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
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Prove product of two positive proper fractions is always smaller than either of them

How would one go about setting out a formal proof that the product of two positive proper fractions will generate a positive number less than either of them? (This is not homework, rather curiosity how to formally prove something that is generally…
ose
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Fractions- differences in interpretation - part of a whole

Imagine a fraction of the form $x/y$, where $y>x.$ It seems to me that this can be interpreted in two ways. The first way is to split one unit (say an object), into $y$ parts, and populate $x$ of those. For instnace, splitting one apple four ways…
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Is $1/(1/0)$ undefined, or does it equal zero?

Is $1/(1/0)$ undefined, or does it equal zero? By one way of thinking, you could say $1/(1/0)=1*0/1=0$ (taking the reciprocal) and thus equals $0$. But by another, the original expression simply cannot be evaluated because there is division by zero.…
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Is this fractional equation true for all real numbers?

Is this equation true for all real values of $a,b,c,x,y,z$? If $$\frac{a}{x} = \frac{b}{y} = \frac{c}{z} = t$$ Then $$\frac{a+b+c}{x+y+z} = t$$ I've tried experimenting with several values and they make an equality, but does this equation hold true…
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How to define a range of divisors that guarantee a fractionless result

I have a number (48000) I want to be able to generate a list of positive integer numbers (within a min/max range) that this number can be divided by that will guarantee a result that is a whole number. Here are some examples: Given the dividend…
jmat
  • 103
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Unsure of what's happening in this fraction

I can't seem to see what is happening to make this equivalence. More specifically, how the left-side's $n+1$ makes it into the right side's numerator. $$ \frac {n(n+1)} 2 + (n+1) = \frac {(n+1)(n+2)}2 $$
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What is this diagram?

This diagram plots every irreducible fraction between 0 and 1 as points, where a point's x coordinate is the fraction's value (from 0 to 1) and its y coordinate is the fraction's denominator (from 2 to whatever the maximum is). It makes really…
dino
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How to show that $\frac{1}{(1-\frac{1}{4}z^{-1})(1-\frac{1}{4}z)} = \frac{-4z^{-1}}{(1-\frac{1}{4}z^-1)(1-4z^{-1})}$

Can anyone help me clarify what rule is used in this rewriting of this fraction? $$\frac{1}{\left(1-\dfrac{1}{4}z^{-1}\right)\left(1-\dfrac{1}{4}z\right)} = \frac{-4z^{-1}}{\left(1-\dfrac{1}{4}z^{-1}\right)\left(1-4z^{-1}\right)}$$
Attaque
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Simplify Fraction with variables

Simplify -270y^2/189x^3 Not too sure how to go about simplifying this. I googled it, and google showed me the steps but no explanation. Step 1: Cancel terms that are in both numerator and denominator -270y^2/189 * x^3 Reduced: -10y^2/7 *…
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Maximum length of a division period

So I heard someone say that if you have $\frac{a}{b}$, then the period will not exceed $b$ digits. He said it can be proved with pigeonhole principle, but did not provide further explanation. Can someone make me understand? Thanks.
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Does a non-fraction number have a reciprocal?

As far as I understand from this Wikipedia page, $\frac 73$ is a reciprocal of $\frac 37$; But can a term "reciprocal" be applied to a non-fraction number? For example, it would be correct to say: reciprocal of $\frac 21$ is $\frac 12$ But would…
brilliant
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Cross Multiplying and Simplifying

In a YouTube video by Michael Penn, at the 3:56 mark, he gets the equation: $$ \frac{4}{2} = \frac{2}{2-x}\Rightarrow 8-4x=4$$ Could someone explain to me how he does this and the process behind it? Thanks for your help! (Im only freshman year of…
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Is the reciprocal of $\cfrac {-(2x-1)}{2}$

$\cfrac{-2}{(2x-1)}$? I want to see if I'm not forgetting reciprocals. And that I'm correct and not misremembering. It's the negative in front of the parentheses that's throwing me off.
user827508
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How to draw how much of a fraction goes into another fraction

I have three questions. All I want to draw a picture to show each of these: a)Determine how many $\frac{1}{8}$’s are in $\frac{1}{4}$. b)Determine how many $\frac{1}{3}$’s are in $\frac{1}{2}$. c)Determine how many $\frac{1}{5}$’s are in…
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What would the denominator of 7 represent in this question?

I'm in year 6 and I just had a question about fractions. If the question was: "What is 4/7 of 56?" Would the 7 denominator represent the 56 and then the 4 would mean your're taking 4 parts of that 56? Thanks.
JamesM
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