac{4}{5}$ for an exam where I have to compute a lot matrix multiplications (programmable calculators aren't allowed). If I compute something like…
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Bar Notation Problem

everyone! I came across a problem in math that dealt with bar notation. Does anyone know how, for instance, 1.234(with a bar notation over the 34) is expressed as a fraction? I know already how 1.22(with a bar notation over the 22) is expressed as 1…
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Turn a number $x$ into a fraction with a denominator with no more than $k$ digits

Is there a function for turning any number $x$ into a fraction with a denominator that has a maximum of $k$ digits? (I'm sure there is, since Excel has one built in, I just can't figure out what it is.) For example, $f(0.1234) =…
Joe
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Can fractions be written as another fraction with a particular denominator?

Suppose we have a fraction $0 < \frac{a}{b} \leq 1$, where $a, b \in \mathbb{Q}, b \neq 0$. Can this fraction be written with another base in its denominator? Say I want to express this fraction with a denominator that its base is $3$. So the new…
Josh
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Are these two methods for obtaining the mid point equivalent?

I was working on computer science problem on LeetCode website. The solution required that the midpoint be calculated between two numbers, lets call them start and end. Ultimately my solution passed the tests. The issue is that one of the other…