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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Find $\frac{x^2}{y^2}$ + $\frac{y^2}{x^2}$

If $\frac{x}{y}$ + $\frac{y}{x}$ = 3 Find $\frac{x^2}{y^2}$ + $\frac{y^2}{x^2}$ Any Ideas on how to begin ?
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Subtraction of two fractions.

I'm learning math by reading books only and the book I'm currently studying is Smart Math by Marcia Learner in which I practice basic operation on fractions. I can't solve the two following problems. Let me show you how I did it but my answers don't…
Bishnu
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Fraction of zeros

What is the definition of "fraction of zeros"? Here is an example of its usage. Sorry for such a simple question, but I have searched quite a bit now and have not been able to find a definition for this.
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Property of fractions

Given two fractions $\frac{h}{k}$ and $\frac{h^{'}}{k^{'}}$ both in reduced form. I am unable to find a case when $\frac{h+h^{'}}{k+k^{'}}$ does not lie in the interval $\big[ \frac{h}{k},\frac{h^{'}}{k^{'}} \big]$. Is there such a case ? PS: I was…
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when the sum of some fractions be $1$

prove if we want that the sum of some fractions be $1$ and the denominators of one of them is $d$ then another denominators should divisible by $d$ or $d$ should be divisible to another denominators. It seems to be easy I tried to prove it.I first…
Taha Akbari
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Solve fractions multiplication

I believe this is a very simple one, but I simply can't figure it out. How to solve? $$\frac12\cdot\frac34\cdot\frac56\cdots\frac{17}{18}\cdot\frac{19}{20}$$
Victor
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Dividing Fractions as Recipricol Multiplication

How do you know the order of operations when dividing by fractions? Recently I've been messing up problems involving dividing fractions. The division is written as fractions over fractions and not as some number divided by a fraction. I was just…
Sam Sabin
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How would one work this out? (Fractions)

One fifth of all value lamps are already defected at the time of purchase. How many do you have to buy to ensure that you have 16 functioning lamps.? Anyone have any advice on how to layout this question mathematically? I struggle to put these sorts…
Nathan
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Here are two fractions, $\frac{2}{3}$,$\frac{7}{8}$, which of these fractions are closer to $\frac{3}{4}$?

I've been throwing this question around my family. No one has a clue, therefore can someone help? I'm pretty sure this will be easy to do
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Fractions and Largest Common Multiple, Algebra, Numerator and Denominator Identical Numbers?

This is the question find $x$ of equation: $$\frac{5x-2}{5} - \frac{2x+3}{2} = 3$$ I tried multiplying this all by 10, the LCM. It ended with: $x -x=49.$ How do you solve this without cancelling the $x$ out of the equation?
Coras
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Sign of fractional exponent

What is the sign of $-1^{\frac{2}{3}}$? I thought it was positive 1 because it involves squaring, but that doesn't seem to be the case. Why?
Tyler
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How is $\frac{(10^{4})^{6}-1}{10^4-1} = 1 + 10^{4} + 10^{8} + 10^{12} + 10^{16} + 10^{20}$?

As the title states, how is: $$\frac{(10^{4})^{6}-1}{10^4-1} = 1 + 10^{4} + 10^{8} + 10^{12} + 10^{16} + 10^{20}$$ I can't see the pattern. Can someone please help? Thanks.
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algebra exponents and fractions

I could be over thinking or tired... But I am to embarrassed to ask my prof. this probably very simple algebra rule I am ignorant of... Also this is just a snip-it from a inductive proof example. Say you have something like this $${\frac{4^k -…
T.Malo
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Why$ 1/12$ is NOT an irreducible basic fraction?

I'm trying to solve this problem. A fraction $m/n$ is basic if $0 \le m < n$, It is irreducible if $\gcd( m,n ) = 1$ (greatest common divisor) In the example, when $n=12$, irreducible basic fractions are: $0/12, 5/12, 7/12, 11/12$. Why is $1/12$…
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Simplifying Square Roots with Fractions?

I know this is a very basic question, but could someone please mathematically explain, why this is true: $\sqrt{x} \cdot \frac{1}{x} = \frac{1}{\sqrt{x}}$ Wolfram|Alpha can confirm this.
Oliver Spryn
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